Optimization for Engineering Problems 9781786304742, 1786304740

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Optimization for Engineering Problems

Series Editor Jean-Paul Bourrières

Optimization for Engineering Problems

Edited by

Kaushik Kumar J. Paulo Davim

First published 2019 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd 2019 The rights of Kaushik Kumar and J. Paulo Davim to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019937810 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-474-2

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

Chapter 1. Review of some Constrained Optimization Schemes . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Jonnalagadda SRINIVAS 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . 1.2. Constrained optimization problems . . . . 1.3. Direct solution techniques . . . . . . . . . . . 1.3.1. Complex search method . . . . . . . . . . 1.3.2. Random search techniques . . . . . . . . 1.3.3. Method of feasible directions. . . . . . . 1.4. Indirect solution techniques . . . . . . . . . . 1.4.1. Penalty function approach . . . . . . . . 1.4.2. Multipliers method . . . . . . . . . . . . . 1.4.3. Simulated annealing search . . . . . . . 1.5. Constrained multi-objective optimization 1.6. Conclusions . . . . . . . . . . . . . . . . . . . . . 1.7. References . . . . . . . . . . . . . . . . . . . . . .

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1 3 4 4 6 7 8 8 10 10 12 14 14

Chapter 2. Application of Flower Pollination Algorithm for Optimization of ECM Process Parameters . . . . . . . . . . . .

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Bappa ACHERJEE, Debanjan MAITY, Arunanshu S. KUAR and Manoj K. DUTTA 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Flower pollination algorithm . . . . . . . . . . . . . . . . .

17 21

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2.3. Optimization of the ECM process: results and discussions. . . . . . . . . . . . . . . . . . . 2.3.1. Experimental data and empirical models. 2.3.2. Single-objective optimization . . . . . . . . . 2.3.3. Multi-objective optimization . . . . . . . . . 2.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 2.5. References . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3. Machinability and Multi-response Optimization of EDM of Al7075/SIC/WS2 Hybrid Composite Using the PROMETHEE Method. . . . . . . . . . . . . . . . . . . . . . . . . . .

23 24 25 31 34 35

39

Mohan Kumar PRADHAN and Brajpal SINGH 3.1. Introduction . . . . . . . . . . . . . . . . . . . . 3.1.1. Overview of metal matrix composites 3.1.2. CNC EDM machine . . . . . . . . . . . . 3.2. Literature review . . . . . . . . . . . . . . . . 3.2.1. Metal removing rate . . . . . . . . . . . . 3.2.2. Tool wear process . . . . . . . . . . . . . . 3.2.3. Radial overcut . . . . . . . . . . . . . . . . 3.2.4. Surface topography or surface finish . 3.3. Optimization process . . . . . . . . . . . . . . 3.3.1. Analytic hierarchy process method . . 3.3.2. PROMETHEE method . . . . . . . . . . 3.3.3. Ranking relations for improved PROMETHEE . . . . . . . . . . . . . 3.4. Result and discussion . . . . . . . . . . . . . . 3.4.1. The effect of EDM parameters on machining characteristics of EDM machine 3.4.2. Optimization of EDM parameters . . . 3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . 3.6. References . . . . . . . . . . . . . . . . . . . . .

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40 41 42 49 51 53 54 54 55 55 60

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Chapter 4. Optimization of Cutting Parameters during Hard Turning using Evolutionary Algorithms . . . . . . . . . . . . . .

77

Vahid POURMOSTAGHIMI and Mohammad ZADSHAKOYAN 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Genetic programming . . . . . . . . . . . . . . . . . . . . . 4.3. Particle swarm optimization . . . . . . . . . . . . . . . . .

78 83 86

Contents

4.4. Materials and methods . . . 4.4.1. Experimental setup . . . 4.4.2. Optimization procedure 4.5. Results . . . . . . . . . . . . . . 4.5.1. Experimental results . . 4.5.2. GP results . . . . . . . . . 4.5.3. Optimization results . . 4.6. Conclusion . . . . . . . . . . . . 4.7. References . . . . . . . . . . . .

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vii

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89 89 90 92 92 93 95 96 96

Chapter 5. Development of a Multi-objective Salp Swarm Algorithm for Benchmark Functions and Real-world Problems . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

Sushant P. MHATUGADE, Ganesh M. KAKANDIKAR, Omkar K. KULKARNI and Vilas M. NANDEDKAR 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Salp swarm algorithm . . . . . . . . . . . . . . . . . . . . 5.2.1. Single-objective salp swarm algorithm (SSA) . 5.2.2. Multi-objective salp swarm algorithm (MSSA) 5.3. Constraint handling techniques . . . . . . . . . . . . . 5.4. Experimental results and discussion . . . . . . . . . . 5.4.1. Single-objective unconstrained test functions . 5.4.2. Single-objective constrained test functions . . . 5.4.3. Multi-objective unconstrained test functions . . 5.4.4. Multi-objective constrained test functions . . . 5.4.5. Real-world application . . . . . . . . . . . . . . . . . 5.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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101 105 107 109 113 114 115 117 120 122 125 127 128

Chapter 6. Water Quality Index: is it Possible to Measure with Fuzzy Logic? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Alexandre CHOUPINA, Elisabeth T. PEREIRA, Samara Silva SOARES, Poliana ARRUDA, Francis Lee RIBEIRO and Paulo Sérgio SCALIZE 6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Data and methodology . . . . . . . . . . . . . . . . . 6.2.1. Data and description of the case study . . . . 6.2.2. Parameters . . . . . . . . . . . . . . . . . . . . . . . 6.2.3. Water quality index . . . . . . . . . . . . . . . . . 6.2.4. Construction of the water quality index by fuzzy logic (WQF) . . . . . . . . . . . . . . . . . . . . . . .

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131 134 134 135 136

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6.3. Results and discussion . . . 6.3.1. Water quality analysis 6.3.2. Index validation . . . . . 6.4. Conclusions . . . . . . . . . . 6.5. Appendix . . . . . . . . . . . . 6.6. References . . . . . . . . . . .

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148 148 150 154 155 156

List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

161

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

Preface

The word “optimization” may be very familiar or may be quite new to you. However, whether or not you are aware of optimization, you are using it on many occasions in your day-to-day life and the concept has been around since from the evolution of mankind. One of the simplest definitions of optimization is “doing the most with the least”. Lockhart and Johnson define optimization as “the process of finding the most effective or favorable value or condition”. The purpose of optimization is to achieve the “best” relative to a set of prioritized criteria or constraints. Today, two distinct types of optimization algorithms are widely used: — deterministic algorithms: they use specific rules for moving from one solution to another. These algorithms sometimes used in suites and have been successfully applied to many engineering design problems; — stochastic algorithms: they use probabilistic translation rules. These are gaining popularity due to certain properties that deterministic algorithms do not have. Optimization is central to any problem involving decision-making, whether in engineering or in economics. The task of decision-making entails choosing between

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various alternatives. This choice is governed by our desire to make the “best” decision. The measure of “goodness” of the alternatives is described by an objective function or performance index. Optimization theory and methods deal with selecting the best alternative in the sense of the given objective function. Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all the areas of applied mathematics, engineering, medicine, economics, management and other sciences. Optimization techniques, having reached a degree of maturity over the past several years, are being used in a wide spectrum of industries, including aerospace, automotive, chemical, electrical and manufacturing industries. With rapidly advancing computer technology, computers are becoming more powerful, and correspondingly the size and the complexity of the problems being solved using optimization techniques are also increasing. Optimization methods, coupled with modern tools of computer-aided design, are also being used to enhance the creative process of conceptual and detailed design of engineering systems. All engineering problems seek to maximize some measure of performance, and an optimization tool could be extremely useful, hence optimization. Structural design is one of its first applications. A typical structural design optimization problem is to minimize the weight by varying structural thicknesses subject to stress constraints. Following the success of the application of optimization techniques to structural design, aircraft design is one of the next applications as there is much to be gained by the simultaneous consideration of the various disciplines

Preface

xi

involved (structures, aerodynamics, propulsion, stability and controls, etc.), which are tightly coupled. Because of the coupled nature of all the aircraft weight dependencies, and the reduction in induced drag, the total reduction in aircraft gross weight will be several times the structural weight reduction (about five times for a typical airliner). This book is mainly focused on two major objectives. First, it has chapters contributed by eminent researchers in the field providing the readers with the current status of the subject. Second, algorithm-based optimization or advanced optimization techniques are mostly applied to non-engineering problems. This will serve as an excellent guideline for people in this field. The book is composed of six chapters. Chapter 1 presents a review of some constrained optimization schemes. It provides a few common schemes for constrained optimization problems and their performances in terms of accuracy/computational requirements/time in addition to the commonly used heuristic simulated annealing algorithm. The rapid breakthrough in metaheuristic optimization methods in recent times has drastically affected the use of conventional optimization techniques. However, in some instances where the computational and other constraints are important, it is always preferable to use the standard schemes. This chapter introduces some cases where the comparison has been efficiently done. Chapter 2 deals with the flower pollination algorithm (FPA), a novel metaheuristic algorithm inspired by natural pollination of flowers. This algorithm is applied to a non-traditional machining technique called the electrochemical machining (ECM) process. This technique develops empirical equations to map the inter-relationship between ECM process parameters such as electrolyte flow rate, electrolyte concentration, feed rate, voltage and inter-electrode gap with response variables. Optimal results

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have been predicted by using the FPA to satisfy both single-criteria and multiple-criteria optimization. This chapter also compares the results of the FPA with those presented by past researchers indicating the superiority of the FPA in terms of accuracy and effectiveness. In Chapter 3, an AHP-based PROMETHEE method is used to optimize the mechanical, thermal and tribological properties of aluminum metal matrix composites, i.e. aluminum with nano- or micro-sized SiC particle reinforcements. Furthermore, the surface integrity, productivity and accuracy are often explored. The influence of different compositions along with machining parameters on the responses is investigated. Subsequently, the optimal set of these parametric combinations is validated to authenticate the use of this technique. Chapter 4 provides the reader with a novel intelligencebased methodology for calculating optimum cutting parameters in hard turning of AISI D2. In the first part, the genetic equation for modeling of tool flank wear is developed using experimentally measured flank wear values and genetic programming. Using these results, genetic models presenting connection between cutting parameters and tool flank wear are extracted. In the second part, based on the defined machining performance index and the obtained genetic equation, optimum cutting parameters are determined. The accuracy of the genetic programming model is evaluated using root mean square error (RMSE) and the coefficient of determination (R2). These results allow us to conclude that the proposed modeling and optimization methodology offers optimum cutting parameters, which can be implemented in real industrial applications. In Chapter 5, the multi-objective salp swarm algorithm for benchmark functions and real-world problem is discussed. The salp swarm algorithm is a recent nature-inspired swarm-based optimization algorithm, which

Preface

xiii

emulates and scientifically models the conduct of salp chains in the remote ocean. The salp swarm algorithm (SSA) and the multi-objective salp swarm algorithm (MSSA) have made progress towards various benchmark test capacities to help and attest the execution of the algorithm. Results from the SSA are compared with the actual values of the test functions, and results from the MSSA are compared with those of other multi-objective algorithms. For obtaining solutions to constrained test functions, a constraint-handling technique is employed to transform the constrained optimization problem into an unconstrained optimization problem for which the interior penalty method is used. The algorithm is successfully applied to a cantilever beam, which is the practical designing problem, and the results are compared with those of NSGA-II. The obtained results are converging and closer to the optimum solution in comparison with NSGA-II. Finally, Chapter 6 presents and evaluates the following question: is it possible to measure water quality index with fuzzy logic? This chapter develops a method for water quality determination using fuzzy logic and compares it with other traditional methods to optimize the existing analytical techniques towards the engineering problem of improving the quality of water. This chapter concludes that fuzzy logic does not statistically differ at the significance level of 5% (α = 0.05), with a smaller number of parameters compared to the other methods. Acknowledgments First and foremost, we would like to thank God. It was your blessing that provided us with the strength to believe in passion and hard work and to pursue our dreams. We thank our families for having the patience with us for taking yet another challenge that decreased the amount of time we could spend with them. They are our inspiration and

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Optimization for Engineering Problems

motivation. We would like to thank our parents and grandparents for allowing us to follow our ambitions. We would like to thank all the contributing authors, as they are the pillars of this structure. We would also like to thank them for having belief in us. We would like to thank all of our colleagues and friends in different parts of the world for sharing their ideas in shaping our thoughts. Our efforts will have been worth it when the professionals concerned with all the fields related to optimization are benefitted. We owe a huge thanks to all of our technical reviewers, Editorial Advisory Board members, Book Development Editor and the team at ISTE Ltd for their availability to work on this huge project. All of their efforts helped us to complete this book, and we could not have done it without them. Last, but definitely not least, we would like to thank all of the individuals who have taken time out and helped us during the process of editing this book. Without their support and encouragement, we would have probably given up the project. Kaushik KUMAR J. Paulo DAVIM April 2019

1 Review of some Constrained Optimization Schemes

With rapid breakthroughs in the metaheuristic optimization methods in recent times, applications of conventional optimization solution techniques have been reduced. However, in some cases, where the computational issues are of major concern, these standard schemes are still in use. Modification to these core approaches can be appropriately incorporated to handle them more effectively. This chapter summarizes the existing important constrained optimization schemes. Many engineering problems are usually multi-objective in nature. Even though several solution approaches are available; a unified method is always preferred to solve such problems. This chapter will review some direct solution schemes including complex search, random search and method of feasible directions, and their performance in terms of accuracy, computational requirements and time at par with commonly used modern heuristic algorithms.

1.1. Introduction In computer-aided design (CAD), optimization plays an important role. Optimization problems arise in many areas of engineering, including product design and operational control. Unit cells of atoms in metals and alloys, honeycomb structures and genetic operations are

Chapter written by Jonnalagadda SRINIVAS.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Optimization for Engineering Problems

some examples of optimized systems in real life. Depending on the objective function and constraints, different types of optimization problems often arise. After Cauchy invented the gradient concept of a function in 1847, several other researchers, including Dantzig (simplex method, 1951), Kuhn—Tucker (conditions of optimality, 1951), Rosen (gradient projection method, 1960), and Fletcher and Reeves (conjugate gradient scheme, 1964), have initiated the foundation for obtaining solutions of complex linear and nonlinear optimization problems. Today, optimization techniques are widely used in operations research and industrial engineering problems, such as inventory control, scheduling and facilities design. Some of the developments in this line are linear programming, sequential quadratic programming, integer programming, dynamic programming (Bellman 1952) and geometric programming (Duffin 1967). The mathematical problem of constrained systems is to simultaneously consider the attainment of objective function and the satisfaction of constraints. Constraints are either of the geometric type or simply the side constraints in the form of variable bounds. The effective objective function therefore first searches for the feasible solution rather than the optimum solution. All the methods start with finding feasible solutions and then move towards the optimum value. This chapter presents a review of a few techniques of obtaining optimum solutions for constrained nonlinear programming problems and attempts to identify their benefits and difficulties over heuristic methods such as simulated annealing. A few methods to handle multi-objective optimization problems are also briefly explained.

Review of some Constrained Optimization Schemes

3

1.2. Constrained optimization problems The constrained optimization problem in general can be stated as: Minimize f(X) Subjected to g j (X) ≤ 0, j=1,2,  m

[1.1]

h k (X)=0, k=m+1,  ,l x iL ≤ x i ≤ x iU , i=1,2, D

where X = [x1, x2, … xD]T ∈RD is a set of design variables, while xiL and xiR are the lower and upper boundaries (limits) of the variable xi, respectively. When both the objective function and constraints are linear functions of X, it is said to be a linear programming problem (e.g. cost minimization with demand (resource) constraints). Similarly, when the objective function is quadratic, while the constraints are linear, it forms a quadratic programming problem. In general, the feasible optimum solution for a nonlinear programming problem with constraints can be obtained from two broad categories of methods, namely direct and indirect methods. In direct methods, constraints are handled explicitly, while in indirect approaches, the problem is solved as a sequence of unconstrained minimization problems. Techniques such as random search, heuristic search methods and Rosen’s gradient project scheme come under direct methods, whereas penalty function methods come under indirect methods. In general, constraints have no effect on the optimum solution. In most of the problems, satisfaction of all the constraints is a mandatory requirement for the optimum solution. Therefore, often a feasible solution satisfying all the constraints is first estimated and then tested for optimality. Usually, the optimum solution occurs on the constraint boundaries.

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1.3. Direct solution techniques In direct search methods for constrained minimization, the structure of constraints is employed. The main advantage of such methods is handling of discontinuous and non-differentiable functions. Some of these techniques are more or less heuristic in nature, which have no convergence proofs. Essentially, these methods start with a feasible point and a new point is created using a fixed transition rule from the chosen initial point. If the new point is infeasible, then the point is not accepted and another point is found again using the transition rule. If the new point is feasible and better than the previous point, then the point is accepted and the next iteration is performed from the new point. The process is continued until some termination criterion is met. 1.3.1. Complex search method The Box complex method is a numerical multi-start constrained optimization algorithm developed by Box (1965). Even though this method cannot handle equality constraints, it works nicely for most design engineering problems. It assumes that an initial feasible point X (satisfying all m constraints) is available. The approach is similar to the simplex optimization method used for unconstrained nonlinear optimization problems. In the simplex method, D + 1 point defines simplex in D-dimensional space. The convex hull of D + 2 or more points is often called complex. In the process, an infeasible point is moved towards the centroid of the previously found feasible points. After feasible points are found, the worst point based on the objective function value is reflected about the centroid of the rest of the points. The point is accepted or modified depending on the feasibility and function value of the new point. When the point is infeasible, it is retracted towards the feasible points. This new feasible point now replaces

Review of some Constrained Optimization Schemes

5

the worst point in the simplex. This completes one iteration and is repeated for other iterations. Various steps of the approach are given as follows: Step 1: initialize reflection coefficient α, termination parameter ε and bounds for the variables X∈[Xmin, Xmax]. Step 2: generate initial set of 2D feasible points and evaluate the function value at each point f(X). If the point is not found as feasible, then a new point is computed by moving the point towards the centroid of the remaining feasible points. Step 3: next, the objective functions are considered at each of these feasible points. Carry out the reflection based on the worst point (say, Q) having maximum function value Fmax according to the formula XR = XO + α(XO − XQ). If the reflected point is feasible and f(XR) > Fmax, then retract the point half the distance to the centroid. If the point is not feasible, then check for feasibility of the solution by setting the point to be within the lower and upper bounds of each variable. If it is still infeasible, then it is retracted by half distance to centroid again. Step 4: replace XQ by XR and check for termination as follows: If

(f ( X P ) − f )  P

2

< ε , then stop

where

f =

1 f (X 1 ) + f (X 2 ) + ... + f (X 2D ) 2D 

[1.2]

otherwise, go to step 3. The algorithm needs a convex feasible region. The procedure becomes slow when the points fall close to the constraint boundary. Therefore, this standard algorithm is not

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efficient when the optimum lies at the constraint boundary or within a narrow feasible space. Box constrained optimization scheme is still widely used in several problems of engineering. The methodology was implemented with genetic algorithms for solving constrained optimization solutions effective in the literature (Deb 2001). 1.3.2. Random search techniques Similarly to the complex search approach, in the random search method the population of points is created, but in a random way. Depending on the function values at a number of random points in the interval, the search interval is reduced at every iteration by a constant factor. The flowchart of such an approach is given in Figure 1.1. Start

Start with initial feasible point X0 and initial range U0, Population P and p = 0 Create points using a uniform random distribution of r in [-0.5, 0.5] and find set of P points XP = X0 + rU0

yes p=p+1

Set X0 as one with lowest f(Xp) and reduce range U0

Is Xp infeasible?

no

no p = P? no

Save Xp and f(Xp)

yes

Max cycles?

yes Stop

Figure 1.1. Flowchart of the random search method

Review of some Constrained Optimization Schemes

7

The reliability of the algorithm increases with the number of sample points. Thus, for every iteration, P such points are taken and repeated until the maximum iterations are reached. The method becomes inefficient when the feasible search space is narrow. Often, this approach is used to find the initial feasible guess points for other methods. Other methods such as sequential linear programming and quadratic programming rely on the fact that the solution of the original nonlinear programming problem is obtained by solving a series of linear programming problems. Each linear programming problem is generated by approximating the nonlinear objective and constraint functions via first-order Taylor series approximations about the current design vector Xi. The resultant linear programming problem is solved by a standard numerical method (simplex) to find new design vector Xi+1. If Xi+1 does not satisfy the stated convergence, then the problem is re-linearized about the point Xi+1 and the procedure is continued until the optimum solution is obtained. 1.3.3. Method of feasible directions In such a method, a starting point satisfying all the constraints is first selected and moved to a better point as Xi+1 = Xi + λSi, where Si refers to the direction of movement, while λ indicates the distance of movement or step length. The step length is selected in such a way that the resulting point always lies in the feasible region. The search direction Si is found such that a small move cannot violate any constraint and the objective function reduces in that direction. Based on the method of selecting Si, different schemes of feasible direction have originated. Two famous approaches are the Zoutendijk method and the Rosen gradient projection method. The Zoutendijk method solves a

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constrained optimization problem by generating an improving feasible direction via a linear programming subproblem or a simple quadratic programming problem with linear constraints. Another technique known as the generalized reduced gradient approach was proposed to solve optimization problems with linear constraints. As these methods require the first-order derivatives of functions, they are not commonly used in most practical situations. 1.4. Indirect solution techniques In indirect approaches, the constrained nonlinear problem is converted into an equivalent unconstrained one. The most commonly used methods for this are transformation techniques. Here, the constrained problem is transformed into sequential unconstrained problems by adding penalty terms for each constraint violation. When a constraint is violated, the objective function is penalized by the extent of its violation. There are two such penalty methods: (i) interior penalty methods and (ii) exterior penalty methods. In the first approach, interior penalty methods, the infeasible points are not considered and feasible points are also penalized, while in the second approach, exterior penalty methods, only the infeasible points are penalized. In the mixed penalty approach, both infeasible and feasible points are penalized. There are many transformation approaches, such as the penalty function method and the method of multipliers. In the penalty function approach, each time, a set of penalty parameters are modified and a previous sequence helps to obtain the solution of the current sequence. 1.4.1. Penalty function approach The constrained problem is converted to unconstrained form as: E(X,R) = f(X) + P(R,g(X), h(X))

[1.3]

Review of some Constrained Optimization Schemes

9

where R is the penalty parameter and P ( ) is a penalty function, which is often defined in terms of constraint violation. If we multiply this penalty term with a large value of penalty parameter, obviously, in the initial rounds, only the minimization of constraint violation would be focused rather than optimization of the function f(X). In the case of interior penalty methods, where initial points are strictly feasible, this practice is followed. As the iterations are progressing, the value of R is slowly reduced and the solution approaches to an optimum feasible point. In the exterior penalty case, as the initial points are taken as either feasible or infeasible, a small initial value of R results in an optimum solution close to the unconstraint optimum point. As R is increased in successive steps, the solution improves and finally approaches the true constrained optimum. The approach is briefly described in the following algorithm: 1) Select an initial point X0, penalty parameter R and penalty function P( ). Set i = 0. 2) Prepare E = f(Xi) + P(R, g(Xi),h(Xi)). 3) Minimize the function E and find Xi + 1. 4) (i) If E(Xi+1) - E(Xi) < error tolerance, then print the final optimum as Xi+1 and stop. (ii) Otherwise, change R as R = c.R, where c∈[0,1] in the interior penalty method, while c > 1 in the exterior penalty method, and go to step 2 with i = i + 1. The approach is relatively simple. Both convex and non-convex constraints can be handled. As in every iteration, the penalty function gets distorted, which reduces the speed of the search process. We also have to maintain the objective function and the constraints in normalized forms before applying the approach.

10

Optimization for Engineering Problems

1.4.2. Multipliers method In order to avoid distortion of penalty functions in a large number of iterations, we can use a single penalty parameter R with weighing factors (multipliers) for each constraint. The constraint violation is increased by the weighing factor before calculating the penalty term. Afterwards, an equivalent term is subtracted from the penalty term. Such an approach works in successive steps, each time updating the weighing factors or multipliers in a prescribed way. For example, for the problem with inequality constraints, the effective objective function is written as: m

(

E = f(X) + R  P (g j (X ) + d j ) 2 − d j 2 j =1

)

[1.4]

where the multiplier dj for each constraint j in successive iterations is updated as

dj = P(gj(X)) + dj

[1.5]

This method requires less computational storage space and the boundary values of the constraints can be determined exactly. In order to improve the effectiveness of classical multiplier methods, today several other approaches such as the space decomposition multiplier method (Patel and Padiyar 2015) are in use. 1.4.3. Simulated annealing search Simulated annealing (SA) is a search-based optimization scheme inspired from metallurgical annealing, in which controlled cooling minimizes the defects and the crystal size in a metal increases. SA starts with a high temperature T and ends with a low temperature to achieve the lowest energy state. The solution at iteration i is Xi, while f (Xi) denotes the corresponding objective function. The subsequent solution Xi+1 is found from a random solution

Review of some Constrained Optimization Schemes

11

close to Xi by applying certain rules. The energy level ΔF = f(Xi+1) - f(Xi) ≤ 0, and the point Xi+1 is always accepted. If not, then the point Xi+1 is still accepted with a probability given by exp(−ΔF/T) > r, where r is a uniform random number in the range [0, 1]. If exp(−ΔF/T) ≤ r, then the point is not accepted, i.e. Xi+1 = Xi. New solutions are continuously produced until a maximum number of iterations is complete. For constrained search optimization, the methodology is given in the following steps: 1) Generate an initial feasible solution X0 randomly. Select the highest temperature Tmax, the lowest temperature Tmin and the inner iteration times N. Set T = Tmax and i = 0. Set the best solution X* = X0 and the best value f* = f(X*). 2) While T > Tmin i) While i ≤ N a) Generate the new solution Xi+1 = Xi + (b − a) × r, where r denotes a normally distributed one-dimensional random number with zero mean and unit standard deviation. Also, a and b are variable bounds. b) Update

X i+1 =a + (X i+1 − b)

if X i+1 >b

=b − (a − X i+1 )

if X i+1 0, then update the current state with a probability exp(−ΔF/T). f) Increment i = i + 1. ii) Increment inner iteration N = N + 1 and set i = 0.

12

Optimization for Engineering Problems

iii) Decrease the temperature T according to the schedule T = αT. 3) Print the best solution X* and the corresponding function value f*. 1.5. Constrained multi-objective optimization Many engineering problems have a requirement of simultaneous satisfaction of two or more objective functions. For example, reducing weight and improving natural frequency are the criteria required for a composite structure. Such a problem is stated as:

Minimize F=[f1 (X), f2 (X),.]  Subject to X ∈ [X min , X max ] 

[1.7]

Sometimes, the criteria do not conflict with one another, where a single optimum X* minimizes all the objectives simultaneously. More often, there is a conflict between different criteria. That is, the minimizer of one function is not necessarily the minimizer of another. In such a case, there is no single optimum point. Such a situation is tackled by weighing criteria as Minimize f(X) = w1f1(X) + w2f2(X) +…..

[1.8]

where the weights w1, w2,… are such that wi = 1 and are chosen from experience. Other way to handle multiple criteria is to designate one of the objectives as primary and others are treated as constraints as follows: Minimize f1 (X) Subject to f2 (X) − c 2 ≤ 0 f3 (X) − c 3 ≤ 0 …………

      

[1.9]

Review of some Constrained Optimization Schemes

13

Here, the selection of constants c2, c3,… to obtain single optimum solution X* is an important issue. When wide ranges of either w1, w2,… or c2, c3,… are sought, the optimum solutions will form a global picture. This global picture will finally aid in selecting the single best compromised solution to the problem. A design variable vector X* is Pareto optimal if and only if there is no vector X with characteristics

  and fi (X) < fi (X*) for at least one i. fi (X) ≤ fi (X*) ∀ i ∈ [1,2,m]

[1.10]

Here, prediction of the best Pareto point from the entire set is required. There is a quantitative criterion where a single best compromise Pareto design is selected. This popular criterion is called the “min-max method”. Consider a Pareto point Q with (f1, f2) as its coordinates in criterion space. Let f1min be the minimum of f1(X) and f2min is the minimum of f2(X). Then, we can define the deviations from the best values as z1 = ⏐f1 - f1min⏐ and z2 = ⏐f2 - f2min⏐. In the min-max approach, a single Pareto point X* is determined from min[max(z1,z2)]. A good number of other methods are also available. The direct multisearch (DMS) method (Liu and Tseng 2001) is one famous approach. It maintains a list of feasible non-dominated points. The approach tries to capture the whole Pareto front from the polling procedure. In each cycle, new feasible evaluated points are added to this list and the dominated ones are removed. Here, the constraints are handled using an extreme barrier function, and the effective objective is written as Minimize F(X) = f(X) if belong to feasible region   =∞ otherwise 

[1.11]

14

Optimization for Engineering Problems

1.6. Conclusions Various constrained optimization approaches have been described briefly. Specifically, the direct search algorithms for tackling constrained optimization problems were summarized in this chapter. Direct handling of constraints to form feasible space is a common method in many practical problems. Methods such as complex search and random search solve constrained optimization problems very effectively. The feasible direction approach, on the other hand, needs the gradient information of objective function and constraints. The indirect methods such as the penalty function approach and the method of multipliers make use of an effective objective function to generate a feasible optimum solution. These methods are also widely used in conventional optimization design. As a global solution strategy, simulated annealing can handle the effective objective functions without much complication. Pareto optimal problems are quite common in most of the present-day problems. A brief description was provided at the end of this chapter. The min-max and direct multisearch methods for tackling multi-objective formulation were briefly presented. According to current requirements, the implementation issues of evolutionary approaches such as simulated annealing will be explored for the solutions of multi-objective constrained optimization problems. The new developments will be seen in the coming days. 1.7. References Arora, J.S., Chahande, A.I., and Paeng, J.K. (1991). Multiplier methods for engineering optimization. International Journal for Numerical Methods in Engineering, 32(7), 1485—1525. Bellman, R. (1952). On the theory of dynamic programming. Proceedings of the National Academy of Science USA, 38, 716—719.

Review of some Constrained Optimization Schemes

15

Box, M.J. (1965). A new method of constrained optimization and a comparison with other methods. Computer Journal, 8(1), 42—52. Chen, X., and Kostreva, M.M. (2000). Methods of feasible directions: A review. In Progress in Optimization: Contributions from Australasia, Yang, X., Mees, A.I., Fisher, M., and Jennings, L. (eds). Springer, Boston. Custódio, A.L., Madeira, J.F.A., Vaz, A.I.F., and Vicente, L.N. (2011). Direct multisearch for multiobjective optimization. SIAM Journal on Optimization, 21, 1109—1140. Deb, K. (2001). Optimization for Engineering Design, Algorithms and Examples. Prentice-Hall of India, New Delhi. Duffin, R.J., Peterson, E.L., and Zener, C. (1967). Geometric Programming. Wiley, New York. Kirkpatrick, S., Gelat, C.D., and Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220, 671—680. Liu, C.S., and Tseng, C.H. (2001). Space decomposition multiplier method for constrained minimization problems. Computers and Mathematics with Applications, 41, 51—62. Patel, N., and Padiyar, N. (2015). Modified genetic algorithm using Box complex method: Application to optimal control problems. Journal of Process Control, 26, 35—50. Yeniay, O. (2005). Penalty function methods for constrained optimization with genetic algorithms. Mathematical and Computational Applications, 10, 45—56.

2 Application of Flower Pollination Algorithm for Optimization of ECM Process Parameters

The flower pollination algorithm (FPA), a novel metaheuristic algorithm inspired by the natural pollination of flowers, is employed for optimization of the electrochemical machining (ECM) process. The objective function used in the FPA for optimization is developed using response surface methodology (RSM). RSM is used to develop empirical equations in order to map the inter-relationship between ECM process parameters (electrolyte flow rate, electrolyte concentration, feed rate, voltage and inter-electrode gap) and response variables. Optimal results are predicted by using the FPA to satisfy single-criteria as well as multiple-criteria optimization. The performance of the FPA is evaluated by accuracy of the results, convergence speed, the number of optimized populations and computational time. The FPA is also used to draw the trend lines of responses corresponding to different ECM parameters. The results of the present research work are compared to those presented by past studies to validate the superiority of the FPA in terms of accuracy and effectiveness.

2.1. Introduction Electrochemical machining (ECM) stands out among the most potential modern machining technologies. It uses the principle of electrolysis to remove the metal from a workpiece. If two electrodes are placed in a liquid bath filled Chapter written by Bappa ACHERJEE, Debanjan MAITY, Arunanshu S. KUAR and Manoj K. DUTTA.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

18

Optimization for Engineering Problems

with conductive fluid and a DC potential is applied between the electrodes, and then the anodic metal starts to deplete and deposits on the cathode. The principle of electrolysis is used for electroplating with the objective of depositing the metal on the workpiece. However, since the objective of ECM is to remove the metal, the workpiece is used as an anode. When the current is passed, electrochemical dissolution starts to occur at the anode at a controlled rate (Kozak 1998). During the process, the tool is provided with a downward feed motion at a controlled rate. The shape to be produced on the workpiece depends on the form of the tool. Electrolyte is pumped in to the passage between the tool and the workpiece to complete the circuit. The electrolyte is selected based on the condition that anodic dissolution takes place, but no deposition occurs at the cathode (Ghosh and Mallik 2010). Figure 2.1 shows the schematic perspective of a normal electrochemical machining setup.

Figure 2.1. Scheme of an electrochemical machining setup

ECM finds several industrial applications, including cutting, drilling, deburring and shaping of metals (Lee et al.

Application of Flower Pollination Algorithm

19

2002; Ebeid et al. 2004; Bhattacharya and Sorkhel 1999; Bhattacharyya et al. 2006; Rao et al. 2008). The ECM process is used for generating intricate shapes in components in the defense and aerospace industries, automotive industries, forging die manufacturing and, recently, micro-manufacturing (Ebeid et al. 2004; Bhattacharya and Sorkhel 1999; Bhattacharyya et al. 2006; Rao et al. 2008; Asokan et al. 2008). Bhattacharya and Sorkhel (1999) built up an electrochemical machining setup with automatic tool feed and controlled electrolyte flow arrangements. The setup is used to perform machining on EN8 steel by using a brass tool. The effect of ECM parameters on machining performances, namely the material removal rate (MRR) and the radial overcut (ROC), is investigated. Bhattacharyya et al. (2006) also carried out an experimental investigation to study the effect of tool vibration on machine performances during micro-ECM of copper. As the process performance depends on several machining parameters, optimization of the ECM parameters is thus gaining much attention among researchers. Rao et al. (2008) investigated and optimized performances of the ECM process, including the MRR, dimensional accuracy, tool life and machining cost, with respect to important ECM parameters such as the tool feed rate, velocity of electrolyte flow and applied voltage. Asokan et al. (2008) developed regression models and artificial neural network models for optimizing process performances, especially the MRR and surface roughness (SR) in terms of control parameters such as current, voltage, electrolyte flow rate and inter-electrode gap during ECM of hardened steel. Samanta et al. (2011) applied the artificial bee colony (ABC) algorithm to determine the optimal settings of machining parameters for some non-traditional machining processes, including ECM. Rao and Kalyankar (2011) obtained a combination of optimal ECM parameters using a teaching—learning-based optimization algorithm. Das et al. (2014) investigated ECM of EN 31 steel with the objective of optimizing the MRR and SR using the ABC algorithm.

20

Optimization for Engineering Problems

The flower pollination algorithm (FPA) is an innovative development in the field of nature-inspired metaheuristic algorithms. The FPA is inspired by the natural pollination process of flowers. Wang et al. (2014) explored the FPA with a dimension-by-dimension update for effectual improvement of convergence speed and solution quality. Sharawi et al. (2014) used the FPA for optimizing the lifetime of wireless sensor networks. Balasubramani and Marcus (2014) studied the applicability and effectiveness of the FPA. The FPA is used to solve intricate optimization problems such as integer programming problems (El-henawy and Ismail 2014) and sudoku puzzles (Raouf et al. 2014). Yang et al. (2012) investigated the FPA by comparing its results for 10 test functions to the results obtained by using the particle swarm optimization (PSO) algorithm and the genetic algorithm (GA) for the validation of results. The results showed that the FPA had higher proficiency than the PSO algorithm and the GA. Yang et al. (2014) used the FPA to solve some multi-criteria and bi-criteria benchmark problems and compared it to some commonly used stochastic algorithms to show the superior convergence speed of the FPA. Prathiba et al. (2014) solved a multi-criteria optimization problem to optimize economic load dispatch by determining an effective setting of power output from the generator to reduce the fuel cost of power system operation. In this chapter, the FPA is used to search for the optimal process zone of ECM to achieve maximum MRR and minimum ROC independently and concurrently. Experimental data from previous investigations on ECM are taken as an explanatory case to check the accuracy, effectiveness and repeatability of the FPA for solving single- and multi-objective optimization problems. The optimal solutions achieved by using the FPA are compared to those derived from past studies using different algorithms such as the artificial bee colony (ABC) algorithm, the

Application of Flower Pollination Algorithm

21

Gauss—Jordan algorithm (GJA) and the teaching—learningbased optimization (TLBO) algorithm. Parametric effects on ECM performance characteristics are also analyzed and discussed. 2.2. Flower pollination algorithm The flower pollination algorithm, a nature-inspired metaheuristic algorithm proposed by Xin-She Yang (2012), is based on the natural pollination process of flowers. The FPA does not come under the category of swarm-based metaheuristic algorithm. Four idealized rules according to the pollination characteristics of flower plants are assumed to frame the structure of the FPA: 1) biotic and cross-pollination are represented as global pollination because pollen-carrying pollinators perform Lévy flights; 2) abiotic and self-pollination are represented as local pollination because these processes do not require pollinators; 3) the probability of reproduction relies on flower consistency, which is proportional to similarities between the two flowers involved; 4) the interaction between local pollination and global pollination is controlled by a switch probability p∈[0, 1], which is significantly biased towards the local pollination due to the physical proximity and external factors such as wind. The biotic flower pollination process always depends on living pollinators such as insects and animals which carry the pollen from one flower to another. Abiotic flower pollination does not require any living pollinators for transferring pollen, but rather relies on wind, rain, etc.

22

Optimization for Engineering Problems

(Stanford University 2001; Glover 2007). Biotic pollination is the most common flower pollination process, which mostly relies on living pollinators for pollen transfer. Although a flowering plant usually has several flowers and each of the flowers releases millions of pollen gametes, for simplicity, it is assumed that each plant has only one flower and each flower releases only one pollen gamete. To generate mathematical expressions for the FPA, the above-stated four idealized rules are converted into equations as given below. In the global pollination step, living pollinators such as insects carry the pollen from one flower to another for a longer distance, as the insects can fly and move longer distances. Thus, for global optimization, global optimization steps (rule 1) and flower consistency (rule 3) are combined into a mathematical expression which is given by: =

+

−

∗

[2.1]

where is the pollen i for the solution vector xi at iteration t, ∗ is the present best solution in the current generation and L denotes the strength of pollination, which is basically the step size. As insects may cover long distances using steps of varying length, a Lévy flight can be used to effectively imitate this behavior. The Lévy distribution follows the following expression: ~

( )

(

)

s>>s0>0

[2.2]

where ( ) is the standard gamma function, and this distribution is valid for large steps s > 0. The local pollination steps (rule 2) and flower consistency (rule 3) are combined as follows: =

+ (

−

)

[2.3]

Application of Flower Pollination Algorithm

23

where and are pollens of different flowers of the same species. For a local random walk, and are selected from the same population and is drawn from a uniform distribution in [0, 1]. Flower pollination can occur at both the local and global scales. In practice, flowers in near or adjacent patches by pollen from flowers are more likely to be pollinated by local flower pollen than that are far away. To imitate this, the switch probability p∈[0, 1] is used to effectively switch the pollination process from local to global and vice versa (rule 4). 2.3. Optimization of the ECM process: results and discussions The FPA is applied to search for optimal electrochemical machining parameters, which fulfills a single objective as well as multiple objectives. The experimental data on ECM presented by past studies are used to develop empirical models, which are further used as objective functions for optimization using the FPA. The optimal results predicted by the FPA are compared to the results of past studies to verify the effectiveness and applicability of the FPA in the optimization of ECM parameters. A computer program is written in the MATLAB® platform based on the logic used in the FPA, and run on a computer with an Intel i3 processor 3 GB RAM. The values of the key algorithm parameters specified for optimization using the FPA are: 1) maximum iterations for each flowering plant or population = 500; 2) function evaluations (total iterations) = 10,000;

24

Optimization for Engineering Problems

3) population size (n) = 20; 4) probability switch (p) = 0.8. It has been noted during a trial run that the FPA can predict the optimum for all the objective functions. 2.3.1. Experimental data and empirical models Bhattacharya and Sorkhel (1999) carried out an experimental investigation on ECM by setting up a microprocessor-controlled ECM setup with automatic tool feed and controlled electrolyte flow arrangements. A cylindrical brass tool is used for ECM of EN 8 steel. The ECM parameters used for carrying out the experiments are electrolyte concentration, electrolyte flow rate, voltage and inter-electrode gap. The performance of the ECM process is measured using responses such as the MRR (metal removal rate) and the ROC (radial overcut). The values of different machining parameters with their units, symbols and levels are presented in Table 2.1. The experimental results reported in Bhattacharya and Sorkhel (1999) are used to develop the empirical models using RSM to correlate the ECM parameters with process responses. The empirical models for the MRR and ROC, in actual parametric values, are given in equations [2.4] and [2.5], respectively:

Y2MRR (g/min) = 1.19263 + 0.05688 E − 0.13590 [2.4] F + 0.09215 V − 5.45671 G − 0.00004 E 2 + 0.01232 2 2 2 F + 0.00029 V − 0.36444 D − 0.00365 E F − 0.00067 E V + 0.01407 E G − 0.01045 F V + 0.26505 F G + 0.09247 VG

Y2ROC (mm) = −2.10705 + 0.01065 E + 0.31849 F + 0.00266 V + 0.48742 G − 0.00002 E 2 − 0.01223 F2 + 0.00011 V 2 + 0.08501 G 2 − 0.00040 E F − 0.00006 E V − 0.00199 E G + 0.00044 F V − 0.02656 FG − 0.00781 VG

[2.5]

Application of Flower Pollination Algorithm

Parameter

Electrolyte concentration Electrolyte flow rate Voltage Inter-electrode gap

Unit

Symbol

25

Levels −2

−1

0

+1

+2

E

15

30

45

60

75

l/min

F

10

11

12

13

14

V

V

10

15

20

25

30

mm

G

0.4

0.6

0.8

1.0

1.2

g/l

Table 2.1. ECM parameters with their units, symbols and levels

2.3.2. Single-objective optimization First, the FPA is used to individually optimize the MRR and ROC. For this purpose, equations [2.4] and [2.5] are used as the objective functions used in the FPA to optimize the MRR and ROC, respectively. The objectives set are to maximize the MRR and to minimize the ROC. The maximum value of the MRR obtained by using the FPA is 1.455 g/min, and the minimum ROC value obtained is 0.082 μm. The single-objective optimization results for the MRR and ROC with the optimal set of ECM parameters determined using the FPA are given in Table 2.2. The optimal set of ECM parameters determined using the Gauss—Jordan algorithm (GJA) by Bhattacharya and Sorkhel (1999) is also presented in Table 2.2. It can be found that the FPA gives better results than those obtained by using the GJA, and also gives an entirely different optimal set of values of ECM parameters. Samanta et al. (2011) employed the artificial bee colony (ABC) algorithm, and Rao et al. (2011) applied the teaching—learning-based optimization (TLBO) algorithm to maximize the MRR and minimize the ROC in ECM using the mathematical models developed by Bhattacharya and Sorkhel (1999). The parametric setting and the optimum results obtained by using the ABC, TBLO and FPA are found to be same up to three decimal points.

26

Optimization for Engineering Problems

Response

MRR

ROC

Nature of optimization

Maximum

Minimum

Optimization technique

Optimal value

Optimal parameter setting

E

F

B

D

FPA

1.455

75.00

10.00

30.00

1.20

ABC

1.455

75.00

10.00

30.00

1.20

TLBO

1.455

75.00

10.00

30.00

1.20

GJA

0.725

57.88

11.98

22.04

1.00

FPA

0.082

15.00

10.00

10.00

0.40

ABC

0.082

15.00

10.00

10.00

0.40

TLBO

0.082

15.00

10.00

10.00

0.40

GJA

0.270

17.55

11.05

21.65

0.87

Table 2.2. Single-objective optimization results for MRR and ROC

Figure 2.2 shows the convergence diagrams for the FPA relating to (a) MRR and (b) ROC. It can be found that during optimization of MRR, the FPA converges to the optima after 440 functional evaluations, whereas only 164 evaluations were conducted for ROC. For MRR, almost 5,522 functional evaluations have been found converged to its optimal value, whereas for ROC, it was 8,208 evaluations, which is the measure of optimized populations. Figure 2.3 shows the histogram of the results of single-objective optimization obtained by using the FPA for (a) MRR and (b) ROC. It is observed from this figure that the mean value of the functional evaluations obtained for MRR is 1.378 g/min (for all 10,000 functional evaluations), and for ROC, it is 0.1099 μm, both of which are close to their respective optimal results, thus ensuring the quality of the convergence. The computational times recorded for the optimization of MRR and ROC (roughness average) are 0.49 seconds and 0.51 seconds, respectively. The average computational time recorded for single-objective optimization is 0.50 seconds.

Application of Flower Pollination Algorithm

Figure 2.2. FPA convergence diagrams for (a) MRR and (b) ROC

27

28

Optimization for Engineering Problems

Figure 2.3. Histogram of functional evaluations obtained by using the FPA for (a) MRR and (b) ROC

Application of Flower Pollination Algorithm

29

Figure 2.4. Scatter diagrams of MRR for (a) electrolyte concentration, (b) electrolyte flow rate, (c) voltage and (d) inter-electrode gap. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

Figure 2.4 shows the scattered diagrams with trend lines predicted by the FPA to study the effects of ECM parameters on MRR. The trends predicted by the FPA are found to be identical in nature and magnitude to those given by Bhattacharya and Sorkhel (1999). It can be depicted from the linear trend lines drawn in Figure 2.4 that the electrolyte concentration, voltage and inter-electrode gap have positive effects on MRR, and thus MRR increases with those parameters. The electrolyte flow rate negatively affects the MRR. Bhattacharya and Sorkhel (1999) reported that the conductivity of an electrolyte increases with electrolytic concentration, which results in enhanced ionic mobility and consequently increases the MRR. Using higher levels of electrolyte flow rate ensures faster flashing of the reaction

30

Optimization for Engineering Problems

products and debris from the machining zone, which also reduces the chance of formation of passive layers on the workpiece. Increasing the voltage and reducing the inter-electrode gap results in the availability of higher current in the tool—workpiece gap, which in turn increases the MRR. The actual trends of MRR with respect to machining parameters in Figure 2.4 show a high degree of nonlinearity for the case of voltage and inter-electrode gap, where the MRR first decreases and then increases, after reaching a threshold value. It can be simply determined from Figure 2.4 that the optimum value of MRR is obtained at an electrolyte concentration of 75 g/l, an electrolyte flow rate of 10 l/min, a voltage of 30 V and an inter-electrode gap of 1.2 mm.

Figure 2.5. Scatter diagrams of ROC for (a) electrolyte concentration, (b) electrolyte flow rate, (c) voltage and (d) inter-electrode gap. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

Application of Flower Pollination Algorithm

31

Figure 2.5 shows the parametric effects on ROC, which depict the same trend as presented in earlier research work by Bhattacharya and Sorkhel (1999). It can be observed from the linear trend lines presented in Figure 2.5 that the ROC increases with all the machining parameters. Bhattacharya and Sorkhel (1999) reported that increasing electrolyte concentration may prompt the formation of reaction products and increase the chances of the passage of stray current to the machining zone. Increasing electrolyte flow rate makes a higher volume of electrolytic ions available at the machining periphery. This simultaneous effect may produce a greater stray current effect at side walls, which results in an increase of ROC. Increasing voltage not only ensures the availability of higher current at machining gap, but also increases stray current intensity. Nevertheless, increasing inter-electrode gap results in the weakening of the stray current effect at flow path boundaries. The actual trends of ROC corresponding to the ECM parameters in Figure 2.5 show a high degree of nonlinearity for electrolyte concentration and electrolyte flow rate, where the ROC first increases and then decreases, after reaching a certain level. It can be found from Figure 2.5 that the optimum value of ROC is obtained at an electrolyte concentration of 15%, an electrolyte flow rate of 10 l/min, a voltage of 10 V and an inter-electrode gap of 0.4 mm. 2.3.3. Multi-objective optimization For simultaneous optimization of multiple objectives, a combined objective function is developed, which is given by: =

×

−

×

[2.6]

32

Optimization for Engineering Problems

where weight factors w1 and w2 are assigned to ROC and MRR, respectively, according to their relative importance, such that the total weight is equal to 1. ROCmin and MRRmax are the optimum values of ROC and MRR, respectively, as determined using the FPA during the single-objective optimization of individual responses. Table 2.3 presents the multi-objective optimization results of ECM following the selected criteria of w1 = w2 = 0.5. Bhattacharya and Sorkhel (1999) did not attempt simultaneous optimization of ROC and MRR. However, Samanta et al. (2011) and Rao et al. (2011) attempted to search for an optimal ECM parametric combination which simultaneously satisfies multiple objectives, using the ABC and TLBO algorithms, respectively, by assigning equal weight to the selected responses. It can be observed that the FPA gives the same response values with exactly the same optimal parametric setting compared to the ABC and TLBO algorithms. Figure 2.6(a) shows the algorithm convergence diagrams for the FPA with respect to the multi-objective optimization function when both MRR and ROC are optimized together. It can be observed that only after 286 functional evaluations does the objective function of multi-objective optimization reach its global optima. Moreover, for multi-objective optimization, 7,744 evaluations have been found converged to its optimal value. Figure 2.6(b) presents the histogram of functional evaluations obtained by using the FPA. The computational time recorded for the multi-objective optimization is 0.54 seconds. Figure 2.7 presents the scattered diagrams with trend lines predicted by the FPA, which shows the variation of the multi-objective function (Z) with the variation of ECM parameters. The optimal setting of the process parameters can be easily determined from these figures, which are presented in Table 2.3.

Application of Flower Pollination Algorithm

Figure 2.6. (a) Convergence diagram and (b) histogram of functional evaluations obtained by using the FPA for the multi-objective function, Z

33

34

Optimization for Engineering Problems

Conditions

w1 = w2 = 0.5

Optimization technique

Zmin

MRR

ROC

FPA

0.349

0.4408

0.0818

ABC TLBO

A

B

C

D

15.00 10.00 10.00 0.40

0.349 0.4408*

0.0818* 15.00 10.00 10.00 0.40

0.349

0.0818

0.4408

15.00 10.00 10.00 0.40

*Corrected values of optimal results, as reported in Rao and Kalyankar (2011).

Table 2.3. Multi-objective optimization results of ECM

Figure 2.7. Scatter diagrams of the multi-objective function (Z) with respect to (a) electrolyte concentration, (b) electrolyte flow rate, (c) voltage and (d) inter-electrode gap. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

2.4. Conclusion The following conclusions can be drawn from the present research work:

Application of Flower Pollination Algorithm

35

1) the FPA is successfully used to determine the optimum set of ECM parameters to satisfy single as well as multiple objectives; 2) the results obtained by using the FPA can be compared to those obtained by using different algorithms such as the Gauss—Jordan algorithm, the artificial bee colony algorithm and the teaching—learning-based algorithm to verify the accuracy of the results; 3) the solutions of the optimization problems show that the algorithm is capable of finding the feasible optimal parametric combinations with a high degree of accuracy; 4) the FPA shows the ability to converge at a faster rate and requires very less computation time; 5) the FPA can predict the true overall parametric trends as, in the FPA, none of the parameters are kept constant during the analysis. 2.5. References Asokan, P., Kumar, R.R., Jeyapaul, R., and Santhi, M. (2008). Development of multi-objective optimization models for electrochemical machining process. International Journal of Advanced Manufacturing Technology, 39, 55—63. Balasubramani, K. and Marcus, K. (2014). A study on flower pollination algorithm and its applications. International

Journal of Application or Innovation in Engineering & Management, 3, 230—235. Bhattacharya, B. and Sorkhel, S.K. (1999). Investigation for controlled electrochemical machining through response surface methodology-based approach. Journal of Material Processing Technology, 86, 200—207.

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Bhattacharyya, B., Malapati, M., Munda, J., and Sarkar, A. (2006). Influence of tool vibration on machining performance in electrochemical micromachining of copper. International Journal of Machine Tools and Manufacturing, 47, 335—342. Das, M.K., Kumar, K., Barman, T.K., and Sahoo, P. (2014). Investigation on electrochemical machining of EN 31 steel for optimization of MRR and surface roughness using artificial bee colony algorithm. Procedia Engineering, 97, 1587—1596. Ebeid, S.J., Hewidy, M.S., EI-Towell, T.A., and Youssef, A.H. (2004). Towards higher accuracy for ECM hybridized with low-frequency vibrations using the response surface methodology. Journal of Material Processing Technology, 149, 432—438. El-henawy, I. and Ismail, M. (2014). An improved chaotic flower pollination algorithm for solving large integer programming problems. International Journal of Digital Content Technology and its Applications, 8(3), 72—81. Ghosh, A. and Mallik, A.K. (2010). Manufacturing Science, 2nd edition. Affiliated East-West Press Private Limited, New Delhi. Glover B.J. (2007). Understanding Flowers and Flowering: An Integrated Approach. Oxford University Press, Oxford. Kozak, J. (1998). Mathematical models for computer simulation of electrochemical machining process. Journal of Material Processing Technology, 76, 170—175. Lee, E.S., Park, J.W., and Moon, V.A. (2002). Study on electrochemical micromachining for fabrication of microgrooves in an air-lubricated hydrodynamic bearing. International Journal of Advanced Manufacturing Technology, 20, 720—726. Prathiba, R., Moses M.B., and Sakthivel, S. (2014). Flower pollination algorithm applied for different economic load dispatch problems. International Journal of Engineering and Technology (IJET), 6(2), 1009—1016. Rao, R.V. and Kalyankar, V.D. (2011). Parameters optimization of advanced machining processes using TLBO algorithm.

International Conference on Engineering, Project, Production Management 2011, Singapore, pp. 21—32.

and

Application of Flower Pollination Algorithm

37

Rao, R.V., Pawar, P.J., and Shankar, R. (2008). Multi-objective optimization of electrochemical machining process parameters using a particle swarm optimization algorithm. Proceedings of

the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 22, 949—958. Raouf, O.A., El-henawy, I., and Baset, M.A. (2014). A novel hybrid flower pollination algorithm with chaotic harmony search for solving sudoku puzzles. International Journal of Modern Education and Computer Science, 3, 38—44. Samanta, S. and Chakraborty, S. (2011). Parametric optimization of some non-traditional machining processes using artificial bee colony algorithm. Engineering Applications of Artificial Intelligence, 24, 946—957. Sharawi, M., Emary, E., Saroit, I.A., and Mahdy, H.E. (2014). Flower pollination optimization algorithm for wireless sensor network lifetime global optimization. International Journal of Soft Computing and Engineering, 4, 54—59. Stanford University (2001). Oily fossils provide clues to the evolution of flowers. Science Daily, April 5. Available: http:// www.sciencedaily.com/releases/2001/04/010403071438.htm. Wang, R. and Jhou, Y. (2014). Flower pollination algorithm with dimension by dimension improvement. Mathematical Problems in Engineering, Article ID 481791. Yang, X.S. (2012). Flower pollination algorithm for global optimization. In Unconventional Computation and Natural Computation, Durand-Lose, J. and Jonoska, N. (eds). 7445, UCNC, Springer. Yang, X.S., Karamanoglu, M., and He, X. (2014). Flower pollination algorithm: A novel approach for multi objective optimization. Engineering Optimization, 46, 1222—1237.

3 Machinability and Multi-response Optimization of EDM of Al7075/SIC/WS2 Hybrid Composite Using the PROMETHEE Method

Hybrid aluminum metal matrix composites are gaining much interest in several applications, such as automobile, aerospace and agricultural farm machinery, and as a substrate in electronics, golf clubs, turbine blades and brake pads. This is due to their exceptional qualities such as high strength, low density, good wear resistance and low thermal expansion coefficient in comparison to many other metals and alloys. Aluminum metal matrix composites can replace many conventional metals owing to high performance, long life, low cost, high efficiency and a good grade of materials. These groups of properties are continuously expanding by reinforcing different materials such as graphite, fly ash, SiC, WS2, TiC, red mud and organic materials on the aluminum metal matrix in various proportions. Every reinforced material has its own advantages and enhances the properties of the base metal or alloy when it is added. Nano- or micro-size SiC particle reinforcement yields better bonding in the matrix, which in turn leads to improvement of the properties. Furthermore, wear resistance can be improved by secondary reinforcement; hence, efforts have been made to investigate various combinations of the composites with different types of reinforcement material to examine their effects on the mechanical, thermal and tribological properties of aluminum hybrid composites. These composites have also often been investigated for their machinability, in order to make them the finished product in different applications. Furthermore, surface integrity, productivity and accuracy have often been explored. The influence of the different compositions along with the machining parameters on the responses has been investigated. Subsequently, the optimal set of these parameter combinations has been investigated. An AHP-based PROMETHEE method has been used to find the rank of the alternatives.

Chapter written by Mohan Kumar PRADHAN and Brajpal SINGH.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Optimization for Engineering Problems

3.1. Introduction Hybrid aluminum alloys have been drawing the attention of researchers owing to their exceptional strength-to-weight ratio and weight reduction without compromising mechanical strength. Conversely, machinability issues have limited their use, as these alloys need to be manufactured to make components from it for various advanced applications. These materials are deemed as “difficult to machine” materials due to their excellent mechanical properties, and the conventional manufacturing process may not be able to machine these materials. Therefore, attention has been turned towards the application of advanced machining processes such as EDM discharge (electrical machining), which uses an alternate energy source to machine such type of materials. EDM is widely used to make more precise, accurate and attractive components in modern manufacturing industries, but its low efficiency and cost make it necessary to optimize the processes (Pradhan 2010). In recent years, multi-objective optimization has drawn attention and several methods have been proposed to help select the best compromise alternatives. Furthermore, these responses have been optimized by an improved PROMETHEE optimization algorithm, which is used in multi-objective problems in various fields. In this study, optimization of EDM process parameters and multi-responses has been performed by using the improved PROMETHEE algorithm. The main focus is to increase the material removal rate and to minimize the surface roughness, tool wear rate (TWR) and radial overcut of composites. In this chapter, the machinability of the hybrid composite and the influences of significant parameters on the responses of the EDMed Al7075/SiC/WS2 hybrid composite have been investigated. The Taguchi method is used for conducting experiments by varying different EDM input parameters

Machinability and Multi-response Optimization of EDM of Hybrid Composite

41

such as discharge voltage (V), discharge current (Ip), pulse on time (Ton) and wt% of reinforcement materials applied to the machine of a composite. To determine the relative importance of various attributes, the AHP method is used in the proposed improved PROMETHEE method, in which a pairwise comparison of each of the attributes is performed to calculate the partial binary relations signifying the strength of preference of an alternative a1 over another alternative a2. The objective of this chapter is to select the best alternatives to obtain optimal attributes in EDM of a hybrid composite (Al7075/SiC/WS2) by using the PROMETHEE method. 3.1.1. Overview of metal matrix composites Hybrid aluminum matrix composites are widely used in various advanced engineering applications such as in the automotive, aircraft and locomotive industries, and as a substitute for traditional metals and alloys, due to their superior mechanical properties such as high specific strength, low thermal coefficient, specific modulus and good wear resistance. Moreover, the demand for smarter materials with high strength-to-weight ratios and efficient materials with minimum cost is increasing day by day, which has driven researchers’ focus on various regenerations and investigations of composite materials in the last few decades. It has been proven that the new-generation metal matrix composites exhibit high strength, unique density and high wear resistance, and are widely used in industries, craft trade, structural applications and different defense systems. Consequently, the study of secondary reinforcement is often imposed to improve other properties such as thermal conductivity, friction of coefficient and strength-to-weight ratio. Essentially, these hybrid nanocomposites show improved wear resistance, satisfactory mechanical properties, high specific resistance, low coefficient of thermal expansion, high thermal resistance, good damping capacity,

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Optimization for Engineering Problems

improved wear resistance, high specific stiffness and corrosion resistance and tribological properties of aluminumbased hybrid metal matrix composites (Bodunrin et al. 2015). Many engineering components made from particulate metal matrix composites are produced by close modeling and casting processes, which often require machining to realize the mandatory dimensions and surfaces. The machining of particulate metal matrix composites offers a significant challenge because several reinforcement materials are significantly harder than the common tool material. The reinforcement phase causes rapid abrasive tool wear and therefore the widespread use of the particulate metal matrix. The composites are heavily influenced by their poor machinability and high machining costs. Due to the qualities often considered as “difficult to machine”, MMCs are not readily machinable. They produce short cutting chips and require medium cutting forces, and the range of machining parameters in which they can be machined is, to a certain extent, wide. However, MMCs are very abrasive and hence the tools wear very rapidly. To avoid these problems, EDM is used due to its non-contact machining characteristic. More optimum machining parameters in the EDM machine are optimized to get a desirable magnitude of EDM responses on particulate metal matrix composites. 3.1.2. CNC EDM machine EDM is one of the most extensively used machines to machine such type of applications due to their non-contacttype machining using thermal energy to remove material in the form of repeated sparks. The hardness and other such properties have no influence as long as the material is conductive. Hence, for testing the machinability, the prepared hybrid material is machined by EDM and the influence of the wt% of the reinforcement’s material is tested along with the machining parameters.

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43

A CNC EDM is shown in Figure 3.1, which commonly uses 3D profile electrodes that are expensive and time-consuming to manufacture for the EDM process. The CNC can provide multi-axis motion for simple electrodes in EDM, in order to produce parts with more complex 3D shapes. Wong and Noble (1986) used machining and testing with cylindrical electrodes with a microcontroller. In recent years, the technology for improving the rate of metal removal has been established by modifying the basic principle of EDM, which provides a single discharge for each electrical pulse. Kunieda and Masuzawa (1988) investigated the multi-electrode discharge system, which simultaneously provides additional discharge with a related electrode connected to the connection. An oxygen-assisted EDM system, which greatly improves the metal removing rate, was tested by supplying oxygen into the discharge gap (Kunieda et al. 1999). In addition, the metal removing rate can be substantially improved with reduced tool wear rate using a multi-electrode discharging system without any improvement in surface roughness. 3.1.2.1. Types of electrical discharge machines EDM facilitates machining in a number of ways, and many of these operations are similar to a conventional machining operation, for instance, milling and die sinking. Various classifications are possible, and recent developments in its technology append new operations owing to increase in various requirements. A simple and general classification can be given in view of standard applications such as: — wire EDM; — EDM milling; — micro-EDM; — electric discharge grinding (EDG);

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Optimization for Engineering Problems

— electrical discharge texture (EDT). 3.1.2.2. Definition of the EDM process parameters (Puhan 2012) EDM parameters are those that affect machining characteristics in terms of productivity, surface integrity and surface quality. MRR, TWR, Surface Roughness (SR) and Radial Over-Cut (ROC) etc. Some of them are recognized by literature and experience. There are some important process parameters that affect the responses are: — discharge voltage (V); — peak current; — pulse on time (Ton); — pulse off time (Toff). 3.1.2.2.1. Discharge voltage (V) This is the voltage applied between the electrodes in the presence of the dielectric medium. Before the current flow, it depends on the strength of the current as well as the dielectric strength. As soon as the current flow begins, the open-circuit voltage drops and stabilizes the electrode gap. The magnitude of the total energy of the spark increases the erosion rate and then the MRR. Apart from this, the high energy is also responsible for the poor quality of the surface and the high wear rate of the equipment. 3.1.2.2.2. Pulse current (Ip) This is another important machining parameter in EDM that determines almost all of the machining characteristics. The current is increased in increments until it reaches the predetermined level, so it is repeatedly used to indicate the highest current during machining. With the increase in the peak current, the discharge energy increases when the rise

Machinability and Multi-response Optimization of EDM of Hybrid Composite

45

of the peak current is very high, thereby possibly resulting in a greater wear of the tool.

Figure 3.1. EDM setup

3.1.2.2.3. Pulse on time (Ton) This is the time duration during which the current is allowed to flow in a cycle, expressed in μs. The energy generated is a function of peak current and the duration up to which it is allowed. Material removal is a function of this parameter. The longer the pulse duration, the greater the spark energy will be, which generates broader and deep craters because the material removal is related to the quantity of energy that goes in during the pulse on time. Although the MRR will be higher with higher Ton, rough surfaces are produced by the higher spark energy.

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Optimization for Engineering Problems

3.1.2.2.4. Pulse off time (Toff) In a cycle, there is a pulse off time or pause time during which the supply voltage is cut off and, as a result, Ip diminishes to zero. It is also the period of time after which the next spark is initiated and is expressed in μs, analogous to Ton. Subsequently, the dielectric must be de-ionized after sparking and should regain its strength, which takes some time. Furthermore, flushing of debris is also carried out during Toff. The cycle is completed when sufficient Toff is allowed before the start of the next cycle. Since pulse off time is a non-productive time, it should not be too small as it makes the next spark unstable. The sum of the pulse on time and pulse off time in a cycle is called the pulse period or total cycle time. 3.1.2.2.5. Duty cycle (Tau) This is the ratio of pulse on time and the pulse period. Duty cycle is defined in the equation below. At higher Tau, the spark energy is provided for the longer pulse period, causing higher machining efficiency: =

× 100

[3.1]

3.1.2.2.6. Polarity Polarity is the potential of the workpiece with respect to the tool, i.e. in straight or positive polarity, the workpiece is positive, whereas in reverse polarity, the workpiece is negative. Changing the polarity can have a vivid effect; normally, the electrode with positive polarity wears less, whereas that with negative polarity cuts faster. On the other hand, some metals do not act this way. Carbide, titanium and copper are normally preferred with negative polarity.

Machinability and Multi-response Optimization of EDM of Hybrid Composite

47

3.1.2.2.7. Dielectric fluid The dielectric fluid carries out three most important functions in the EDM. The first function is to insulate the inter-electrode gap and, after breaking down at the appropriately applied voltages, conduct the flow of current. The second function is to flush away the debris from the machined area. Finally, the dielectric acts as a coolant to assist in heat transfer from the electrodes. The most commonly used dielectric fluids are hydrocarbon compounds such as light transformer oil and kerosene. 3.1.2.2.8. Inter-electrode gap (G) The inter-electrode gap is a primary factor for spark stability and proper flushing. The most vital needs for a good operation are gap stability and reaction speed; the existence of backlash is predominantly unwanted. The reaction speed must be higher, so that it responds to short circuits or open gap conditions. The gap width is not directly measured, but can be decided from the average gap voltage. The tool servomechanism is accountable for maintaining a working gap at a predetermined value. Usually, electromechanical (DC or stepper motors) and electrohydraulic systems are used, which are normally designed to respond to average gap voltage. 3.1.2.2.9. Flushing pressure (P) and type of flushing Flushing is a significant factor in EDM since debris must be removed from the inter-electrode gap for effective erosion, as well as to ensure fresh dielectric fluid flows in the between electrodes. Flushing is not easy if the cavity is deep, and inefficient flushing may initiate arcing and unwanted cavities, which can destroy the workpiece. Several methods are used to flush the EDM gap, jet or side wash, pressure wash, vacuum wash and pulse wash. In jet flushing, hoses or fixtures are used and directed at the inter-electrode gap to

48

Optimization for Engineering Problems

wash away the debris, in pressure and vacuum flushing dielectric flow through the drilled holes in the electrode, workpiece or fixtures. The typical range of pressure is 0.1—0.4 kgf/cm2. The composite samples fabricated by using the stir casting method, which is the most economical process, are shown in Figure 3.2. The vertical milling machine is used to finish the casting material to give the shape and size to fix on the EDM machine table. EDM was done to find the metal removing rate, tool wear rate, roughness and radial overcut, and by analyzing these parameters and applying the PROMETHEE method, we obtain the optimum EDM condition for composite. 3.1.2.3. Performance characteristics The significant performance characteristics that are mostly studied in the EDM are as follows: — material removal rate (MRR); — tool wear ratio; — radial overcut; — surface quality or surface integrity. The phenomenon of EDM is very complex as many disciplines of science and branches of engineering are involved. Theories about the creation of a plasma channel between the electrodes, the thermodynamics of the repetitive sparks producing melting and evaporating of the electrodes, the microstructural changes and the metallurgical transformations of the material are still not understood (Pradhan 2010). Thus, the challenge posed is to understand the effects and interactions of the parameters on the machining characteristics. In order to obtain the desired response, the parameters should be optimized to obtain the following machining characteristics:

Machinability and Multi-response Optimization of EDM of Hybrid Composite

49

— increase in material removal rate, i.e. reduction in machining time; — improvement in surface integrity; — reduction in tool wear; — reduction in overcut. 3.1.2.4. Equations used to calculate the responses of EDM machine  mm 3  Weight Loss (gm)× 60 MRR  = 3  min  Density of Sample (gm/mm ) × Machining Time (sec.)  mm 3  Weight Loss (gm)× 60 TWR  = 3  min  Density of Tool (gm/mm ) × Machining Time (sec.)

ROC=

D1 − D2 2

where D1 = Right side reading on digital micrometer and D2 = Left side reading on digital micrometer. The Toolmaker microscope was used to calculate the ROC. A digital surface roughness meter is used to calculate surface roughness of cavity on the composite surface generated by the EDM machine. 3.2. Literature review Researchers have been paying attention to a methodology of yielding optimal EDM performance measures of high MRR, low TWR and acceptable ROC. This section provides a study of each of the performance measures and the scheme for their enhancement. In the past, considerable improvement has been achieved in increasing productivity, accuracy and versatility of the EDM process. The crucial issue is to select the process parameters such as Ip, Ton, Tau,

50

Optimization for Engineering Problems

V, flushing pressure, dielectric fluid and polarity in such a way that MRR and accuracy increase, and concurrently ROC or G, TWR and SR diminish. Roy et al. (2016) investigated the optimization of the process parameters of powder-mixed EDM. Response surface methodology has been used to plan and investigate the effects of the process parameters, namely Ip, Ton and concentration of the Al powder in kerosene dielectric medium, as well as on MRR, TWR and Ra, which are optimized for high MRR, low TWR and low Ra using the desirability function approach. Due to frequent short-circuiting, addition of Al powder to the dielectric fluid reduces the MRR, whereas TWR decreases for a low peak current of 2 amp with increase in the concentration of powder. Addition of Al powder further increases the surface roughness to 3.31 (μm). Huang and Shen (2017) studied metal matrix composites (MMCs) of aluminum alloy (AA6061) with 0.1, 0.2 and 0.5 wt% WS2 inorganic nanotubes (INT) and fabricated AA6061 MMCs with 0.1 and 0.2 wt% WS2 inorganic fullerene-like nanoparticles (IF) by the stir casting method to enhance the mechanical properties. The aluminum MMCs reinforced by WS2 INT or WS2 IF exhibit excellent mechanical properties compared to the AA6061 alloy. They found an improvement in the mechanical properties of the alloys, i.e. both the tensile strength of the AA6061 alloy MMCs and their elongation. Yielding strength, ultimate tensile strength and ductility of AA6061/0.2wt%WS2 IF MMCs were enhanced by 12.3%, 15.8% and 39.3%, respectively. Yielding strength, ultimate tensile strength and ductility of AA6061/0.2wt%WS2 INT MMCs were improved by 15.0%, 20.6% and 67.8%, respectively. Finally, it was shown that AA6061/0.5wt%WS2 INT exhibited the best result in hardness, which was improved by a factor of 5.

Machinability and Multi-response Optimization of EDM of Hybrid Composite

51

Figure 3.2. EDMed workpiece

3.2.1. Metal removing rate Wang and Tsai (2001) presented semi-empirical models of MRR for various workpieces shown in Figure 3.2, and tool electrode combinations (copper, graphite and silver—tungsten alloy). To achieve higher MRR in EDM, a stable machining process is required, which is partly influenced by the contamination of the G between the workpiece and the electrode, but also depends on the size of the eroding surface at the given machining regime (Josko and Junkar 2004). Jaharah et al. (2008) investigated the MRR and TWR of a steel tool. Ip was found to be the major factor influencing MRR. A higher MRR was obtained with high Ip, medium Ton and low Toff. However, a smaller TWR was obtained with high Ip, high Ton and lower Toff. Kanagarajan et al. (2008) used electrode rotation, Ton, Ip and FP to study MRR on tungsten carbide/cobalt-cemented carbide and experimentally showed that Ip and Ton are the most significant factors. Puertas et al. (2004) analyzed the impact of EDM parameters on the MRR and electrode wear of a cobalt-bonded tungsten carbide workpiece. A quadratic model was developed for each of the responses, and it was reported that for MRR, the current intensity factor was the most influential, followed by Tau, Ton and the interaction

52

Optimization for Engineering Problems

effect of the first two. The value of MRR increased when the current intensity and Tau were increased and decreased with Ton. Khan et al. (2009) discussed the performance (MRR and TWR) of EDMed mild steel due to the shape configuration of the electrode. The maximum MRR was found for round electrodes, followed by square-, triangleand diamond-shaped electrodes. However, the highest TWR values were found for the diamond-shaped electrodes. It is also considered as an offline process planning technique as the simulation algorithm is largely based on the MRR, TWR and spark gap. However, the simulation of discharge location and spark gap, which are dependent on the distribution of debris concentration, was reported to yield a more realistic representation of the sparking phenomenon. Dhar et al. (2007) estimated the effect of Ip, Ton and V on MRR, TWR and EDM gap of Al-4Cu-6Si alloy-10 wt% SiCp composites. Using three factors, and three-level full factorial designs, a second-order nonlinear mathematical model was developed for establishing the relationship among machining parameters. It was revealed that the MRR, TWR and G increase with an increase in Ip and Ton. Dvivedi et al. (2008) identified the machining performance in terms of MRR and TWR by achieving an optimal setting of process parameters (Ton, Toff and Ip) during the EDM of Al6063 SiCp metal matrix composite. It was revealed that Ip is more predominant on MRR than other significant parameters. MRR increases with increasing Ip and Ton up to an optimal point and then decreases. Karthikeyan et al. (1999) developed mathematical models for optimizing EDM characteristics such as the MRR, TWR and the surface roughness on aluminum silicon carbide particulate composites, using full factorial design. The process parameters taken into consideration were Ip, Ton and the

Machinability and Multi-response Optimization of EDM of Hybrid Composite

53

percent volume fraction of SiC (V) present in LM25 aluminum matrix. 3.2.2. Tool wear process Tool wear is moderately analogous to the MRR in EDM. Mohri et al. (1995) found that tool wear is affected by the precipitation of turbostratic carbon from the hydrocarbon dielectric on the electrode surface during sparking. Also, the rapid wear on the electrode edge was because of the failure of carbon to precipitate at difficult-to-reach regions of the electrode. Marafona and Wykes (2000) conducted energy-dispersive X-ray analysis of tool surfaces measuring their compositions and established a wear inhibitor carbon layer on the electrode surface by adjusting the settings of the machining parameters prior to normal EDM conditions. Although the thickness of the carbon inhibitor layer contributed to a significant improvement on the TWR, it had little effect on the MRR. Conversely, for applications requiring higher MRR, a large pulse current is encouraged to increase electrode wear implanting electrode material onto the workpiece. Kunieda and Kobayashi (2004) clarified the mechanism of determining tool electrode wear ratio in EDM by spectroscopic measurement of the vapor density of the tool electrode material. Longer Ton is known to result in lower TWR and deposition of a thicker carbon layer on the tool electrode surface. Conversely, the density of copper vapor evaporated from the tool electrode surface was found to be lower when the carbon layer was thicker, indicating that tool electrode wear is prevented by the protective effects of the carbon layer. A well-known machining strategy of recompensing the tool wear is the orbiting of the electrode relative to the workpiece, where a planetary motion creates an effective flushing action that shows improved part accuracy and process efficiency.

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3.2.3. Radial overcut The EDMed cavity produced is always larger than the electrode, and this difference (between the size of the electrode and the size of the cavity) is referred to as the ROC. It becomes important when close-tolerance components are required to be produced for space application, and also in tools, dies and molds for press work. The dimensional accuracy of EDM is greatly influenced by the ROC resulting from the discharge gap and electrode wear. The parameters such as Ip, Ton, applied voltage and the workpiece material are significantly influenced by ROC. It increases with the increase of Ip but only up to a certain limit. It also depends upon the G, voltage, and chip size, which vary with, the amperage used (Singh et al. 2004). 3.2.4. Surface topography or surface finish Surface texture, surface topography and surface finish are the terms used to express the machined surface related to geometric irregularities and surface quality. An ideal surface roughness is commonly specified by the peak-to-valley height or the center line average, Ra (μm). The EDMed surfaces consist of several craters formed by the discharge energy. If the energy content is high, then deeper craters will be accomplished, leading to poor surface. The surface roughness has also been found to be inversely proportional to the frequency of discharge (Pandey and Shan 1980). A spark-eroded surface is a surface with a matt appearance and random distribution of overlapping craters and is often covered with a network of micro-cracks. The surface characteristics of the machined surface were extensively explored by Kanagarajan et al. (2008). They chose Ip, Ton, electrode rotation and flushing pressure as design factors to study the performance of the EDM process on tungsten carbide/cobalt cement carbide. The most effective parameters have been identified to reduce Ra using

Machinability and Multi-response Optimization of EDM of Hybrid Composite

55

RSM, and the experiments have been experimentally tested by confirmatory experiments. Chiang (2008) proposed a mathematical model and investigated the influence of Ip, Ton, Tau, voltage and their interactions on Ra. The experiments are conducted on the Al2O3 + TiC workpiece and it was found that Ip and Ton have a statistical significance on Ra. It is claimed to narrowly fit and predict Ra with a 95% confidence interval. 3.3. Optimization process To get the optimum value of the responses on EDM of hybrid composite (Al7075+SiC+WS) the optimum levels of the machining parameters need to be identified and used in combination. On the basis of the multi-criteria decisionmaking (MCDM) process, we optimize the EDM parameters, which are recorded during the time of experiment for the machining of the hybrid composite. The AHP method is used to find the normalized weight of EDM responses, and then we find preference function values by using the empirical formula of the PROMETHEE method. The PROMETHEE method is used to find the rank of alternatives by using Visual PROMETHEE-GAIA 1.4 Academic Edition software, which is already programmed on the PROMETHEE method to give the rank of alternatives. 3.3.1. Analytic hierarchy process method The AHP is one of the most common analytical techniques to solve complex decision-making problems. To completely characterize a specific decision problem, the AHP hierarchy has many levels. A number of functional characteristics are used in the AHP method, which makes it a beneficial methodology. It is used to handle decision-making situations involving subjective judgments, multiple decision makers and the ability to provide measures of preference consistency. It is designed to reflect how people actually

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Optimization for Engineering Problems

think. AHP continues to be the most highly regarded and commonly used decision-making method. It can efficiently deal with subjective as well as objective attributes. By using a scale of relative importance in this method, a pairwise comparison matrix is created. The fundamental scale is used for entering judgments of the AHP method. The method is used to determine the consistent weights and calculate the composite performance score of alternatives to get the rank of the alternatives. The greater the composite performance scores of the alternative, the better the rank of that alternative. The AHP method involves the following steps. 3.3.1.1. Formulating the decision table Step 1: First, we find attributes for the considered decision-making problem and the alternatives on the basis of the identified attributes filling the requirements. The EDM parameters and responses are shown in Table 3.1, and the selection of alternatives and attributes in Table 3.2. Exp. Ip Ton V MRR TWR ROC no (amp) (μsec) (volts) (mm3/min) (mm3/min) (μm)

Ra (μm)

1

8

75

50

38.1444

0.1457

5.6458 7.1

2

10

100

60

17.7636

0.0905

5.7056 11.328

3

12

150

70

56.0699

0.119

5.6782 12.51

4

8

100

70

18.3321

0.2923

5.6931 8.041

5

10

150

50

19.132

0.3783

5.6258 10.381

6

12

75

60

39.2196

0.3627

5.6365 8.844

7

8

150

60

18.0327

0.2306

5.6248 10.323

8

10

75

70

18.2871

0.0467

5.6782 7.12

9

12

100

50

39.7156

0.1016

5.5806 9.723

Table 3.1. Experimental parameters and responses on EDM machine

Machinability and Multi-response Optimization of EDM of Hybrid Composite

57

3.3.1.2. Deciding weights of the attributes Step 2: To find the relative importance for various attributes according to the requirement of our objective, we make a pairwise comparison matrix on the basis of scale of relative importance. Whenever an attribute is compared to itself, it gives the value 1 in pairwise comparison matrix. Therefore, in the pairwise comparison matrix, the main diagonal values are all 1. The numbers 3, 5, 7 and 9 correspond to the verbal judgments moderate importance, strong importance, very strong importance and absolute importance (with 2, 4, 6 and 8 for compromise between the previous values). This relative importance scale was used in the AHP method (Rao 2007). Table 3.3 shows the preference matrix of attributes. MRR (mm3/min) TWR (mm3/min) ROC (μm) Ra (μm)

Attributes a2

17.7636

0.0905

5.7056

11.328

a3

56.0699

0.119

5.6782

12.51

Alternative a4

18.3321

0.2923

5.6931

8.041

a5

19.132

0.3783

5.6258

10.381

a6

39.2196

0.3627

5.6365

8.844

a7

18.0327

0.2306

5.6248

10.323

a8

18.2871

0.0467

5.6782

7.12

a9

39.7156

0.1016

5.5806

9.723

Table 3.2. Selection of attributes and alternatives

MRR

TWR

Ra

ROC

MRR 1.0000 3.0000 3.0000 5.0000 TWR 0.3333 1.0000 2.0000 3.0000 Ra

0.3333 0.5000 1.0000 2.0000

ROC 0.2000 0.3333 0.5000 1.0000 Table 3.3. Preference matrix or pairwise comparison matrix

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1) We calculate the value of relative normalized weight wj of all attributes by calculating the geometric mean of the ith row of the matrix and normalizing the geometric means values of the rows in the comparison matrix, which can be given as ⁄

={

}

MRR

TWR

Ra

ROC

GM

MRR

1.0000

3.0000

3.0000

5.0000

2.5900

TWR

0.3333

1.0000

2.0000

3.0000

1.1892

Ra

0.3333

0.5000

1.0000

2.0000

0.7598

ROC

0.2000

0.3333

0.5000

1.0000

0.4273

Sum

4.9663

GM of preference matrix =

and = Normalized wt

/∑

MRR

TWR

Ra

ROC

0.52152

0.23945

0.152995

0.086035

GM 1

In the AHP method for this chapter, the geometric mean method is used to find the relative normalized weights of the attributes because it is simple and easy to calculate the maximum eigenvalue and to reduce the inconsistency in judgments. 3.3.1.3. Consistency ratio The consistency ratio is calculated to find the consistency in our judgment; in other words, we can say that if the value of the consistency ratio is lower than 0.1, then our

Machinability and Multi-response Optimization of EDM of Hybrid Composite

59

consistency judgment is right. If the value of consistency ratio is higher than 0.1, then our consistency judgment is wrong and again we set the value of attributes in the preference matrix. Different steps can be used to find the consistency ratio: 1) Calculate the matrices A3 and A4 such that A3 = A1×A2 and A4 = A3÷A2, where

= [w1 w2 w3… … …wm]T

A2 = [0.52152, 0.23945, 0.152995, 0.086035]T

=

0.52152 0.23945 0.152995 0.086035

=

2.12903 0.977368 0.618613 0.346645

=

4.082355 4.081719 4.043352 4.029118

2) Calculate the maximum eigenvalue of matrix A4):

(i.e. the average

= 4.059136 3) Calculate the consistency index =( − )/( − 1). The smaller the value of CI, the smaller the deviation from consistency:

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Optimization for Engineering Problems

CI = (4.059136 − 4) ÷ (4 − 1) CI = 0.019712 M 1 2

3

4

5

6

7

8

9

10

11

12

13

14

15

RI 0 0 0.52 0.89 1.11 1.25 1.35 1.4 1.45 1.49 1.51 1.54 1.56 1.57 1.59

Table 3.4. Random Index Value (RI)

4) Take the random index (RI) for the number of attributes used in decision-making. Table 3.4 presents the RI values for different number of attributes: RI = 0.9 5) Calculate the consistency ratio CR = CI/RI: CR = 0.019712 /0.9 CR = 0.021902. Usually, a CR of 0.1 or less is considered as acceptable and it reflects an informed judgment that could be attributed to the knowledge of the analyst about the problem under study. CR less than 0.1 indicates a good consistency in the judgments made. 3.3.2. PROMETHEE method 3.3.2.1. Improved PROMETHEE calculations (Rao 2007) Step 3: After calculating the weights of the attributes using the AHP method, we find the decision-maker preference function, which we use to compare the contributions of the number of experiments (alternatives) in terms of each response (attribute). The preference function (Pj) is used to calculate the difference between the evaluations obtained by two alternatives (a1 and a2) in terms of a particular attribute, into a preference degree

Machinability and Multi-response Optimization of EDM of Hybrid Composite

61

ranging from 0 to 1. Let Pj,a1a2 be the preference function associated with the attribute. Gi is a non-decreasing function, which observed a deviation (d) between two alternatives a1 and a2 over the attribute bj, in order to facilitate the selection of a specific preference function. The normal function is equal to the simple difference between the attribute values bj for alternatives a1 and a2. For further preference functions, no more than two parameters (threshold q, p or s) must be fixed. The indifference threshold q is the largest deviation to consider as negligible on that attribute, and it is a small value with respect to the scale of measurement (Rao 2007); p is the smallest deviation to consider decisive in the preference of one alternative over another, and it is a large value with respect to the scale of measurement. Gaussian threshold s is only used with the Gaussian preference function. In general, it is set in the form of an intermediate value between the independent and preference thresholds. The preference threshold and indifference threshold values are shown in Table 3.5 for attributes. 3.3.2.2. Calculating the threshold values p

q

MRR

34.47567

3.83063

TWR

0.29844

0.03316

Ra

4.869

0.541

ROC

0.07272

0.00808

Table 3.5. Preference threshold and indifference threshold

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Optimization for Engineering Problems

1) p (highest value of attribute - lowest value of attribute) ×0.9 (p is assumed to be 90% of the maximum difference in the values of attribute). 2) q (highest value of attribute - lowest value of attribute) ×0.1 (q is assumed to be 10% of the maximum difference in the values of attribute). 3) d is the difference of an attribute for a1 and a2 alternatives. 4) if d ≤ 0, then

= 0.



5) if q ≤ d ≥ p, then

=



or ,



=

[ ( 1) −

where 0 ≤

,

( 2)]

≤ 1.

If the decision-maker specifies a preference function and weight for each attribute , j = 1, 2,…, M of the problem, then the multiple attribute preference index is defined as the weighted average of the preference functions .

=∑

,

represents the intensity of preference of the decision-maker of alternative a1 over alternative a2, when looking at all the features together. Its value ranges from 0 to 1. This preference indexes a valuable outranking relationship in the set of available outranking.

Machinability and Multi-response Optimization of EDM of Hybrid Composite

63

3.3.3. Ranking relations for improved PROMETHEE The leaving flow (Φ + (a)), entering flow (Φ−(a)) and the net flow (Φ(a)) for an alternative belonging to a set of alternatives are calculated by using Visual PROMETHEEGAIA 1.4 Academic Edition software and are defined by the following equations: ( ) =

( ) = ( )=

( )−

( )

( ) is called the leaving flow, ( ) is called the ( ) is called the net flow. Table 3.6 entering flow and shows the ranking of alternatives used in EDM. The alternative 1 is the best alternative to machining of the hybrid composite (Al7075 + SiC + WS2). 3.3.3.1. Graphical view of PROMETHEE ranking The graphical views of net flow and rank on partial and complete ranking of alternatives in EDM shown in Figures 3.3(a) and 3.3(b), respectively, are drawn by using Visual PROMETHEE-GAIA 1.4 Academic Edition software, which are given below, from which we can see that alternative 1 has the first rank and alternative 2 has the ninth rank on the graphs.

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Optimization for Engineering Problems

Figure 3.3(a). Partial ranking of alternatives by the PROMETHEE method. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

Machinability and Multi-response Optimization of EDM of Hybrid Composite

Figure 3.3(b). Complete ranking of alternatives by the PROMETHEE method. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

65

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Optimization for Engineering Problems

Figures 3.3(a) and 3.3(b) show the partial and complete rankings of alternatives, respectively. The partial ranking graph represents the entering flow and leaving flow values for alternatives, and the complete ranking graph represents the net flow values of the alternatives. We can see in the partial ranking graph that alternative 1 has the highest value for the entering flow and the lowest value for the leaving flow, and it has the highest net flow in the complete ranking graph. Therefore, alternative 1 has the first rank. The graph shows that the alternative having the highest net flow will have rank 1 (Table 3.6). Alternatives

Φ(a)

Φ + (a)

Φ−

Rank

Alternative 1

0.2842

0.3357

0.0516

1

Alternative 6

0.1757

0.2529

0.0771

2

Alternative 9

0.1093

0.2244

0.1151

3

Alternative 8

0.0539

0.1789

0.1250

4

Alternative 3

0.0256

0.2500

0.2244

5

Alternative 4

0.0213

0.1463

0.1250

6

Alternative 5

-0.1896

0.0459

0.2355

7

Alternative 7

-0.2055

0.0314

0.2369

8

Alternative 2

-0.2749

0.0057

0.2806

9

Table 3.6. Rank of the alternatives

3.4. Result and discussion 3.4.1. The effect of EDM parameters on machining characteristics of EDM machine The EDM process parameters and machining characteristics are recorded from the EDM machine, which are shown in Table 3.7).

Machinability and Multi-response Optimization of EDM of Hybrid Composite

Wt (%)

Ip Ton V MRR TWR (amp) (μsec) (volts) (mm3/min) (mm3/min)

ROC (μm)

0.145768 5.6458

67

Ra (μm)

0.75

8

75

50

38.14446

7.1

0.75

10

100

60

17.76367

0.090511

5.7056 11.328

0.75

12

150

70

56.06992

0.119039

5.6782

12.51

1

8

100

70

18.3321

0.292309

5.6931

8.041

1

10

150

50

19.13204

0.378279

5.6258 10.381

1

12

75

60

39.21962

0.362711

5.6365

1.5

8

150

60

18.03273

0.230593

5.6248 10.323

1.5

10

75

70

18.2872

0.046769

5.6782

7.12

1.5

12

100

50

39.71567

0.101573

5.5806

9.723

8.844

Table 3.7. Parameters of EDM machine and machining characteristics

In the table, 0.75, 1 and 1.5 represent wt% of WS2 in composite with constant 10 wt% of SiC. 3.4.1.1. On metal removing rate To analyze the mean of means and S/N ratios, the Taguchi technique is used, which is a theoretical approach that involves graphing the special effects and visually making out the important influences of various influencing factors. Figure 3.4 plots the signal-to-noise ratio (S/N) to examine the effect of EDM parameters on metal removing rate by Taguchi using Minitab software. The figure shows the graphical view of EDM parameters on metal removing rate and it was seen that when the wt% of reinforcements (SiC + WS2) increases, the MRR decreases, and when Ip increases from 8 to 10 amp, the MRR first decreases and then abruptly increases. Simultaneously, on increasing Ton

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Optimization for Engineering Problems

and voltage from 75 to 100 μsec and 50 to 60 V respectively the MRR first decreases and then gradually increases.

Figure 3.4. Main effects plot of the factors on material removal rate

3.4.1.2. On tool wear rate To analyze the mean of means and S/N ratios, the Taguchi technique is used, which is a theoretical approach that involves graphing the special effects and visually making out the important influences of various influencing factors. Figure 3.5 plots the signal-to-noise ratio (S/N) to examine the effect of EDM parameters on metal removing rate by Taguchi using Minitab software. Figure 3.5 shows the graphical view of EDM parameters on tool wear rate, and it can be observed that the TWR increases when the wt% of reinforcements (SiC + WS2) in the hybrid composite sample and voltage (V) increase up to 0.75—1 wt% and 50—60 V, respectively, and then decreases.

Machinability and Multi-response Optimization of EDM of Hybrid Composite

69

Simultaneously, the TWR decreases first when Ip and Ton increase up to 10 amp and then gradually increases.

Figure 3.5. Main effects plot of the factors on tool wear rate

3.4.1.3. On radial overcut To analyze the mean of means and S/N ratios, the Taguchi technique is used, which is a theoretical approach that involves graphing the special effects and visually making out the important influences of various influencing factors. Figure 3.6 plots the signal-to-noise ratio (S/N) to examine the effect of EDM parameters on metal removing rate by Taguchi using Minitab software. Figure 3.6 shows the graphical view of the effect of EDM parameters on radial overcut, and it can be observed that when the wt% of reinforcements (SiC + WS2) increase, the ROC decreases. The ROC increases when the Ip and Ton increase up to 8—10 amp and 75—100 V, respectively, and then gradually

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Optimization for Engineering Problems

decreases. Simultaneously, the ROC gradually increases with increments in V.

Figure 3.6. Main effects plot of the factors on radial over cut

3.4.1.4. On surface roughness To analyze the mean of means and S/N ratios, the Taguchi technique is used, which is a theoretical approach that involves graphing the special effects and visually making out the important influences of various influencing factors. Figure 3.7 plots the signal-to-noise ratio (S/N) to examine the effect of EDM parameters on surface roughness by Taguchi using Minitab software. Figure 3.7 shows the graphical view of the effect of EDM parameters on surface roughness, and it can be observed that when the wt% of reinforcements (SiC + WS2) increases, Ra decreases. When Ip and Ton increase, Ra gradually increases. Ra increases with increase in voltage from 50 to 60 V, and then decreases upon increasing the voltage up to 70 V.

Machinability and Multi-response Optimization of EDM of Hybrid Composite

71

Figure 3.7. Main effects plot of the factors on surface roughness

3.4.2. Optimization of EDM parameters To achieve optimal results of the machining parameters and reduce the manufacturing cost of the composite product, an AHP-based PROMETHEE method was used to optimize the EDM parameters for machining of the hybrid composite (Al7075 + SiC + WS2) and to find the rank of alternatives. Alternative 1 has the first rank and alternative 2 has the ninth rank; therefore, the result shows that alternative 1 is best suitable alternative to EDM of the hybrid composite. 3.5. Conclusion This research studied the machinability of the hybrid composite (Al7075 + SiC + WS2) on EDM machine and also examined the influence of EDM parameters on machining characteristics in a hybrid composite surface using a copper electrode for the EDM process.

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Optimization for Engineering Problems

The experiments were performed under a number of parameter settings of discharge current, pulse on time and discharge voltage. The best alternative was found by using the AHP method and the PROMETHEE method. Minitab 18 software was used for the Taguchi method to model and analyze the effect of EDM parameters on the responses. Finally, soft computing techniques were employed for the modeling of MRR, TWR, Ra and ROC. These responses were experimentally validated. It was observed that Ip is the most effective parameter, compared to Ton and voltage (V), on the EDM characteristics. It was also observed that Ip increases the MRR, ROC and Ra for sample 1 (Al7075 + 10 wt% SiC + 0.75 wt% WS2), and decreases TWR; Ip increases the MRR, TWR and Ra for sample 2 (Al7075 + 10 wt% SiC + 1.0 wt% WS2) and decreases ROC; and Ip increases MRR, and Ra for sample 3 (Al7075 + 10wt%SiC + 1.5 wt% WS2) and decreases TWR and ROC, though for TWR it is greater than sample 2. The machining time reduces the increase in Ip. In the optimization of EDM parameters by using the AHP method, we calculated the normalized weight for attributes such as MRR, TWR, ROC and Ra, and the PROMETHEE method was used to find the rank of the alternatives. We concluded that alternative 1 has the first rank and alternative 6 has the second rank out of nine alternatives, so we can say that alternatives 1 and 6 are the most preferable alternatives in machining of the hybrid composite (Al7075 + SiC + WS2) by EDM machine. 3.6. References Bodunrin, M.O., Alaneme, K.K., and Chown, L.H. (2015). Aluminium matrix hybrid composites: A review of reinforcement philosophies; mechanical, corrosion and tribological characteristics. Journal of Materials Research and Technology, 4(4), 434—445.

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Chiang, K. (2008). Modeling and analysis of the effects of machining parameters on the performance characteristics in the EDM process of Al2O 3+TiC mixed ceramic. International Journal of Advanced Manufacturing Technology, 37(5—6), 523—533. Dhar, S., Purohit, R., Saini, N., Sharma, A., and Kumar, G.H. (2007). Mathematical modeling of electric - discharge machining of cast Al-4Cu-6Si alloy-10 wt.% SiCP composites. Journal of Materials Processing Technology, 194, 24—29. Dvivedi, A., Kumar, P., and Singh, I. (2008). Experimental investigation and optimization in EDM of al 6063 SiCp metal matrix composite. International Journal of Machining and Machinability of Materials, 3(3—4), 293—308. Huang, G. and Shen, Y. (2017). The effects of processing environments on the microstructure and mechanical properties of the Ti/5083AL composites produced by friction stir processing. Journal of Manufacturing Processes, 30, 361—373. Jaharah, A.G., Liang, C.G., Wahid, S.Z., Rahman, M.N.A., and Hassan, C.H.C. (2008). Performance of copper electrode in electrical discharge machining (EDM) of AISI H13 harden steel.

International Journal Engineering, 3(1), 25—29.

of

Mechanical

and

Materials

Josko, V. and Junkar, M. (2004). On-line selection of rough machining parameters. Journal of Materials Processing Technology, 149, 256—262. Kanagarajan, D., Karthikeyan, R., Palanikumar, K., and Sivaraj, P. (2008). Influence of process parameters on electric — discharge machining of WC/30%Co composites. In Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 222(7), 807—815. Karthikeyan, R., Lakshmi Narayanan, P.R., and Naagarazan, R.S. (1999). Mathematical modelling for electric — discharge machining of aluminum-silicon carbide particulate composites. Journal of Materials Processing Technology, 87, 59—63.

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Khan, A., Ali, M., and Haque, M. (2009). A study of electrode shape configuration on the performance of die sinking EDM.

International Journal Engineering, 4(1), 19—23.

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and

Materials

Kunieda, M. and Kobayashi, T. (2004). Clarifying mechanism of determining tool electrode wear ratio in EDM using spectroscopic measurement of vapor density. Journal of Materials Processing Technology, 149(1—3), 284—288. Kunieda, M. and Masuzawa, T. (1988). A fundamental study on a horizontal EDM. CIRP Annals — Manufacturing Technology, 37(1), 187—190. Kunieda, M., Kowaguchi, W., and Takita, T. (1999). Reverse simulation of die-sinking EDM. CIRP Annals — Manufacturing Technology, 48(1), 115—118. Marafona, J. and Wykes, C. (2000). A new method of optimising material removal rate using EDM with copper tungsten electrodes. International Journal of Machine Tools & Manufacture, 40, 153—164. Mohri, N., Suzuki, M., Furuya, M., Saito, N., and Kobayashi, A. (1995). Electrode wear process in electrical discharge machinings. CIRP Annals — Manufacturing Technology, 44(1), 165—168. Pandey, P.C. and Shan, H.S. (1980). Modern Machining Processes. Tata McGraw-Hill, New Delhi. Pradhan, M.K. (2010). Experimental investigation and modelling of surface integrity, accuracy and productivity aspects in EDM of AISI D2 steel (Doctoral dissertation). Pradhan, M.K. and Biswas, C.K. (2010). Investigating the effect of machining parameters on EDMed components an RSM approach. Journal of Mechanical Engineering, 7.1, 47—64. Puertas, I., Luis, C.J., and Alvarez, L. (2004). Analysis of the influence of EDM parameters on surface quality, MRR and Ew of WC-Co. Journal of Materials Processing Technology, 153—154(1—3), 1026—1032.

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Puhan, D. (2012). Non-conventional machining of Al/SiC metal matrix composite, PhD thesis, National Institute of Technology Rourkela. R.V. (2007). Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods. Springer-Verlag, London.

Rao,

Roy, C., Syed, K.H., and Kuppan, P. (2016). Machinability of al/10% sic/2.5% tib2 metal matrix composite with powder-mixed electrical discharge machining. Procedia Technology, 25, 1056—1063. Singh, S., Maheshwari, S., and Pandey, P. (2004). Some investigations into the electric — discharge machining of hardened tool steel using different electrode materials. Journal of Materials Processing Technology, 149(1—3), 272—277. Wang, P.-J. and Tsai, K.-M. (2001). Semi-empirical model on work removal and tool wear in electrical discharge machining. Journal of Materials Processing Technology, 114(1), 1—17. Wong, Y. and Noble, C. (1986). Electrical discharge machinings with transverse tool movement. In Proceedings of the 26th International Machine Tools Design and Research Conference, Manchester, England, September 17—18, 399—413.

4 Optimization of Cutting Parameters during Hard Turning using Evolutionary Algorithms

Optimum selection of cutting conditions drastically contributes to the increase of productivity and the reduction of costs; therefore, determination of optimum cutting parameters to minimize total machining time and process cost is the most essential task in cutting processes. This matter is more critical in hard turning in which the costs of machining are higher because of high tool wear rate. Efficiency and productivity of hard turning can be enhanced impressively by using accurate predictive models for cutting tool wear. The ability of genetic programming to present an accurate analytical model is a notable characteristic, which makes it more applicable than other predictive modeling methods. In this chapter, a novel intelligence-based methodology for calculating optimum cutting parameters in hard turning of AISI D2 is proposed. In the first step, the genetic equation for the modeling of tool flank wear is developed with the use of the experimentally measured flank wear values and genetic programming. In this order, a series of tests were conducted over a range of cutting parameters and the values of tool flank wear were measured. Using the obtained results, genetic models presenting connections between cutting parameters and tool flank wear are extracted. In the second step, based on the defined machining performance index and the obtained genetic equation, optimum cutting parameters are determined. The accuracy of the genetic programming model was evaluated using root mean square error (RMSE) and 2 coefficient of determination (R ). Results indicated that the genetic programming model predicted flank wear over the specified cutting range accurately high enough to be used in a real industrial optimization process. The calculated optimum cutting parameters improved the machining performance compared to the traditional machining method. These results allow us to conclude that the proposed modeling and optimization methodology offer the optimum cutting parameters and can be implemented in real industrial applications.

Chapter written by Vahid POURMOSTAGHIMI and Mohammad ZADSHAKOYAN.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Optimization for Engineering Problems

4.1. Introduction Hard turning is defined as the turning process of workpieces that have hardness values over 45 HRC (Saini et al. 2012). This process is intended for finish machining of a wide range of hardened steel workpieces. Hard turning enables manufacturers to simplify the machining process and achieve an acceptable surface quality in manufactured parts. Its advantages such as increased flexibility of the manufacturing process, higher rate of material removal, better environmental characteristics and low cost make it an undeniably economical manufacturing process (Bensouilah et al. 2016). Nowadays, increasing the profit of produced products in the manufacturing industry has become an important issue. This matter is more vital in finishing processes such as finish hard turning, which determines the final quality of manufactured workpiece (Raja and Baskar 2010). In finish hard turning, tool wear is considered as the most important factor affecting the surface quality of finished workpieces. Accordingly, using accurate predictive models for tool wear to maximize the productivity of the hard turning process is inevitable (Özel and Karpat 2005). Because of the complexity of phenomena occurring in the cutting zone, deriving an analytical model for tool wear modeling is impossible; therefore, soft computing tools are extensively used to model machining processes (Adnan et al. 2015). Özel and Karpat (2005) used artificial neural networks to evaluate tool wear and surface roughness for different cutting conditions in finish hard turning. In order to capture process-specific parameters, regression models were extracted. Then, some experiments for the turning of AISI 52100 steel with hardness 58 HRC were performed, and on the basis of the obtained information, the neural network was trained. It resulted that the neural network model

Optimization of Cutting Parameters

79

provided better prediction capabilities because of its ability to model complex nonlinearities and interactions. In a similar work, Wang et al. investigated an intelligent model, based on a fully forward connected neural network with cutting parameters and processing time as the inputs and tool wear, as the output of the network. The results of experiments showed that the proposed method had acceptable convergence speed (Wang et al. 2008). Benkedjouh et al. (2015) investigated the support vector methodology in the health evaluation of cutting tools. The purpose was to predict the amount of tool wear and calculate the remaining useful life of the cutting tool. They proposed a technique for tool condition estimation and life prediction based on support vector regression. The proposed method was applied on experimental data, and its results demonstrated that the proposed method was appropriate for assessing the gradual wear evolution of the cutting tools. Azmi (2015) suggested a new neuro-fuzzy modeling methodology to predict tool wear. The research studied the development of a tool condition monitoring technique using a dynamometer and adaptive network-based fuzzy inference systems in the milling process of composites. The proposed modeling method applied two various data partitioning techniques to improve the predictability of machinability response. In particular, it was found that the proposed models were able to match the nonlinear relationship of the tool. Nakai et al. (2015) studied the application of neural network models for the estimation of tool wear in the grinding of special materials. In their study, diamond tool wear was predicted during the grinding using fully intelligent systems. Training and validating processes were performed accurately for proposed intelligent systems to obtain the best estimation models. The results demonstrated that the obtained models were highly successful in predicting diamond tool wear. In some presented models, the efficiency and accuracy of models are very low, which made them not ideal in real

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Optimization for Engineering Problems

industrial conditions. Other proposed models offer only an ambiguous relation between input cutting parameters and the value of tool wear. Consequently, there is a need for a modeling technique that, in addition to producing high accuracy, could present an analytical model to explain output changes on the basis of input parameters. Genetic programming (GP) is one of the most general evolutionary computation methods (Gusel and Brezocnik 2011). GP is a domain-independent technique that, due to its characteristics and functionality in finding models in high-dimensional, noisy and stochastic environments, became an effective method to model various phenomena (Jamali et al. 2017). To date, many studies have been conducted to investigate the performance of GP methodology in manufacturing and machining processes. A wide range of GP applications have been reported on the improvement of dispatching rules for complex shop floor scenarios (Hildebrandt et al. 2010), modeling of material characteristics (Gusel and Brezocnik 2011), prediction of tool-chip contact length (Zadshakoyan and Pourmostaghimi 2013), modeling of complex manufacturing processes (Jamali et al. 2017), optimization of parameters in rapid prototyping (Garg et al. 2014), prediction of cutting tool crater wear (Zadshakoyan and Pourmostaghimi 2015) and comparing the wear values in drilling operation of various materials (Mehrabad and Pourmostaghimi 2017). There are some advantages of the proposed genetic programming approach over other studied intelligence-based methods: 1) the learning converge speed and accuracy of a trained model are high enough to be used in real industrial conditions; 2) the proposed genetic programming approach presents a mathematical equation on the basis of independent input cutting parameters and tool flank wear. By using the proposed model, it is possible to evaluate the effect of each cutting parameter on the value of flank wear;

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3) the most important advantage of the proposed model, which distinguishes it from other intelligent predictive models, is its dynamic characteristics. In other words, the value of flank wear in next times can be generalized as a function of cutting parameters and current tool wear. This ability increases the efficiency of the model in cutting parameters selection and real-time optimization during machining processes. To enhance the profitability of the machining process, the machine tool and cutting tool should be operated as efficiently as possible. This matter is of great importance in hard turning in which the cost and final quality of the process greatly depend on the selection of cutting parameters such as feed rate and cutting speed. In the past, cutting parameters have been selected based on operators’ experience or from data given in handbooks. However, these parameters could not yield optimal machining criteria. Therefore, there is an economic need to handle machinery in a real optimized condition that fulfills certain objectives. In the field of optimization of machining processes, various research works have been reported. These works can be categorized into two groups. The first group contains conventional optimization algorithms such as geometric programming and dynamic programming. These methods do not offer a reliable optimal cutting condition and can only be used for specific problems. The second group is composed of evolutionary optimization methodologies such as simulated annealing (SA), genetic programming (GP) and particle swarm optimization (PSO). These methods can solve more complicated problems with numerous objectives, especially in actual manufacturing practices. In the field of optimum parameters selection in machining, some studies have been performed. Agapiou (1992) studied the optimization of a machining system to minimize process costs by using the Nelder—Mead method. Shin and Joo (1992) proposed the dynamic programming method for the optimization of multi-pass turning. Wen et al. (1992) used quadratic

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programming to improve the surface quality in grinding processes. Since the conventional methods have little success in finding global optimum cutting parameters, numerous studies have been conducted in the field of machining optimization by using evolutionary algorithms. Chen and Tsai (1996) studied the ability of SA in various machining processes. Reddy et al. (1998) investigated GA in the optimization of production costs by selecting the optimum depth of cut in multi-pass turning. Gopal and Rao (2003) proposed GA to maximize material removal rate (MRR) in grinding processes of silicon carbide. They put constraints on the surface quality of produced parts. Asoknan et al. (2003) presented a novel methodology by using SA and GA to optimize the costs of turning processes. By using the GA, Cus and Balic (2003) minimized the cost of machining processes in turning operations. Li-Ping et al. (2005) studied the PSO technique to find optimum cutting parameters in machining processes. They also investigated the effect of variable parameters of the PSO algorithm such as population size on convergence speed and accuracy. Mukherjee and Ray (2006) investigated the ability of various optimization techniques in machining processes. They found that the PSO algorithm has acceptable convergence speed and accuracy in finding optimum cutting parameters. This chapter investigates an intelligence-based system to optimize tool life and material removal rate in finish hard turning processes of AISI D2. For this purpose, the GP modeling technique is used to model the effect of cutting speed, feed rate and cutting time on tool flank wear using genetic programming. Then, the optimum cutting parameters that maximize the defined performance index are determined by using the PSO algorithm. An overview of the proposed methodology is shown in Figure 4.1.

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Figure 4.1. Schematic overview of the proposed optimization method

This chapter is organized as follows: sections 4.2 and 4.3 provide a theoretical background of genetic programming and the particle swarm optimization algorithm, respectively. Section 4.4 describes the experimental setup. Section 4.5 presents the results of the experiments. Finally, section 4.6 concludes this chapter. 4.2. Genetic programming Genetic programming (GP) is an evolutionary computation method in which the structures subject to adaptation are those hierarchically organized computer programs whose size and form dynamically change during simulated evolution (Gusel and Brezocnik 2011). A schematic diagram of a GP model, which shows its stages, is presented in Figure 4.2. The aim of GP is to find the member or offspring that best solves the problem (Zadshakoyan and Pourmostaghimi 2013).

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Figure 4.2. Schematic overview of GP model application (Zadshakoyan and Pourmostaghimi 2013)

Figure 4.3 shows an example of a genetic chromosome. A population is made from such chromosomes. During the process of modeling, these chromosomes are subject to some operations. The crossover operation of two parents’ chromosomes consisting of several functions and terminal genes and the mutation operation is shown in Figure 4.4.

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Figure 4.3. An example tree representation of a member corresponding to the equation (2 − x)*(y + 5) (Zadshakoyan and Pourmostaghimi 2013)

In this chapter, for the determination of the relationship between flank wear and cutting parameters in hard finish turning of AISI D2, a genetic equation with genetic programming is developed. The genetic equation for the flank wear characteristics was developed as follows: = ( , ,∆ ,

)

[4.1]

where VBi+1 is the flank wear after time ∆t, VBi is the primary flank wear, v is the cutting speed and f is the feed rate. F is the function that correlates the value of flank wear after ∆t seconds with the primary flank wear VB, the cutting speed v and the feed rate f. Arithmetic functions were selected as follows: = +, −,×, 1⁄ ,

,

,

[4.2]

The evolutionary parameters for the determination of the genetic equation are the number of chromosomes, Ms = 60, and the number of generations, G = 2,000. The genetic operation rates are selected as Pm = 0.044 for mutation and Pc = 0.1 for crossover.

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Figure 4.4. GP method mathematical operations (Zadshakoyan and Pourmostaghimi 2013)

4.3. Particle swarm optimization The PSO algorithm is inspired from the complex social behavior of birds flocking. The basic principle of PSO is to share the place of food between groups of birds. In other words, data about the food place are transmitted from one bird to another. In the PSO algorithm, each answer acts as a “bird” and is called a “particle”. All particles have two

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important indexes: (I) fitness value of the particle, which is calculated based on the defined cost function for the problem, and (II) velocity, which determines the direction of the particle in answer space. The particles freely move in space based on the position of optimum answers or particles. In each iteration of the solving process, the velocity and position of particles are updated by using the following equations: = 1× − =

×

−

+ 2×

× [4.3]

+

[4.4]

where V is the velocity, c1 and c2 are the learning factors chosen between 1 and 4, rand is a random number between 0 and 1, pbest is the best position of the particle until this iteration and gbest is the best position of the particle in the neighborhood until now. In this research, the number of iterations was 1,000, population was 100 and both c1 and c2 were 2. In Figure 4.5, a schematic diagram of the PSO methodology is demonstrated. The optimization process triggers with the initial population. The fitness values for each particle are calculated. The best reached values are assigned for optimum particles. Based on the obtained values, particles update their velocity and position. When the desired number of epochs is reached or any defined target value is achieved, the algorithm will stop and the article with the best position or fitness value is selected as the answer. The movement of particles in answer space in search of an optimal answer is shown in Figure 4.6.

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Figure 4.5. Flow diagram illustrating the particle swarm optimization algorithm

Figure 4.6. Movement of particles in PSO to find an optimal answer

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4.4. Materials and methods 4.4.1. Experimental setup All the experimental tests were performed on a Cincinnati CNC lathe machine and under dry conditions. The workpiece was round bar (60 mm diameter and 250 mm long) AISI D2 alloy steel with hardness 46 HRC. A large-diameter workpiece was used to decrease the variation of cutting speed across the cutting edge. Experiments were performed with different cutting speeds (v), feed rates (f) and cutting times (∆t), while the depth of cut was selected to be constant at 1 mm. The values of cutting speeds were selected as 40, 60 and 80 m/min, and the feed rates were 0.02, 0.04 and 0.06 mm/rev. The TiN-coated carbide insert type TNMG-220408 with grade NC3030 was used. The sampling times for selected cutting parameters are shown in Figure 4.7. The tests lasted until the maximum value of tool flank wear (VBmax) of 0.3 mm was reached. Prior to modeling, all datasets, parameters and measurements were normalized in [0.1—0.9]. To use the data driven from model, denormalization should be performed.

Figure 4.7. Cutting parameters and sampling times regarding each cutting condition

In addition to 108 mentioned experiments, some extra experiments were performed to validate the genetic equation quantitatively. For the measurement of wear parameters, cutting inserts were carefully examined using an optical

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microscope equipped with image processing software. The accuracy of the developed equations was analyzed in terms of two statistical measures. These measures were the root mean square error (RMSE) and friction of variance (R2). 4.4.2. Optimization procedure The first step in any optimization problem is to define a performance index (PI), which completely depends on the characteristics of phenomena or nature of the process being optimized. In the field of machining, many characteristics were considered to be optimized, such as surface roughness, MRR and tool life. Industrially, it is important to optimize some outputs of machining together. For example, in the machining industry, it is desired to obtain the maximum MRR and maximum tool life together. However, the effect of the influential parameters on these outputs is contradictory. Higher values of cutting speed and feed rate increase the MRR but, on the other hand, shorten the tool life. On the contrary, lower values of cutting speed and feed rate cause the tool life to increase, but adversely affect removal rate. Therefore, it is significantly important to define realistic performance indexes that demonstrate the real cutting condition. In this research, a combinatorial performance index was used. The defined performance index is as follows: ×

=

[4.5]

Subject to the following constraints: ≤ ≤

≤

≤ [4.6]

≤ where T is the tool life, α and β are the power of influence for MRR and T, respectively, and both were selected as 0.5,

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vmax and vmin are the maximum and minimum cutting speeds and were selected as 40 m/min and 80 m/min, respectively, fmax and fmin are the maximum and minimum feed rates and were selected as 0.02 mm/rev and 0.06 mm/rev, respectively, depth of cut was selected as 1 mm since the research has been performed for finish hard turning and Ramax was 0.5 μm. As mentioned, tool life ends when tool flank wear (VB) reaches 0.3 mm. Based on the genetic equation which will be obtained for tool flank wear according to equation [4.1], for specified cutting speeds and feed rates, VB can be predicted in various times. It means that the useful remained tool life can be calculated. In this research, for more accurate results, ∆t = 1 was selected. Based on the values of tool life for each cutting couple, PSO tries to find optimum cutting parameters that optimize defined performance index.

Figure 4.8. Schematic diagram of the optimization procedure

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The schematic diagram of the optimization procedure is shown in Figure 4.8. According to experiments, genetic equation is obtained. Based on the results calculated by genetic equation, PSO finds the optimum cutting parameters, which optimize the performance index without any violation of constraints. 4.5. Results 4.5.1. Experimental results The values of tool flank wear versus the time for different cutting parameters are shown in Figure 4.9.

Figure 4.9. Plots of VB with machining time for various cutting conditions

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As shown in Figure 4.9, increasing the feed rate had a slight effect on tool life. By increasing the feed rate, tool life decreased slightly. On the contrary, the effect of cutting speed on tool flank wear growth was strong. Tool life dropped from approximately 150 seconds at v = 40 m/min and f = 0.06 mm/rev to approximately 60 seconds at v = 80 m/min and f = 0.06 mm/rev. 4.5.2. GP results For determining the relationship between tool flank wear and cutting parameters in the turning process of hardened AISI D2, the genetic equation with GP was developed. In this order, 100 tests were used according to the mentioned cutting parameters (Figure 4.7). The independent variables considered were v, f, ∆t and VB. Arithmetic functions were set as described in section 4.4. The best GP model for tool flank wear was obtained as follows: = (2 ×

+

(

.

)× .

×

+

(

∆ ) .

×

− 6.9) + ( × ∆ ) × ( + 5.3753)

[4.7]

Figure 4.10. Variation of fitness functions (a) R2 and (b) RMSE

Figure 4.10 shows the variation of RMSE and R2 between the best flank wear models regarding individual generation

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and experimental results. In early generations, the best models were not as precise as the models generated in later generations. The relatively slow improvement of the best models in later generations (after generation 1800) was due to the unification trends of the population leading to the shortage of new genetic ideas. From equation [4.7] and Figure 4.9, it can be concluded that the cutting speed has the highest impact on the flank wear, whereas the feed rate has the minor effect. This reveals that regulating the cutting speed generates a greater amount of variation in tool flank wear in the turning of hardened AISI D2. The values of input cutting parameters along with the measured and predicted wear values of tests used to validate the genetically obtained equation are shown in Table 4.1. These tests were not presented to the network for training and were only used for the validation of the accuracy and reliability of the obtained genetic equation. Flank wear VBi+1 (mm) Test no. 1 2 3 4 5 6 7 8 9 10 11 12

Cutting speed (m/min) 40 60 60 80 40 50 70 85 40 60 60 80

Feed rate (mm/rev)

Time (sec)

VBi (mm)

Measured

Predicted

0.04 0.02 0.04 0.02 0.035 0.05 0.03 0.06 0.04 0.02 0.06 0.04

20 20 5 5 15 10 15 5 10 5 20 10

0.269 0.245 0.108 0.206 0.232 0.091 0.149 0.092 0.126 0.08 0.209 0.081

0.288 0.314 0.137 0.221 0.271 0.132 0.19 0.126 0.143 0.099 0.25 0.131

0.2958 0.2841 0.1513 0.2476 0.2581 0.1158 0.1879 0.1132 0.1365 0.1033 0.2435 0.156

Table 4.1. Experimental validation tests

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The values of RMSE and R2 for selected genetic equation were obtained by described fitness functions as given in Table 4.2. The results presented in Table 4.2 allow us to conclude that the proposed genetic equation has an acceptable accuracy and reliability. R2

RMSE

Training

0.9902

0.0102

Validation

0.9473

0.0163

Table 4.2. Fitness values of the obtained genetic equation

Similarly, the results of this chapter showed the success of the method employed for estimating tool wear. Besides, after the learning process, any model studied herein has the capability of being easily implemented using elementary algebraic operations. 4.5.3. Optimization results Based on the genetically obtained equation [4.7], the PSO algorithm calculates the optimum cutting speed and the feed rate in order to obtain the optimum value for the performance index. Optimum cutting parameters are given in Table 4.3. v 67.5 m/mm

f 0.0425 mm/rev

MRR 47.81 mm3/sec

T 93 sec

PI 66.67

Ra 0.08 µm

Table 4.3. Optimum cutting parameters and resultant outputs

From Table 4.3, it is evident that in the mentioned cutting parameters, the value of PI is optimum. Moreover, the tool has worked for 93 seconds during the cutting process. The surface roughness of the workpiece was measured and recorded as 0.48 μm, which is in the permissible range.

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4.6. Conclusion In this chapter, using GP methodology, a new model for tool wear monitoring the hard turning of AISI D2 in terms of cutting parameters and cutting duration was developed. Then, the optimum cutting parameters to optimize a defined performance index was calculated. The accuracy of the developed model was evaluated by statistical measures. The results obtained from the proposed genetic programming approach prove its effectiveness. Furthermore, the implication of the encouraging results obtained from the present approach is that such an approach can be applied to an online turning system for automated machining processes. Integration of the proposed methodology with an intelligent manufacturing system could lead to a reduction in machining costs and production time and an improvement of product quality. The particle swarm optimization algorithm tends to converge to an optimum solution as quickly as possible with acceptable accuracy. By considering the overall results obtained from the experiments, it can be concluded that using evolutionary algorithms in modeling and optimization could have promising applications in the field of machining processes. The future works will include the application of the proposed method for turning of different materials, investigating the optimal evolutionary parameters of genetic programming to increase the accuracy of the obtained models and using the GP method with other soft computing techniques to enhance its applicability. 4.7. References Adnan, M.M., Sarkheyli, A., Zain, A.M., and Haron, H. (2015). Fuzzy logic for modeling machining process: A review. Artificial Intelligence Review, 43, 345—379.

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Agapiou, J. (1992). Optimization of multistage machining systems, Part 1: Mathematical solution. Journal of Engineering for Industry, 114, 524—531. Asokan, P., Saravanan, R. and Vijayakumar, K. (2003). Machining parameters optimisation for turning cylindrical stock into a continuous finished profile using genetic algorithm (GA) and simulated annealing (SA). The International Journal of Advanced Manufacturing Technology, 21, 1—9. Azmi, A. (2015). Monitoring of tool wear using measured machining forces and neuro-fuzzy modelling approaches during machining of GFRP composites. Advances in Engineering Software, 82, 53—64. Benkedjouh, T., Medjaher, K., Zerhouni, N. and Rechak, S. (2015). Health assessment and life prediction of cutting tools based on support vector regression. Journal of Intelligent Manufacturing, 26, 213—223. Bensouilah, H., Aouici, H., Meddour, I., Yallese, M.A., Mabrouki, T. and Girardin, F. (2016). Performance of coated and uncoated mixed ceramic tools in hard turning process. Measurement, 82, 1—18. Chen, M.-C. and Tsai, D.-M. (1996). A simulated annealing approach for optimization of multi-pass turning operations. International Journal of Production Research, 34, 2803—2825. Cus, F. and Balic, J. (2003). Optimization of cutting process by GA approach. Robotics and Computer-Integrated Manufacturing, 19, 113—121. Garg, A., Tai, K. and Savalani, M. (2014). Formulation of bead width model of an SLM prototype using modified multi-gene genetic programming approach. The International Journal of Advanced Manufacturing Technology, 73, 375—388. Gopal, A.V. and Rao, P.V. (2003). Selection of optimum conditions for maximum material removal rate with surface finish and damage as constraints in SiC grinding. International Journal of Machine Tools and Manufacture, 43, 1327—1336. Gusel, L. and Brezocnik, M. (2011). Application of genetic programming for modelling of material characteristics. Expert Systems with Applications, 38, 15014—15019.

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Hildebrandt, T., Heger, J. and Scholz-Reiter, B. (2010). Towards improved dispatching rules for complex shop floor scenarios: A genetic programming approach. Paper presented at the Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, 257–264, ACM, 2010. Jamali, A., Khaleghi, E., Gholaminezhad, I., Nariman-Zadeh, N., Gholaminia, B. and Jamal-Omidi, A. (2017). Multi-objective genetic programming approach for robust modeling of complex manufacturing processes having probabilistic uncertainty in experimental data. Journal of Intelligent Manufacturing, 28, 149—163. Li-Ping, Z., Huan-Jun, Y. and Shang-Xu, H. (2005). Optimal choice of parameters for particle swarm optimization. Journal of Zhejiang University-Science A, 6, 528—534. Mehrabad, V.Z. and Pourmostaghimi, V. (2017). Tool wear modeling in drilling process of AISI1020 and AISI8620 using genetic programming. International Journal of Advanced Design and Manufacturing Technology, 10. Mukherjee, I. and Ray, P.K. (2006). A review of optimization techniques in metal cutting processes. Computers & Industrial Engineering, 50, 15—34. Nakai, M.E., Aguiar, P.R., Guillardi, H., Bianchi, E.C., Spatti, D.H. and D’Addona, D.M. (2015). Evaluation of neural models applied to the estimation of tool wear in the grinding of advanced ceramics. Expert Systems with Applications, 42, 7026—7035. Özel, T. and Karpat, Y. (2005). Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks. International Journal of Machine Tools and Manufacture, 45, 467—479. Raja, S.B. and Baskar, N. (2010). Optimization techniques for machining operations: A retrospective research based on various mathematical models. The International Journal of Advanced Manufacturing Technology, 48, 1075—1090.

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Reddy, S.B., Shunmugam, M. and Narendran, T. (1998). Optimal sub-division of the depth of cut to achieve minimum production cost in multi-pass turning using a genetic algorithm. Journal of Materials Processing Technology, 79, 101—108. Saini, S., Ahuja, I.S. and Sharma, V.S. (2012). Residual stresses, surface roughness, and tool wear in hard turning: A comprehensive review. Materials and Manufacturing Processes, 27, 583—598. Shin, Y. and Joo, Y. (1992). Optimization of machining conditions with practical constraints. The International Journal of Production Research, 30, 2907—2919. Wang, X., Wang, W., Huang, Y., Nguyen, N. and Krishnakumar, K. (2008). Design of neural network-based estimator for tool wear modeling in hard turning. Journal of Intelligent Manufacturing, 19, 383—396. Wen, X.M., Tay, A.A.O. and Nee, A.Y.C. (1992). Micro-computed-based optimization of the surface grinding process. Journal of Materials Processing Technology, 29, 75–90. Zadshakoyan, M. and Pourmostaghimi, V. (2013). Genetic equation for the prediction of tool—chip contact length in orthogonal cutting. Engineering Applications of Artificial Intelligence, 26, 1725—1730. Zadshakoyan, M. and Pourmostaghimi, V. (2015). Cutting tool crater wear measurement in turning using chip geometry and genetic programming. International Journal of Applied Metaheuristic Computing (IJAMC), 6, 47—60.

5 Development of a Multi-objective Salp Swarm Algorithm for Benchmark Functions and Real-world Problems

The salp swarm algorithm is a recent optimization technique. This algorithm is a swarm-based nature-inspired algorithm, which emulates and scientifically models the conduct of salp chains in the remote ocean. The proposed calculation can be used for managing linear and nonlinear optimization problems. The salp swarm algorithm (SSA) and the multi-target salp swarm algorithm (MSSA) have made progress towards various benchmark test capacities to aid and demonstrate the execution of the algorithm. Results from the SSA are compared with genuine esteems of the test functions, and results from the MSSA are compared with those of other multi-objective algorithms. For obtaining solutions of constrained test functions, the constraints handling technique is employed to transform the constrained optimization problem into an unconstrained optimization problem for which the interior penalty method is used. The algorithm is successfully applied to a cantilever beam, which is the practical designing problem, and compared with the results of NSGA-II. The obtained results converge and are nearer to an optimum solution in comparison with NSGA-II.

5.1. Introduction Optimization is known as the way to deal with discovering ideal course of action under given conditions. In design problems, engineers need to take a few administrative and specific decisions at different stages. A definitive objective of Chapter written by Sushant P. MHATUGADE, Ganesh M. KAKANDIKAR, Omkar K. KULKARNI and Vilas M. NANDEDKAR.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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every such choice is either to limit the exertion required or to amplify the coveted advantage. Since the exertion required or the advantage needed in any down-to-earth circumstance can be communicated as an element of certain choice factors, optimization can be characterized as the way towards finding the conditions that give the greatest or least estimation of a capacity (Rao 2009). Presently, metaheuristic strategies are impressively applied for optimization in engineering problems. Three reasons that make them applicable are: flexibility, avoidance of local optima and gradient-free mechanisms. The first two advantages begin from the undeniable reality that metaheuristics take care of optimization problem-searching by exclusively converging from random to optimum. In other words, an optimization problem is considered as a black box in metaheuristics techniques. In this way, the derivative of the search space is not required. This makes them to a great degree adaptable for taking care of a diverse range of problems. Local optima can be kept away when tackling problems that ordinarily have various local optima (Mirjalili et al. 2017a). Because of these advantages, the metaheuristic strategy is applied in various industries and branches of science. These methodologies are primarily distinguished into two prevalent classes: — evolutionary; — swarm intelligence techniques. Evolutionary algorithms are based on processes of evolution in nature. Optimization problems including many typically conflicting objectives can be proficiently solved by evolutionary algorithms (EA) (Back 1996). There are a large number of evolutionary methodologies produced for multi-objective optimization, which helps in discovering multiple solutions in the meantime amid a single run

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103

(Zitzler and Thiele 1999). A highly regarded algorithm in this classification is the genetic algorithm (GA) (Bhoskar et al. 2015), which mimics the ideas of the Darwinian theory of evolution (Goldberg and Holland 1988). The intelligence of swarms, schools, groups or flocks of a living being of nature is the core of the swarm intelligence technique (Blum and Li 2008). Aggregate execution of a gathering of a living being is the essential establishment for these algorithms. Independent intelligence of individuals in swarms is amassed to frame the swarm innovation. There are homogeneous and additionally heterogeneous individuals in the intelligent swarm. Due to their contrasting surroundings, individuals can turn into a heterogeneous swarm as they learn totally unique assignments and create distinctive objectives, although they start as homogeneous individuals. Delegate swarms have been used by research scholars for computer demonstrating technique and as an instrument to study complex systems (Kulkarni et al. 2015). In a flock of birds, each bird tries to find another bird to fly with and then flies at a marginally higher elevation to decrease drag. Alternative assortments of swarm simulations exhibit unlikely emergent practices that are sums of simple individual practices that form complicated and sometimes unexpected practices once aggregated (Hinchey et al. 2007). Ant colony optimization and particle swarm optimization are highly regarded algorithms demonstrating this technique. The literature distinguishes optimization algorithms into two essential classes: — deterministic; — stochastic. The deterministic technique finds a practically identical response for a given problem. Reliability is the fundamental

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advantage of such methodologies since they discover an answer in each run. Since the deterministic algorithms usually do not have randomization in behaviors when solving optimization problems, local optima stagnation is created. Stochastic strategies profit by random administrators. This helps to find entirely different solutions in spite of the fact that the starting point stays unaltered and subsequently makes stochastic algorithms less reliable compared to the deterministic approaches. Randomized direction of these calculations contributes to neighborhood optima evasion. The dependability of stochastic strategies can be enhanced by calibrating and expanding the quantity of runs. Such strategies are separated into individualist and aggregate calculations. In the primary technique, the calculation starts and performs optimization with one solution. It is arbitrarily balanced and upgraded for a pre-defined number of steps or satisfaction of an end criterion. The upside of this gathering is the low computational cost and, furthermore, the requirement for a small number of function assessments. Collective techniques start with various arbitrary solutions and drive them over the course of several iterations towards the global optimum. This is especially important for local optima stagnation on account of multiple solutions. The usage of these techniques is regularly found in science as well as industry. One of the essential reasons is the high limit in the maintenance of a key separation from local solutions; further reasons are flexibility and ease. Multi-objective methodologies: — a priori; — a posteriori.

problems

can

be

handled

by

two

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105

In the first method, the multi-objective problem is transformed to a single-objective one by gathering the objectives. This is usually done using a set of weights that are occasionally delineated by a scholar and which dictate the importance of each objective. After modification of the objective, a solitary objective streamlining agent searches for the best solution. A disadvantage of this method is that the Pareto optimal set will be made by rerunning the algorithm and changing the weights (Parsopoulos and Vrahatis 2002). The multi-objective formulation is maintained with

a posteriori technique. Here, we can obtain the optimum Pareto solution in a single run (Deb 2012). There are no weights to be laid out by specialists. In contrast to a priori strategies, many alternative solutions can be obtained that assist decision-makers. Disadvantage include the requirements for addressing multi-objectives and the special mechanisms to decide the Pareto optimal set and front, which make it difficult and computationally costlier. The salp swarm algorithm is analyzed in this chapter for various test functions and problems. 5.2. Salp swarm algorithm Salps have a barrel-shaped body. Impetus happens by drawing water through the body (Madin 1990). The research for this creature is at a very basic level, as their living surroundings are incredibly difficult to access and investigate and they cannot be kept them in the laboratory. The most fascinating behavior of salps is their swarming conduct. The primary reason for this conduct is not clear yet; however, analysts are confident that this works in favour of the situation, accomplishing better movement using expedient coordinated changes and chasing (Anderson and Bone 1980).

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Salp chains contain a leader and a follower. The leader guides the swarm and the followers tail each other. Similarly, it is expected that there is a sustenance source implied as F inside the chase zone as the swarm’s goal. The leader updates position using the following equation: = + ( = − ((

− −

)

+ +

)

< 0.5 ≥ 0.5

[5.1]

where: = position of the leader in the

dimension;

= position of the food source in the = upper bound of the = lower bound of the ,

and

dimension;

dimension; dimension;

are random numbers.

is the crucial parameter in this The coefficient algorithm because it adjusts exploration and exploitation, characterized as follows: =2

( / )

[5.2]

where:

l = current iteration; l = maximum number of iterations. and are random numbers reliably generated in the interval [0, 1]. The accompanying condition is used to refresh the position of the followers: = where:

i ≥ 2;

+

[5.3]

Development of Multi-Objective Salp Swarm Algorithm

= position of the

follower salp in the

107

dimension;

T = time; = initial speed; = =

; −

Considering follows: = (

= 0, this condition can be communicated as +

)

[5.4]

where:

i ≥ 2; = position of the

follower salp in the

dimension.

Equations [5.1] and [5.4] simulate the salp chain. 5.2.1. Single-objective salp swarm algorithm (SSA) The mathematical model for recreating salp chains cannot be specifically used to tackle optimization problems. In other words, it is necessary to marginally change the model to make it appropriate to optimization problems. A single-objective optimizer finds the global optimum. In the event that the food source gets replaced by the global optimum, the salp chain naturally moves towards it. In any case, the problem is that the global optimum of optimization problems is obscure. It is accepted that the best solution acquired so far is the global optimum and it is expected that the food source be pursued by the salp chain.

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Figure 5.1 presents the pseudo-code of the SSA. In this figure, the SSA starts approximating the global optimum by initiating several salps with different random positions. It then finds the salp with the best fitness and appoints the position of the best salp to the variable F as the source food to be pursued by the salp chain. In the interim, the coefficient c is refreshed using equation [5.2]. For each dimension, the position of leading salp is refreshed using equation [5.1] and the salp chain is refreshed by equation [5.4]. In the event that any of the salps goes outside the pursuit space, it will be brought back on the boundaries. Initialize the salp population (i = 1, 2, ..., n) considering ub and lb while(end condition is not satisfied) Calculate the fitness of each search agent (salp) F = the best search agent Update by Eq. [5.2] foreach salp ( ) if(i==1) Update the position of the leading salp by Eq. [5.1] else Update the position of the follower salp by Eq. [5.4] end end Amend the salps based on the upper and lower bounds of variables end return F

Figure 5.1. Pseudo-code of the SSA (Mirjalili et al. 2017a)

All the above steps except initialization are iteratively executed until the fulfillment of an end criterion. It ought to be noted that the food source will be updated during optimization on the grounds that the salp chain is probably going to locate a superior solution by exploring and exploiting the space around it. The salp chain can possibly move towards the global optimum that progresses through the span of emphases. To see how the proposed salp chain model and the SSA are reasonable in dealing with

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optimization problems, some remarks can be summarized as follows: — SSA retains the best solution achieved up to the current point and relegates it to the food source variable, so it never gets lost regardless of whether the entire population breaks down; — SSA refreshes the situation of the main salp with respect to the sustenance source, which is the best arrangement achieved up until this point; — SSA refreshes the situation of supporter salps concerning each other, so they logically move towards the main salp; — slow development of adherent salps keeps the SSA from effortlessly stagnating in nearby optima; — parameter (c1) is reduced adaptively, so the SSA first investigates the hunt space and then traverses it; — SSA has just parameter (c );

a

single

fundamental

controlling

— SSA is straightforward and simple to actualize. 5.2.2. Multi-objective salp swarm algorithm (MSSA) The solution of a multi-objective problem is obtained in the form of the Pareto optimal. In any case, this algorithm cannot take care of multi-objective problems primarily because of the following two reasons: — SSA retains just one solution as the best solution, so it cannot store multiple solutions as the best solutions; — SSA refreshes the food source with the best solution obtained so far in every cycle, but there is no single best solution for multi-objective problems. This problem is handled by furnishing the SSA with a repository of food sources. This repository keeps up the best

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non-dominated solutions obtained so far amid optimization. Each salp looks at the repository using Pareto dominance operators. In the event that a salp dominates a solution in the repository, it ought to be swapped. On the off chance that a salp dominates a set of solutions in the repository, they all ought to be expelled from the repository and the salp ought to be added to the repository. In the event that no less than one of the repository residents dominates a salp in the new population, it ought to be disposed of quickly. Salp is nondominated in correlation with all repository residents; it must be added to the chronicle. These fundamentals can guarantee that the repository dependably stores the non-dominated solutions acquired so far by the algorithm. There is a unique situation where the repository turns out to be full and a salp is non-dominated in comparison with the repository residents. Obviously, the most effortless move is to randomly erase one of the solutions in the archive and supplant it with the non-dominated salp. A better way is to swap out one of the practically identical non-dominated solutions in the repository. Since a posteriori multi-objective algorithms ought to have the capacity to discover uniformly distributed Pareto optimal solutions, the best candidate to expel from the archive is the one from a populated locale. This technique enhances the circulation of the archive residents through the span of cycles. To find the non-dominated solutions within the populated neighborhood, the number of neighboring solutions with a particularly notable detachment is counted and acknowledged. This separation is characterized by d = (max-min)/repository size where max and min are two vectors for eliminating the most extreme and least extreme for each objective individually. The repository with one solution in each portion is the best

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case. In the wake of delegating a rank to every repository inhabitant in view of the quantity of neighboring solutions, a roulette wheel is used to pick one of them. Figure 5.2 presents a case of this repository update system. Note that the area ought to be characterized for each of the solutions; however, just four of the non-dominated solutions are explored in this figure. As mentioned above, the second problem when tackling multi-objective problems using the SSA is the choice of the food source in light of the fact that there is more than one best solution in a multi-objective pursuit space. Once more, the food source can be randomly picked from the repository. In any case, a more fitting path is to choose it from a set of non-dominated solutions within the smallest swarmed neighborhood. This should be possible using a similar ranking procedure and roulette wheel choice as that used by the repository maintenance administrator. In the archive maintenance, the solutions with the higher rank will probably be picked. In Figure 5.2, for example, the non-dominated solutions in the center with no neighboring solution have the highest likelihood to be picked as the food source. All things considered, the pseudo-code of the multi-objective salp swarm algorithm (MSSA) is shown in Figure 5.3.

Figure 5.2. Update mechanism of the repository when it is full (Mirjalili et al. 2017a)

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Initialize the salp population (i = 1, 2, ..., n) considering ub and lb while(end criterion is not met) Calculate the fitness of each search agent (salp) Determine the non-dominated salps Update the repository considering the obtained non-dominated salps ifthe repository becomes full Call the repository maintenance procedure to remove one repository resident Add the non-dominated salp to the repository end Choose a source of food from repository: F=SelectFood(repository) Update using Eq. [5.2] foreach salp ( ) if(i==1) Update the position of the leading salp using Eq. [5.1] else Update the position of the follower salp using Eq. [5.1] end end Amend the salps based on the upper and lower bounds of variables end return repository Figure 5.3. Pseudo-code of the MSSA (Mirjalili et al. 2017a)

Figure 5.3 demonstrates that the MSSA initially introduces the population of salps with regard to the upper and lower bounds of variables. In case the store is full, the vault maintenance is rushed to erase the solutions within the swarm neighborhood. In the wake of expelling enough archive inhabitants, the non-dominated salps can be added to the archive. Subsequent to refreshing the repository, a food source is chosen from the non-dominated solutions in the repository within the minimum swarmed neighborhood. Essential to the archive maintenance, this is finished by ranking the solutions and using a roulette wheel. The following stage is to refresh ( ) using equation [5.2] and refresh the position of leading/follower salps using either equation [5.1] or [5.4]. During the position refreshing

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process, if a salp exceeds the boundaries it will be fetched back into the boundary. We can summarize the advantages of MSSA as follows: — the non-dominated solutions obtained so far are put away in a repository, so they never get lost even though the entire population deteriorates; — the solutions from the swarm neighborhood are disposed of each time the repository maintenance is called, which brings about enhanced coverage of non-dominated solutions’ overall objectives; — a food source looks to over the summary of non-dominated solutions with the minimal number of neighboring solutions, which enhances the coverage of solutions found; — MSSA acquires the operators of the SSA because of the use of a comparable population division (leading and follower salps) and a position refreshing procedure; — MSSA has just two fundamental controlling parameters ( and archive size); — MSSA is straightforward and simple to actualize. 5.3. Constraint handling techniques In these types of problems, the arrangement must fulfill a few conditions known as constraints. The following are the types of constraints: equality constraints, inequality constraints and whole number constraints. The set that fulfills all constraints in the issue is known as the feasible set. It is difficult to take care of programming with both equality and inequality constraints. This is often a direct result of the fact that a solution methodology must ensure the reduction of the objective function as well as the feasibility of solutions created (Kulkarni et al. 2016). Such necessities cause challenges for discovering optimum

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solutions. To streamline an optimization methodology, it is necessary to change an equality to inequality, a constrained problem to an unconstrained problem and a nonlinear programming problem to a linear programming problem (Liu et al. 2003). We settled on the system of interior penalties that comes underneath dual methods. Inside the interior penalty strategy, the penalty term can even be taken as the logarithm of the constraint functions, known as the logarithmic interior penalty method. Let Min f(x) s.t. g (x) ≤ 0, j = 1,2, … , lx ∈ S ⊂ R

[5.5]

where S could be a set of real or integer numbers. Then, the logarithmic interior penalty function (Hinchey et al. 2007) is given by P(x, τ ) = f(x) − τ ∑

ln −g (x)

[5.6]

By using this logarithmic interior penalty method, all constrained problems are converted to unconstrained problems and nonlinear programming problems to linear programming problems. 5.4. Experimental results and discussion In this discussion, we describe the outcomes acquired from a set of investigations for assessing the SSA and MSSA. The aim of the first set of experiments was to test the algorithms for single-objective optimization using unconstrained as well as constrained testing functions. In the second set of trials, the objective was to assess the algorithms for multi-objective optimization problems using unconstrained and constrained functions. In all

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examinations, the objective was to perceive how the proposed algorithm performs in comparison with unique outcomes. For settling the test functions, the algorithm was coded in MATLAB (R2017a) on a Windows 10 platform with I53210M Processor, 2.5 GHz processor speed and 4 GB RAM. The objective of this chapter is to assess the SSA and MSSA and compare them with actual outcomes. In this analysis, 13 test functions and one practical application were used; these test functions are the outstanding test suite. The results of these tests and practical outcomes are outlined in result tables. 5.4.1. Single-objective unconstrained test functions The following single-objective unconstrained functions were implemented with the SSA:

test

1) Booth function (Yang 2014) Definition: ( ) = (

− 7) + (2

+2

Search domain: −10 ≤

+

− 5)

[5.7]

≤ 10

2) Sphere function (Yang 2014) Definition: ( ) = ∑

[5.8]

This function consists of n variables, but we have tested it for n = 10. Search domain: 0 ≤

≤ 10

3) Easom function (Yang 2014) Definition: ( ) = − ( − ) ]

( )

( )

[−(

− ) − [5.9]

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Search domain: −100 ≤

≤ 100

4) Branin function (Yang 2014) Definition: ( ) = [( 10(1 −

)

−

.

) +

− 6] +

( ) + 10

Search domain: −5 ≤

≤ 10

0≤

≤ 15

[5.10]

Figure 5.4. Convergence for unconstrained test functions

To unravel the test functions, 1,000 generations alongside 50 search agents were used. Each test function was settled 30 times to produce the optimum outcomes. The best solution among all outcomes was picked as the last optimum solution. Figure 5.4 indicates convergence curves

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for unconstrained test functions. The curves demonstrate the dropping conduct, and prove that the SSA upgrades the underlying random population and enhances the precision of the approximated optimum throughout the search. The test functions were initially solved by the SSA, and the solution obtained from this algorithm is compared with actual results (Yang 2014), which are given in Table 5.1. From the table, it can be observed that the solutions obtained by the SSA are consistent with the actual results of test functions. Results prove that the SSA gives values closer to the actual results, and it can be noted that the performance of the SSA towards solving single-objective unconstrained problems is better. Test function

Actual results (Yang 2014) ∗

SSA results

( ∗)

( ∗)

∗

Booth

(1,3)

0

(1,3)

2.654e-15

Sphere

(0,…,0)

0

(0,…,0)

0

Easom

( , )

−1

(3.14,3.14)

−1

Branin

(− ,12.27), ( ,2.27), (9.42,2.47)

0.39

(−3.14,12.27), (3.14,2.27), (9.42,2.47)

0.39

Table 5.1. Results of single-objective unconstrained test functions

5.4.2. Single-objective constrained test functions The following single-objective constrained test functions were implemented with the SSA: 1) Rosenbrock function constrained with a cubic and a line (Simionescu and Beale 2002, MathWorks n.d.) Definition: ( ) = (1 − Subject to (

− 1) −

) + 100( +1≤0

−

)

[5.11]

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Optimization for Engineering Problems

+

−2≤0

[5.12]

Search domain: −1.5 ≤

≤ 1.5

−0.5 ≤

≤ 2.5

2) Rosenbrock function constrained (MathWorks n.d., Mishra 2006) Definition: ( ) = (1 −

) + 100(

−

to )

a

disk [5.13]

Subject to +

≤2

[5.14]

Search domain: −1.5 ≤

≤ 1.5

−1.5 ≤

≤ 1.5

3) Bird function constrained (Deb 2001) Definition: ( ) = ( ) ( ) ] +( − ) ( ) [(

)

+ [5.15]

Subject to (

+ 5) + (

+ 5) < 25

[5.16]

Search domain: −10 ≤

≤0

−6.5 ≤

≤0

Figure 5.5 shows the convergence curve for constrained test functions. Salps tend to look at the actual zone of the interest area around the global optima within the long run. This graph demonstrates the objective estimation of the best solutions acquired up until now (target) in each iteration. These curves indicate that the SSA wholly balances exploration and exploitation to drive the salps near to the global optimum.

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Figure 5.5. Convergence for constrained test functions

In Table 5.2, the results of single-objective constrained test functions are compared. To solve the constrained optimization problem in the SSA, the constraints handling technique is required. Here, the interior penalty technique is applied. By taking advantage of this technique, the problem is converted into an unconstrained problem and then solved. The results gained from the constrained test functions by the SSA are then compared with the actual results of test functions (Simionescu and Beale 2002, Mishra 2006, Deb 2001). From the comparison, we can definitely say that the results given by the SSA are very much near to the actual solution and can be treated as the optimum of the problem.

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Test function

Actual results (Simionescu and Beale 2002, Mishra 2006, Deb 2001)

SSA results

( ∗)

∗

( ∗)

∗

Rosenbrock function 1

(1,1)

0

(1,1)

3.08e-15

Rosenbrock function 2

(1,1)

0

(1,1)

8.22e-16

Bird function — constrained

(−3.13, −1.58)

−106.76

(−3.13,−1.58)

−106.76

Table 5.2. Result of single-objective constrained test functions

5.4.3. Multi-objective unconstrained test functions The following multi-objective unconstrained test functions were implemented with the MSSA: 1) Schaffer function N. 1 (Zhang et al. 2003) Definition:

( )=

( ) = ( − 2)

[5.17]

Search domain: −10 ≤

≤ 10

2) Fonseca—Fleming function (Zhang et al. 2003) Definition:

( ) = 1 − exp [− ∑

( ) = 1 − exp [− ∑ Search domain: −4 ≤

(

+

√

≤4

) ]

(

−

√

) ] [5.18]

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3) Kursawe function (Zhang et al. 2003) Definition: ( )=∑

( )=∑ [| |

.

]+5

Search domain: −5 ≤

[−10 (

( −0.2 )]

+

)] [5.19]

≤5

Figure 5.6. Pareto optimal solutions by the MSSA, MOPSO and MOGOA with unconstrained test functions. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

To comprehend the test functions, 100 iterations alongside 50 search agents were used. Each test was

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implemented 20 times to deliver the optimal results. The best solution among all results was picked as the final optimum solution. Figure 5.6 gives the Pareto fronts obtained from different algorithms for multi-objective unconstrained test functions. It shows that the MSSA achieved results better than all the other algorithms in most cases. The MSSA achieved the best results with all testing functions, and it achieved the second-best results with the Kursawe function. Furthermore, the MOPSO (Mirjalili et al. 2017b) and MOGOA (Kulkarni and Kulkarni 2018) obtained the second- and third-best solutions, respectively. As shown in Figure 5.6, the MOGOA demonstrates the most notably ineffectual convergence, which is not in concurrence with the acquired outcomes. In addition, the MSSA and MOPSO give a decent convergence towards all obvious Pareto-optimal fronts. To conclude, the MSSA accomplishes the best outcomes and, in addition, demonstrates better convergence towards all the Pareto optimal fronts with the exception of the Kursawe function. 5.4.4. Multi-objective constrained test functions The following multi-objective constrained test functions were implemented with the MSSA: 1) Constr-Ex Function (Zhang et al. 2003) Definition:

( )=

( )= Subject to −

+9

[5.20] +9 ≥1

≥6 [5.21]

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123

This function consists of two variables, and the Pareto optimal front for this function is convex. It has variable upper and lower bounds as given below. Search domain: 0.1 ≤

≤1

0≤

≤5

2) Binh and Korn function (Zhang et al. 2003) ( )=4

Definition: ( )=(

− 5) + (

Subject to ( (

+4 − 5)

− 5) +

− 8) + (

[5.22]

≤ 25

+ 3) ≥ 7.7

Search domain: 0 ≤

≤5

0≤

≤3

[5.23]

3) TNK function (Zhang et al. 2003) Definition:

( )=

( )= Subject to (

[5.24] +

− 0.5) + (

− 1 − 0.1 − 0.5) ≤ 0.5

Search domain: 0 ≤

≤

0≤

≤

(16

)≥0 [5.25]

When performing the test functions, 100 generations alongside 50 search agents were used with a repository size of 100. Each test was performed 10 times to create the factual outcomes. The best solution among all outcomes was picked as the definite optimum solution.

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Figure 5.7. Pareto optimal solutions by the MSSA, MOPSO and MOGOA with constrained test functions. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

Figure 5.7 shows the Pareto fronts acquired from various algorithms for the multi-objective constrained test functions given above. As shown in the figure, the constrained test functions have altogether different Pareto fronts correlated with the unconstrained test functions. It is observed that the MSSA performs better than all the other algorithms in most cases and it achieves the second-best results with the BINH and KORN function.

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In addition, MOPSO and MOGOA acquired the secondand third-best solutions, respectively. The CONSTR function has a curved front attached to a linear front. As shown, the MSSA and MOPSO managed to approximate the CONSTR function successfully. Moreover, the TNK function has a front the same as two perpendicular lines joined together. As shown in Figure 5.7, the MSSA and MOPSO give a decent convergence towards a large portion of the genuine Pareto-optimal fronts. By and large, the MSSA obtained the best outcomes and an aggressive convergence towards all the genuine Pareto optimal fronts compared with MOPSO and MOGOA. 5.4.5. Real-world application — Cantilever Beam Problem (Zhang et al. 2003). Let us consider a cantilever design problem with two choice factors: diameter ( ) and length (l). The shaft needs to carry an end load P. Let us opt for two clashing design objectives: minimization of weight and minimization of end deflection . The primary objective will depend on an optimum solution having smaller dimensions of d and l, so the general weight of the shaft is minimal. Since the dimensions are small, the bar will be adequately rigid and the end deflection of the bar will be huge. Then again, if the pillar is limited for end deflection, the dimensions of the shaft will be huge, in this manner making the weight of the bar vast. For this design, we must think about two constraints: is less than the the developed maximum stress admissible strength and the end deflection is smaller . Taking into account the than the indicated limit

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above considerations, the accompanying optimization problem is planned as follows: Minimize

( , )=

Minimize

( , )=

=

two-objective

[5.26]

≤

Subject to ≤

[5.27] 10 200

≤

≤ 50

≤ ≤ 1000

where =

32

= 7800

⁄

= 1 = 207

= 300



= 5

There are numerous solutions for diversely trading-off between two objectives. For certain pairs of solutions, it is observed that one solution is better than other in both objectives. For certain other pairs, it can be observed that one solution is better than the other in one objective, but it is worse in the second objective. Keeping in mind the end goal of building up which solution(s) is/are optimal concerning the two objectives,

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let us hand-pick a couple of solutions from the search space. Figure 5.8 shows Pareto optimal solutions from different algorithms. From the MSSA, two of these solutions (A, D) are presented in Table 5.3 and compared with NSGA II results. Solution A gives minimum weight, while solution D gives minimum deflection. It can be seen that solution A has least weight, but has a larger end-deflection than solution D. Hence, neither of these two solutions can be said to be better than the other with respect to both objectives.

Figure 5.8. Pareto optimal solutions by the MSSA, MOPSO and MOGOA for a cantilever beam problem. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

Solution

NSGA II (Zhang et al. 2003)

MSSA

Weight (kg) Deflection (mm) Weight (kg) Deflection (mm) A

0.44

2.04

0.47074

1.7799

D

3.06

0.04

2.5445

0.0536

Table 5.3. Results of cantilever beam problem

5.5. Conclusion This work examined the optimization algorithm known as the salp swarm algorithm. The SSA and MSSA were checked and validated for the 13 optimization test functions, both single objective and multi-objective. Constrained and unconstrained optimization test functions were used to validate the results obtained from the SSA and MSSA.

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Furthermore, the MSSA was used for the validation of the results of a real-world application, i.e. a cantilever beam. A mathematical model that relies on the swarming behavior of salps for locomotion in deep ocean was studied. This mathematical model simulates the foraging of a salp chain in search of a food source. The food source is nothing but our optimum solution. The mathematical model has a coefficient that balances exploration and exploitation. Finally, the most effective solution given by the swarm is considered the optimum solution of the optimization problem. In order to validate the performance of the SSA and MSSA, different test functions were used in this chapter. The test functions were solved by using the SSA and MSSA. The results obtained by the SSA were observed and compared with actual results, and the results obtained by the MSSA were compared with similar algorithms (MOPSO, MOGOA) to ascertain the performance of the algorithm. The findings of our experiments evidenced that the results obtained from the SSA are precisely or nearly the same as the actual results. The MSSA was able to find the optimum Pareto front (PF) and provide superior quality solutions in comparison with a variety of alternative algorithms such as multi-objective particle swarm optimization (MOPSO) and multi-objective grasshopper optimization algorithm (MOGOA). In general, according to the reported results, the MSSA offers competitive solutions compared with the other multi-objective algorithms and it offers a wider range of non-dominated solutions. 5.6. References Anderson, P.A.V. and Bone, Q. (1980). Communication between individuals in salp chains. II. Physiology. Proceedings of the Royal Society of London. Series B. Biological Sciences, 210(1181), The Royal Society.

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Back, T. (1996). Evolutionary Algorithms in Theory and Practice:

Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, New York, NY. Bhoskar, T., Kulkarni, O.K., Kulkarni, N.K., Patekar, S.L., Kakandikar, G.M., and Nandedkar, V.M. (2015). Genetic algorithm and its applications to mechanical engineering: A review. Materials Today: Proceedings, 2(4—5), 2624—2630. Blum, C. and Li, X. (2008). Swarm intelligence in optimization. In Swarm Intelligence, pp. 43—85. Springer, Berlin, Heidelberg. Deb, K. (2001). Multi-objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, New York, NY. Deb, K. (2012). Advances in evolutionary multi-objective optimization. In International Symposium on Search Based Software Engineering. Springer, Berlin, Heidelberg. Goldberg, D.E. and Holland, J.H. (1988). Genetic algorithms and machine learning. Machine Learning, 3(2—3), 95-99. Hinchey, M.G., Sterritt, R., and Rouff C. (2007). Swarms and swarm intelligence. Computer, 40(4), 111—113. Kulkarni, O. and Kulkarni, S. (2018). Process parameter optimization in WEDM by Grey Wolf Optimizer. Materials Today: Proceedings, 5(2), 4402—4412. Kulkarni, N.K., Patekar, S., Bhoskar, T., Kulkarni, O., Kakandikar, G.M., and Nandedkar, V.M. (2015). Particle swarm optimization applications to mechanical engineering. A review. Materials Today: Proceedings, 2(4-5), 2631—2639. Kulkarni, O., Kulkarni, N., Kulkarni, A.J., and Kakandikar, G. (2016). Constrained cohort intelligence using static and dynamic penalty function technique for mechanical components design. International Journal of Parallel, Emergent and Distributed Systems, 33, 1—19. Liu, G.P., Yang, J.-B., and Whidborne, J.F. (2003). Multiobjective Optimisation and Control. Research Studies Press, Baldock. Madin, L.P. (1990). Aspects of jet propulsion in salps. Canadian Journal of Zoology, 68(4), 765—777.

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MathWorks (n.d.). Solve a Constrained Nonlinear Problem — MATLAB & Simulink. www.mathworks.com (Retrieved 29 August 2017). Mirjalili, S., Gandomi, A.H., Mirjalili S.Z., Saremia, S., Farisd, H., and Mirjalilie, S.M. (2017a). Salp Swarm Algorithm: A bioinspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163—191. Mirjalili, S.Z., Mirjalili, S., Saremi, S., Faris, H., and Aljarah, I. (2017b). Grasshopper optimization algorithm for multi-objective optimization problems. Applied Intelligence, 48(7), 1—16. Mishra, S.K. (2006). Some new test functions for global optimization and performance of repulsive particle swarm method. 23 August. Available at: https://ssrn.com /abstract=926132 or http://dx.doi.org/10.2139/ssrn.926132 Parsopoulos, K.E. and Vrahatis, M.N. (2002). Particle swarm optimization method in multiobjective problems. In Proceedings of the 2002 ACM Symposium on Applied Computing. ACM. Rao, S.S. (2009). Engineering Optimization: Theory and Practice. John Wiley & Sons, New York, NY. Simionescu, P.-A. and Beale, D.G. (2002). New concepts in graphic visualization of objective functions. In ASME 2002

International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers. Yang, X.-S. (2014). Nature-Inspired Optimization Algorithms. Elsevier, Oxford. Zhang, L.B., Zhou, C.G , Liu, X.H., Ma, Z.Q., Ma, M., and Liang, Y.C. (2003). Solving multi objective optimization problems using particle swarm optimization. Evolutionary Computation, 2003. CEC'03. Vol. 4. IEEE. Zitzler, E. and Thiele, L. (1999). Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto technique. IEEE Transactions on Evolutionary Computation, 3(4), 257—271.

6 Water Quality Index: is it Possible to Measure with Fuzzy Logic?

6.1. Introduction Water is an essential resource for the survival of living beings on our planet. The excessive use and disproportionate pollution of water can make the planet’s environmental resources scarce in the future. The World Health Organization (WHO) estimates that currently about 1.1 billion people worldwide consume contaminated water (Wu et al. 2018). The water supply crisis was identified as the main risk of our current times by the World Economic Forum (2015). Although the analysis of water quality has gained prominence over the last three decades, the concept in its most rudimentary form was first introduced more than 170 years ago, in 1848, in Germany, where the presence or absence of certain organisms in water was used as an aptitude indicator (Abbasi et al. 2012).

Chapter written by Alexandre CHOUPINA, Elisabeth T. PEREIRA, Samara Silva SOARES, Poliana ARRUDA, Francis Lee RIBEIRO and Paulo Sérgio SCALIZE.

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Unlike the quantity of water, which can be expressed in precise terms, water quality is a multi-parameter attribute. The water quality assessment depends mainly on the aggregation of information on water quality parameters at different times and places, this information being processed and culminating in a scoring scale that could be represented by an index (Terrado et al. 2010). Many water quality indices have been formulated around the world, such as the United States National Sanitation Foundation Water Quality Index — NSFWQI (Brown et al. 1970), the Canadian Council of Ministers of the Environment Water Quality Index — CCMEWQI (Khan 2003, 2005), the British Columbia Water Quality Index — BCWQI and the Oregon Water Quality Index — OWQI (Debels et al. 2005; Kannel et al. 2007). Most of these indices are based on the NSFWQI (Şener

et al. 2017). The NSFWQI was developed to provide a method for comparing the water quality of various sources based on nine parameters. The water quality rating is according to a scale of 0—100, defined as: very bad (0—25), bad (25—50), medium (50—70), good (70—90) and excellent (90—100). However, the traditional methods have limitations of deterministic modeling (Lermontov et al. 2009). For example, according to Katyal (2011), the NSFWQI, due to the number of parameters and their weights, presents a failure in its sum of products and that water quality can be considered “good” even if one of the parameters is classified as “bad”. In the CCMEWQI and OWQI, the same importance is given to all parameters and it is not possible to determine the quality of the water for specific use (Abbasi et al. 2012; Cude 2001).

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Su et al. (2014) emphasize two types of uncertainties that can be applied to water quality: (1) internal uncertainties that are rooted in the ambiguity or imprecision of an index, or misinterpretation of an alternative that causes a different assessment of results under the same index, and (2) external uncertainties that contribute to the imperfect understanding of the decision environment, together with the lack of information on the consequences of each available alternative. In this sense, new methods that evaluate water quality have been developed in order to overcome such situations. Fuzzy logic, introduced by Zadeh (1965), has been the most common approach to dealing with the uncertainties associated with environmental problems (Azarnivand 2017). In addition, fuzzy logic has been applied to a number of studies involving the determination of water quality (Azarnivand et al. 2015; Gharibi et al. 2012; Ocampo-Duque et al. 2013; Sutadian et al. 2016). Among the main advantages of this method, when compared to traditional ones, we have to deal with missing data, allow the insertion of parameters according to the use of water and incorporate the expert opinion in its formulation. This study aims to develop a method of water quality determination using fuzzy logic and compare it with other traditional methods with the purpose to optimize the existing analytical techniques towards the engineering problem of improving the quality of water. The premise of the research is that fuzzy logic does not differ statistically at a significance level of 5% (α = 0.05), with a smaller number of parameters when compared to the other methods.

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6.2. Data and methodology 6.2.1. Data and description of the case study The present study applies the fuzzy logic methodology as an optimization technique to a case study. The sample that will be used to test the optimization of fuzzy logic will consist of a section of the Bois River in the Brazilian State of Goiás, in the central region of Brazil, which, in turn, integrates into the hydrographic region upstream of the mouth of the Anicuns river with a drainage area of 1,255 km² of the hydrographic basin of the Turvo and the Bois River, which has the second lowest index of plant cover (15%) among the 11 Water Resources Planning and Management Units of the state of Goiás (Secretary of Environment 2016). The 35.6 km stretch runs through the municipalities of Nazário and Palmeiras de Goiás, respectively 70 km and 100 km from Goiânia, the capital of the state of Goiás. This source is used for water supply in the city of Palmeiras of Goiás by the state sanitation company, serving a population of approximately 27,000 inhabitants. This water stock is of paramount importance to the state of Goiás since it concentrates diverse economic activities. Meanwhile, a large part of untreated domestic sewage as well as effluents from refrigerators, beverage factories, tanneries and others is discharged into the river. In addition, numerous sand extraction points are concentrated here, which causes deforestation of riparian forests and floodplain areas, leading to severe erosive processes, increased levels of water turbidity, and chemical pollution through oils, greases and detergents (Secima 2003). The data were collected in March and July of 2016 and in February and September of 2017, at four points distributed over a 35.6 km stretch (Figure 6.1). Between points 1 and 2 were identified effluent releases from two leather-processing industries. Point 3 is an intermediate point for measuring

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the dilution of the analyzed parameters. Point 4 is located upstream of the water supply for the public.

Figure 6.1. The hydrographic region upstream of the Anicuns river mouth of the Turvo and the Bois River basin, a central region of Brazil, and spatial distribution of water quality sampling points

6.2.2. Parameters The analyses of water quality parameters were performed according to the Standard Methods procedures (Rice et al. 2012). Five parameters were selected corresponding to 60% of the total weight of the NSFWQI. The classification of the parameters and their respective amounts are described in Table 6.1.

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Parameters

Classification Relevance

Reference

Dissolved oxygen

Chemical

Vital in the anaerobic Sener et al. process in water (2017) resources

Thermotolerant coliform

Microbiologic

Indicator of fecal pollution

Turbidity

Physics

Indicator of microbial contamination

Phosphorus

Nutrient

Eutrophication of water resources

et al. (2001)

Nitrates

Nutrient

Methemoglobinemia disease in infants

Varol et al. (2015)

Odonkor

et al. (2013) WHO (2011) Shapley

Table 6.1. Water quality parameters with respective classifications and importance in the water quality assessment process

6.2.3. Water quality index In general, a water quality index is based on three steps (Tyagi et al. 2013): (1) selection of parameters: this is done by judgment of professional experts, agencies or governmental institutions; (2) determination of the curve for each parameter: parameter limits are transformed into non-dimensional scale values from variables of different units, and (3) aggregation with mathematical expression: this step is commonly performed by means of arithmetic or geometric means. For Sobhani (2003), the water quality indices are divided into four main groups: (i) public index, (ii) specific consumption index, (iii) statistical indices, and (iv) developed indices for specific purposes (e.g. to evaluate the physicochemical composition of water). In general, the water quality indices depend on the normalization of the selected parameters. Then the parameters are weighted according to their importance and, finally, the index is calculated according to a scale of values

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and the results are interpreted in linguistic terms (e.g. good, fair and bad). The main differences in the various water quality indices are based on the selected parameters, the statistical inference used, the scale of values of each parameter and the term of the final result (Lumb et al. 2011). Among the variously proposed water quality indices, the NSFWQI and the CCMEWQI are widely accepted for validating water quality (Tyagi et al. 2013). These are public indices that present the result in similar linguistic terms. In this way, these indices were selected to be applied in the present study with the purpose of comparing its results with those of fuzzy logic. 6.2.3.1. NSFWQI The NSFWQI was proposed by the National Sanitation Foundation (NSF) of the United States of America, through a survey of 142 specialists, and developed by Brown et al. (1970). In the study that subsidized the development of the NSFWQI, each specialist indicated the variables considered relevant for the determination of water quality, and determined for each variable a relative weight, between 0 and 1, proportional to their importance. In addition, weighting curves were calculated and constructed for each parameter. Of the 35 initial parameters proposed, nine were selected as part of the final model. The parameters and weights used to calculate the NSFWQI are shown in Table 6.2. Considering the parameter weights, the WQI value is obtained by the weighted product of the parameters raised to their respective weight according to equation [6.1]:

=∏

[6.1]

where WQI is the water quality index (0—100), qi is the quality of the variable i obtained through the quality-specific

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mean curve (0—100), n is the number of variables used, wi is the weight attributed to each variable in function of its importance in water quality (0—1). Variables

Unit of measurement

Weights

Thermotolerant coliform

NMP/100 mL

0.16

Biochemical oxygen demand

mg/L

0.11

Total phosphate

mg/L

0.10

Nitrates

mg/L

0.10

Dissolved oxygen

% Saturation

0.17

pH

---

0.11

Total dissolved solids mg/L

0.07

Temperature

°C

0.10

Turbidity

NTU

0.08

Source: NSF (2018).

Table 6.2. Variables and respective weights adopted in the model of the NSFWQI

The values obtained are classified into bands ranging from 0 to 100. The bands and their respective qualifications are shown in Table 6.3. WQI bands

Classification

0—25

Very bad

26—50

Bad

51—70

Medium

71—90

Good

91—100

Excellent

Colors

Table 6.3. The WQI bands and its respective classifications and related colors. For a color version of this table, see www.iste.co.uk/kumar/optimization.zip

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6.2.3.2. CCMEWQI The CCMEWQI is calculated on the basis of three factors: F1 (Scope) — which represents the percentage of parameters that do not meet their guidelines at least once during the considered period of time (“failed parameters”), in relation to the total number of parameters measured (equation [6.2]); F2 (Frequency) — which represents the percentage of individual tests that do not meet the guidelines (“failed tests”) (equation [6.3]):

=



=

















∗ 100



∗ 100

[6.2] [6.3]

and F3 (Amplitude) — which represents the value by which the failed test values do not meet the previous guidelines and is calculated in three steps: i) The number of times that an individual concentration is greater than (or less than, when the guideline is minimum) the guideline is called “excursion”, and it is expressed as follows: When the test value should not exceed the guideline: =









−1

[6.4]

For cases where the value of the test should not fall below the guideline: =







−1

[6.5]

ii) The collective value by which the individual tests are out of compliance is calculated by summing individual test tours of their guidelines and dividing by the total number of tests (both those who meet the guidelines and those who do

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not meet the guidelines). This parameter, referred to as the normalized sum of excursions (nse), is calculated as follows: ∑

=





[6.6]



iii) F3 is then calculated by an asymptotic function that scales the normalized sum of the excursions of the guidelines (nse) to produce a range between 0 and 100: =

,

[6.7]

,

Once the factors have been obtained, the index itself can be calculated by summing the three factors as if they were vectors and using the Pythagorean Theorem. The sum of the squares of each factor is therefore equal to the square of the CCMEWQI. This approach treats the index as a three-dimensional space defined by each factor along with an axis. With this model, the index changes in direct proportion to changes in all three factors: = 100 −

,

[6.8]

The divider 1,732 allows the normalization of the resulting values for a range between 0 and 100, where 0 represents the “worst” water quality and 100 represents the “best” water quality which is divided into five descriptive categories to simplify the presentation (i.e. excellent, good, fair, marginal or bad). The values and meanings of each category are shown in Table 6.4. This index is flexible with regard to the type and number of water quality parameters to be tested, the period of application and the type of the body of water (flow, river reach, lake, etc.) tested. Based on the recent analysis of the sensitivity and behavior of the CCMEWQI, it is

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recommended to use at least eight but not more than 20 parameters (CCME 2017). For the application of the index, nine parameters were selected that are more usual in water quality and adapted to the guidelines of CONAMA Resolution No. 357 of March 17, 2005, which provides for the classification of bodies of water and environmental guidelines for their classification, and gives other measures (CONAMA 2005). Category

CCMEWQI value

Meaning

Excellent

95—100

Water quality is protected with a virtual absence of threat or injury; conditions very close to natural levels

Good

80—94

Water quality is protected with only a small degree of threat or injury

Fair

65—79

Water quality is generally protected but occasionally threatened or impaired

Marginal

45—64

Water quality is often threatened or impaired

Bad

0—44

Water quality is almost always threatened or impaired

Table 6.4. Classification of values and meanings of categories resulting from the application of the CCMEWQI

The upper and lower limits of each parameter were defined according to the most restrictive classification of bodies of freshwater of the above-mentioned norm, i.e. class 1, whose purpose is directed to several uses, highlighting the supply for human consumption. The only parameter that is not standardized is the temperature. The temperature range used in Table 6.5 comprises the thermal amplitude of the study site in conjunction with the aquatic life maintenance activities.

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Parameters

Unit

Lower limit Upper limit

pH

-

6

9

Temperature*

(°C)

20

30

Dissolved oxygen

(mg/L)

6

Nitrate

(mg/L)

10

Phosphate

(mg/L)

0.1

Biochemical oxygen demand (mg/L)

3

Thermotolerant coliform

(NMP/100 mL)

200

Turbidity

(NTU)

40

Total dissolved solids

(mg/L)

500

*The temperature limits are not contained in Resolution CONAMA no. 357/05. Table 6.5. Lower and upper limit of the guidelines used in the calculation of the CCMEWQI according to CONAMA Resolution 357/05 with the exception of the temperature parameter (CONAMA 2005)

Although the calculation of the CCMEWQI index values can be done by hand, it is not practical even for a moderate number of monitoring stations, guidelines or samples. An application provided by the CCME (CCME 2018) that automates the process was used. 6.2.3.3. Fuzzy logic The evaluation of water quality is a subjective task that must be performed with tools capable of managing information subjectivity and imprecision of data (Ocampo-Duque et al. 2013). A number of studies have shown that the linguistic calculations used in fuzzy inference systems are superior to common algebraic expressions for water quality index assessment (Lermontov et al. 2009; Li et al. 2016; Sahoo et al. 2015).

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Fuzzy logic was introduced by Zadeh (1965). The information processing takes place through linguistic variables, which are associated with a set of rules linked by operators. Each rule consists of the premise (if) that infers in the consequence (then) that generates a conclusion, according to equation [6.9]: :

ℎ



[6.9]

where i = 1,2,...,n, n is the number of rules, X is the linguistic variable of input, Y is the linguistic variable of output, and Ai and Bi are fuzzy subsets of the discourse universe of X. The membership function for a fuzzy set A on the universe of discourse X is defined as ∶ → 0,1 , where each element of X is mapped to a value between 0 and 1. This value is called the degree of membership, which quantifies the grade of membership of the element in X to fuzzy set x A. The relations between the fuzzy subsets are defined as operators, being this: union (OR), intersection (AND) and negation (NOT) (Ma et al. 2017). If two fuzzy sets A and B are defined in the universe X, for a given element x belonging to X, the following operations can be performed, according to equations [6.10], [6.11] and [6.12]:

:

=

∪





: :

, ∩

= =1−

[6.10] ,

[6.11] [6.12]

The final step of fuzzy inference is the defuzzification process. The defuzzification involves providing a mean index of the linguistic fuzzy sets with their respective degrees of adhesion. Among the methods used for defuzzification, the center of gravity is the most conventionally and physically

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applicable method (Gharibi et al. 2012). The derivation of this method is described in equation [6.13]:

Z=

 u( z) zdz  u( z) zdz

[6.13]

where Z is considered in our study as the water quality index with the range of values between 0 and 100, obtained from the aggregations of the rules, and z is the independent variable of the fuzzy set of rules. 6.2.4. Construction of the water quality index by fuzzy logic (WQF) The membership functions can be defined as triangular, trapezoidal, sigmoid and others. The choice of the relevance function format is not always obvious and may not be within the scope of knowledge for a particular application. In environmental issues, the choice of trapezoidal and triangular functions is more common, since the idea of defining regions of the total, average and null relevance is more intuitive than the specification of mean value and dispersion. In our study, we used the trapezoidal (end) and triangular (center) functions equations [6.14] and [6.15], respectively:

:

; , , ,

=

0 < < ≤ ≤ 1 ≤

≤

≤

:

; , ,

=

≤

0 < < ≤ ≤ ≤

≤

[6.14]

[6.15]

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Five parameters were selected: the dissolved oxygen (DO), thermotolerant coliform (TC), turbidity (Turb), phosphorus (PO4) and nitrates (NO3). The importance of the parameters is presented in section 6.2.2. The fuzzy sets were defined by five linguistic terms, namely very low (VL), low (L), medium (M), high (H) and very high (VH). In turn, the WQF output language terms were defined as very bad (VB), bad (B), regular (R), good (G) and excellent (E). Each parameter as input was assigned to one of the five fuzzy sets in terms of membership functions. Table 6.6 describes the language terms and membership sets used in the parameters and for the WQF. Figure 6.2 presents the pertinence functions used for dissolved oxygen. Each input parameter was assigned one of the five fuzzy sets. It was adopted as reference to the degree of pertinence 0.5 for the intersection between the sets. In general, when the intersection between fuzzy sets occurs with values smaller than 0.5, there are more regions in the universe of discourse characterized by a low degree of truth, leading to underestimating observation. On the other hand, when the value is greater than 0.5, there are areas characterized by some useless redundancy, if not detrimental (Bouchon-Meunier et al. 1996). Developing an index based on fuzzy inference requires understanding three important parts, including membership functions, fuzzy set operations and inference rules. Inference rules define the relationships between the subsets of the inputs and outputs. The number of rules can increase considerably, especially if rules with more than one antecedent are desired. In continuous variables, the number of fuzzy sets can be selected to represent any interval from three to seven linguistic terms, where five is a reasonable number (Ocampo-Duque et al. 2013). In this sense, we used five qualifiers trying to equally divide the universe of discourse with the appropriate intersection between sets.

a

b

c

d

DO (mg/L)

a

b

c

d

FC (MPN/100 mL) a

b

c

Turb (NTU) d

a

b

c

PO4 (mg/L)

Very bad

Very low

Bad

Low

Regular

Medium

Good

High

Excellent

0

2

4

6

0

4

6

8

2

6

8

10

4

0

100

500

900

0

500

900

500

0

0

10 30

30 50

50 70

10

50

70

90

30

b

c

d

0.25 0.75 1.25

0.75 1.25 1.75

1.25 1.75 2.25

1.75 2.25 3.00 3.00

a

NO3 (mg/L)

0.00 0.00 0.25 0.50 0.00 0.00 0.25 0.75

0.25 0.50 0.75

0.50 0.75 1.00

0.75 1.00 1.25

1.0

d

Table 6.6. Parameters of the fuzzy inference system

100

900

1300

1300 1700

Very high 8 10 12 12 1300 1700 2000 200 70 90 100 100 1.00 1.25 1.50

Linguistic terms b

c

d

0

0

10 30

30 50

50 70

10

50

70

90

30

70 90 100 100

a

WQF

146 Analytical Overview on Secure Information Flow in Android Systems

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Figure 6.2. Example of membership functions for dissolved oxygen

With the purpose of reaching the objectives proposed by the present index, 3250 rules were performed. The importance of the rule was defined according to the importance of the variables involved. Rules with DO and TC received the weight of 1.0. Rules with NO3 and PO4 received a weight of 0.75. Finally, the rules with Turb received the weight of 0.5. Rules and intervals were defined by environmental experts and research institutions. Some examples of rules are as follows:

if DO is “M” then water quality is “R”; if Turb is “VL” then water quality is “E”; if DO is “VH” and TC is “VL” and Turb is “VL” and PO4 is “VL” and NO3 is “VL” then WQF is “E”; if DO is “VH” and TC is “VL” and Turb is “VL” and PO4 is “VH” and NO3 is “VH” then WQF is “VB”. The conceptual model of the development of fuzzy logic is presented in Figure 6.3. The data were tabulated using the

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MATLAB software (R2015). The values of the parameters used in the study are described in Appendix A.

Figure 6.3. Graphic flow of process

6.3. Results and discussion 6.3.1. Water quality analysis The water quality analysis values are shown in Figure 6.4. It shows the water quality values of the three indices used in the survey at the four sampling points in 2016 (Figure 6.4a) and 2017 (Figure 6.4b). In general, water quality at all sampling stations over the years of the study period is regular (mean values 65—75), implying that this water is acceptable for human consumption. In all the sampling stations of our study, according to the results of a variance analysis (ANOVA), the water quality did not change significantly in time (p > 0.05). In addition, for each specific year, the water quality did not vary significantly in different sampling stations (p > 0.05). This may be because no proper pollution control was being implemented to improve water quality in the region analyzed.

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The obtained results for the four analyzed points verified the lowest values (55—59) of water quality, for all the calculated indices, at point 3, during the rainy season, in all the years of the survey (Figure 6.3). This was due to rapid industrial development, which causes increased wastewater discharge and domestic sewage being dumped into the rivers. In addition, point 3 is a point of confluence of the catchment area that facilitates the accumulation of pollution dumped during the entire sampling period. For points 1 and 4, during the rainy season, better water quality results are presented, with values of 86.25 and 82.30, respectively. The first sampling point is a region where there is no industrial and urban pollution processes. Point 4 is the local water catchment for public supply. Due to the increase in the ends of the river basin and the long stretch between points 3 and 4, there is a dispersion of the waste, making the quality of the surface water in better condition at the last point.

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Figure 6.4. Annual averages of the WQF values in all sampling stations compared with those of the NSFWQI and the CCMEWQI for the years 2016 (a) and 2017 (b)

6.3.2. Index validation Figure 6.5 (a—d) shows the water quality values calculated by the proposed index (WQF), the NSFWQI and the CCMEWQI in the four sampling stations for the years 2016 and 2017. The indices showed similar results. The WQF presented intermediate values between the other two indices. Regarding CCMEWQI, although any parameters can be included (here we apply the same parameters used in the NSFWQI), the values were higher than the proposed index with fuzzy logic. The index proposed by NSFWQI presented conservative values in comparison with the others. This result occurred because combining water quality data from several monitoring sites and months can homogenize discrepancies between datasets.

Water Quality Index: is it Possible to Measure with Fuzzy Logic?

a)

b)

151

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c)

d)

Figure 6.5. Comparison of the results of the WQF, NSFWQI and CCMEWQI indices at the four sampling stations. For a color version of this figure, see www.iste.co.uk/kumar/optimization.zip

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Table 6.7 presents the level of significance (p < 0.05) of the calculated indices. The proposed index (WQF) does not differ significantly from NSFWQI and CCMEWQI. However, the traditional indices (NSFWQI and CCMEWQI), according to the analysis of variance (ANOVA), are statistically different (p < 0.05). Average difference (I-J)

Sig.

NSFWQI

6.34

CCMEWQI

(I) Index

Lower limit

Upper limit

0.163

−1.93

14.60

−7.08

0.110

−15.35

1.18

WQF

−6.34

0.163

−14.60

1.93

CCMEWQI

−13.42*

0.001

−21.69

−5.15

WQF

7.08

0.110

−1.18

15.35

NSFWQI

13.42*

0.001

5.15

21.69

WQF

NSFWQI CCMEWQ I

Confidence interval 95%

*The mean difference is significant at the 0.05 level.

Table 6.7. Analysis of significance of research indices

In spite of the fact that it is not so easy to validate the proposed index, this can be achieved by comparing the proposed index with the traditional indices, since the water quality results are statistically similar. The advantages of using WQF over NSFWQI are the flexibility of parameter insertion. Fuzzy logic also has the ability to reflect the opinion of experts according to water use, which allows it to deal with nonlinear questions, and uncertain, ambiguous and subjective information. The CCMEWQI has similar characteristics to the WQF in the flexibility of insertion of parameters to calculate the water quality index. However, the water quality index proposed by CCME cannot be used to attribute weights

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according to the importance of parameters. Another disadvantage of this method (CCMEWQI) is the absence of determining the water quality according to its use. 6.4. Conclusions Although there are many water quality indices that have been developed, and applied, worldwide, it is not possible to say which index is the best or even which indices are the best. Our research does not have the arrogance to affirm which of the indices developed and studied is better. In fact, we developed a choice to assess the quality of water under various conditions and types of water use. Even though the study applied different water quality indices, it can be inferred that the objective of the WQF is to provide a water quality index that allow us to reduce the number of used parameters in a simple expression, resulting in an easy interpretation of the water quality monitoring data. In addition, the use of the WQF allows us to assess the water quality according to its use from the configuration of the pertinence curves of the parameters. According to the results of the present study, the following conclusions can be inferred: (a) the water quality index, based on fuzzy logic, which we have developed in this study, produces statistically similar results to traditional indices with fewer relevant parameters, as well as the inclusion of parameters for water use, particularly for human consumption, and (b) the index proposed by the present study seems to produce accurate and reliable results. In this sense, the WQF can be used as a comprehensive tool for water quality assessment by agencies, managers and research institutions according to their environmental realities and purposes, with minor modifications.

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6.5. Appendix 2016 Station

1

2

3

4

2017

Parameters Wet

Dry

Wet

Dry

OD (mg/L)

6.5

7.5

6.4

7.2

TC (MPN/100 mL)

517.5

580.0

685.0

167.5

Turb (NTU)

57.5

8.06

73.7

5.7

PO4 (mg/L)

0.73

0.1

0.3

0.01

NO3 (mg/L)

0.5

0.00

0.0

0.0

OD (mg/L)

6.5

7.8

6.6

6.9

TC (MPN/100 mL)

571.5

272.50 250.0

123.12

Turb (NTU)

55.8

8.17

49.7

7.8

PO4 (mg/L)

0.90

0.1

0.23

0.01

NO3 (mg/L)

0.6

0.2

0.0

0.1

OD (mg/L)

5.5

7.8

5.8

4.5

TC (MPN/100 mL)

761.25

356.25 787.50

185.0

Turb (NTU)

76.5

10.3

54.0

10.1

PO4 (mg/L)

1.4

0.35

0.5

0.13

NO3 (mg/L)

1.1

0.8

0.3

1.1

OD (mg/L)

5.6

6.2

5.1

5.2

TC (MPN/100 mL)

301.25

213.75 125.0

150.0

Turb (NTU)

50.6

14.5

69.7

10.7

PO4 (mg/L)

1.10

0.35

0.0

0.11

NO3 (mg/L)

1.2

2.1

1.0

3.1

Table 6.8. Values applied in research according to the used parameters

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6.6. References Abbasi, T. and Abbasi, S.A. (2012). Water Quality Indices. Elsevier, Oxford, UK. Azarnivand, A. (2017). Comment on “Assessing water quality of five typical reservoirs in lower reaches of Yellow River, China: Using a water quality index method” by Wei Hou, Shaohua Sun, Mingquan Wang, Xiang Li, Nuo Zhang, Xiaodong Xin, Li Sun, Wei Li, and Ruibao Jia (2016)[Ecological Indicators, 61, 309—316]. Ecological Indicators, 75, 8—9. Azarnivand, A., Hashemi-Madani, F.S., and Banihabib, M.E. (2015). Extended fuzzy analytic hierarchy process approach in water and environmental management (case study: Lake Urmia Basin, Iran). Environmental Earth Sciences, 73(1), 13—26. Bouchon-Meunier, B., Dotoli, M., and Maione, B. (1996). On the choice of membership functions in a mamdani-type fuzzy controller. Proceedings of the First Online Workshop on Soft Computing. Nagoya, Japan. Brown, R.M., McClelland, N.I., Deininger, R.A., and Tozer, R.G. (1970). A water quality index — Do we dare? Water Sewage Works, 117(10), 339—343. CCME (Canadian Council of Ministers of The Environment) (2017). Canadian Water Quality Guidelines for the Protection of Aquatic Life: CCME Water Quality Index, User’s Manual 2017 Update. Canadian Council of Ministers of the Environment, Winnipeg. CCME (Canadian Council of Ministers of the Environment) (2018). WQI Calculator. Avaialbe at: https://www.ccme.ca/en/resources /canadian_environmental_quality_guidelines/calculators.html (Accessed on May 2018). CONAMA (2005). Resolução n. 357, de 17 de março de 2005. Conselho Nacional do Meio Ambiente. Cude, C.G. (2001). Oregon water quality index: A tool for evaluating water quality management effectiveness. Journal of the American Water Resources Association, 37(1), 125—137.

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Debels, P., Figueroa, R., Urrutia, R., Barra, R., and Niell, X. (2005). Evaluation of water quality in the Chillán River (Central Chile) using physicochemical parameters and a modified water quality index. Environmental Monitoring and Assessment, 110(1—3), 301—322. Gharibi, H., Mahvi, A.H., Nabizadeh, R., Arabalibeik, H., Yunesian, M., and Sowlat, M.H. (2012). A novel approach in water quality assessment based on fuzzy logic. Journal of Environmental Management, 112, 87—95. Kannel, P.R., Lee, S., Lee, Y.S., Kanel, S.R., and Khan, S.P. (2007). Application of water quality indices and dissolved oxygen as indicators for river water classification and urban impact assessment. Environmental Monitoring and Assessment, 132(1— 3), 93—110. Katyal, D. (2011). Water quality indices used for surface water International Journal of vulnerability assessment. Environmental Sciences, 2(1), 20. Khan, A.A., Paterson, R., and Khan, H. (2003). Modification and application of the CCME WQI for the communication of drinking water quality data in newfoundland and labrador.

38th Central Symposium on Water Quality Research, Canadian Association on Water Quality, 10—11. Khan, A.A., Tobin, A., Paterson, R., Khan, H., and Warren, R. (2005). Application of CCME procedures for deriving site-specific water quality guidelines for the CCME Water Quality Index. Water Quality Research Journal, 40(4), 448—456. Lermontov, A., Yokoyama, L., Lermontov, M., and Machado, M.A.S. (2009). River quality analysis using fuzzy water quality index: Ribeira do Iguape river watershed, Brazil. Ecological Indicators, 9(6), 1188—1197. Li, R., Zou, Z., and An, Y. (2016). Water quality assessment in Qu River based on fuzzy water pollution index method. Journal of Environmental Sciences, 50, 87—92. Lumb, A., Halliwell, D., and Sharma, T. (2006). Application of CCME Water Quality Index to monitor water quality: A case study of the Mackenzie River basin, Canada. Environmental Monitoring and Assessment, 113(1—3), 411—429.

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List of Authors

Bappa ACHERJEE Birla Institute of Technology Ranchi India

Manoj K. DUTTA Birla Institute of Technology Deoghar India

Poliana ARRUDA Federal University of Goiás São Paulo Brazil

Ganesh M. KAKANDIKAR Maharashtra Institute of Technology Pune India

Alexandre CHOUPINA Federal University of Goiás São Paulo Brazil

J. Paulo DAVIM University of Aveiro Portugal

Arunanshu S. KUAR Jadavpur University Kolkata India Omkar K. KULKARNI Maharashtra Institute of Technology Pune India

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Kaushik KUMAR Birla Institute of Technology Ranchi India

Francis Lee RIBEIRO Federal University of Goiás São Paulo Brazil

Debanjan MAITY Indian Institute of Technology Kharagpur India

Paulo Sérgio SCALIZE Federal University of Goiás São Paulo Brazil

Sushant P. MHATUGADE Maharashtra Institute of Technology Pune India

Brajpal SINGH Maulana Azad National Institute of Technology Bhopal India

Vilas M. NANDEDKAR Shri Guru Gobind Singhji Institute of Engineering & Technology Nanded India

Samara Silva SOARES Federal University of Goiás São Paulo Brazil

Elisabeth T. PEREIRA University of Aveiro Portugal Vahid POURMOSTAGHIMI University of Tabriz Iran Mohan Kumar PRADHAN Maulana Azad National Institute of Technology Bhopal India

Jonnalagadda SRINIVAS National Institute of Technology Rourkela India Mohammad ZADSHAKOYAN University of Tabriz Iran

Index

A, C, E accuracy, 1, 39, 40, 49, 50, 53, 54, 154 AHP method, 39, 41, 55—58, 60, 71, 72 Al7075 alloy, 39, 40, 55, 63, 71, 72 cantilever beam, 101, 125, 127, 128 constrained optimization problems, 3, 8, 14, 101, 119 conventional optimization solution techniques, 1, 14 electric discharge machining (EDM), 39, 40, 42—56, 57, 63—72 F, H, I fuzzy logic, 133, 134, 137, 142—144, 147, 150, 153, 154 hybrid metal matrix composites, 42 inter-electrode gap, 47 M, N, O

material removal rate (MRR), 44, 45, 48—53, 56—58, 61, 67, 68, 72 matrix, 39, 41, 50, 52, 55—60 mechanical properties, 40, 41, 50 multi-objective problems, 1, 2, 12, 14, 40, 101, 102, 104, 105, 109—111, 114, 120, 122, 124, 127, 128 NSGA-II, 101 objective function, 2—5, 7—10, 12, 14, 113 optimal results, 71, 122 optimization multi-objective, 12, 40 single-objective, 104, 114, 115, 117, 119, 120, 127 P, R, S process parameters, 40, 44, 49, 50, 52, 54, 66 PROMETHEE method, 39, 40, 41, 48, 55, 60, 63—65, 71, 72 radial over-cut (ROC), 44, 49, 50, 54, 56—58, 61, 67, 69, 72

machinability, 39, 40, 42, 71

Optimization for Engineering Problems, First Edition. Edited by Kaushik Kumar and J. Paulo Davim. © ISTE Ltd 2019. Published by ISTE Ltd and John Wiley & Sons, Inc.

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reinforcement, 39—42, 50, 67— 70 response surface methodology (RSM), 55 salp chains, 101, 107, 108, 128 salp swarm algorithm (SSA), 101, 105, 107—109, 111, 113—115, 117—119, 127, 128 multi-objective (MSSA), 101, 109, 111—115, 120—122, 124, 125, 127, 128 significance level, 133 silicon carbide (SiC), 39, 52, 53, 55, 56, 63, 67—72 stir casting, 48, 50 surface roughnes0073, 40, 43, 44, 49, 50, 52, 54, 70 T, V, W thermal properties, 39, 41 titanium carbide (TiC), 39, 55

tool wear rate, 40, 43, 44, 48— 53, 56—58, 61, 67—69, 72 tribological properties, 42 tungsten disulphide (WS2), 39—41, 50, 55, 64, 67—72 voltage, 41, 44, 46, 47, 54, 55, 56, 67, 68, 70, 72 water quality, 131—133, 135, 136, 140, 142, 147—149, 154 water quality indices (WQI), 131, 132, 136—138, 142, 144, 153, 154 BCWQI, 132 CCMEWQI, 132, 137, 139—142, 150, 152—154 NSFWQI, 132, 135, 137, 138, 150, 152, 153 OWQI, 132 World Economic Forum (WEF), 131 World Health Organization (WHO), 131, 136

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