OPTIMIZATION FOR ENGINEERING DESIGN
Second EditionOPTIMIZATIONFOR ENGINEERINGDESIGNAlgorithms and ExamplesKalyanmoy Deb
OPTIMIZATION FOR ENGINEERING DESIGN
Optimization forEngineering DesignAlgorithms and ExamplesSECOND EDITIONKALYANMOY DEBDepartment of Mechanical EngineeringIndian Institute of Technology KanpurNew Delhi-1100012012
OPTIMIZATION FOR ENGINEERING DESIGN—Algorithms and Examples, Second EditionKalyanmoy Deb 2012 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this bookmay be reproduced in any form, by mimeograph or any other means, without permission inwriting from the publisher.ISBN-978-81-203-4678-9The export rights of this book are vested solely with the publisher.Twelfth Printing (Second Edition).November, 2012Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus,New Delhi-110001 and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV, HSIDC,Kundli-131028, Sonepat, Haryana.
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ContentsPreface. xiPreface to the First Edition. xiiiAcknowledgements. xvii1. Introduction. 1–421.1 Optimal Problem Formulation 21.1.1 Design Variables 31.1.2 Constraints 41.1.3 Objective Function 51.1.4 Variable Bounds 61.2 Engineering Optimization Problems 81.2.1 Design and Manufacturing 91.2.2 Modelling 171.2.3 Data Fitting and Regression 211.2.4 Control Systems 221.2.5 Inverse Problems 241.2.6 Scheduling and Routing 261.2.7 Data Mining 311.2.8 Intelligent System Design 321.3 Classification of Optimization Algorithms 351.4 Summary 40References 402. Single-variable Optimization Algorithms. 43–842.12.22.3Optimality Criteria 44Bracketing Methods462.2.1 Exhaustive Search Method 462.2.2 Bounding Phase Method 49Region-Elimination Methods 512.3.1 Interval Halving Method 52vii
Contentsviii2.3.2 Fibonacci Search Method 542.3.3 Golden Section Search Method 572.4 Point-Estimation Method 602.4.1 Successive Quadratic Estimation Method 602.5 Gradient-based Methods 632.5.1 Newton-Raphson Method 632.5.2 Bisection Method 652.5.3 Secant Method 672.5.4 Cubic Search Method 682.6 Root-finding Using Optimization Techniques 712.7 omputer Programs 783. Multivariable Optimization Algorithms.85–1423.1 Optimality Criteria 853.2 Unidirectional Search 873.3 Direct Search Methods 893.3.1 Box’s Evolutionary Optimization Method 903.3.2 Simplex Search Method 953.3.3 Hooke-Jeeves Pattern Search Method 983.3.4 Powell’s Conjugate Direction Method 1033.4 Gradient-based Methods 1083.4.1 Cauchy’s (Steepest Descent) Method 1123.4.2 Newton’s Method 1143.4.3 Marquardt’s Method 1183.4.4 Conjugate Gradient Method 1203.4.5 Variable-metric Method (DFP Method) 1243.5 30Computer Program 1344. Constrained Optimization Algorithms.143–2624.14.24.34.44.5Kuhn-Tucker Conditions 144Lagrangian Duality Theory 151Transformation Methods 1544.3.1 Penalty Function Method 1544.3.2 Method of Multipliers 162Sensitivity Analysis 167Direct Search for Constrained Minimization 1734.5.1 Variable Elimination Method 1734.5.2 Complex Search Method 1774.5.3 Random Search Methods 182
Contentsix4.6 Linearized Search Techniques 1854.6.1 Frank-Wolfe Method 1864.6.2 Cutting Plane Method 1924.7 Feasible Direction Method 2034.8 Quadratic Programming 2124.8.1 Sequential Quadratic Programming 2184.9 Generalized Reduced Gradient Method 2244.10 Gradient Projection Method 2324.11 Summary 239References 242Problems 243Computer Program 2535. Specialized Algorithms.263–2915.1 Integer Programming 2645.1.1 Penalty Function Method 2655.1.2 Branch-and-Bound Method 2705.2 Geometric Programming 2785.3 Summary 288References288Problems 2896. Nontraditional Optimization Algorithms.292–3686.1 Genetic Algorithms 2926.1.1 Working Principles 2936.1.2 Differences between GAs and Traditional Methods 2986.1.3 Similarities between GAs and Traditional Methods 3016.1.4 GAs for Constrained Optimization 3116.1.5 Other GA Operators 3146.1.6 Real-coded GAs 3156.1.7 Multi-objective GAs 3196.1.8 Other Advanced GAs 3236.2 Simulated Annealing 3256.3 Global Optimization 3306.3.1 Using the Steepest Descent Method 3306.3.2 Using Genetic Algorithms 3326.3.3 Using Simulated Annealing 3346.4 40Computer Program 348Appendix:Linear Programming Algorithms.369–415Index.417–421
PrefaceThe first edition of this book which was published in 1995 has been welltested at IIT Kanpur and at many other universities over the past 17years. It is unusual to have the second edition of a book being publishedafter so many years, but it is the nature of the book that prompted me towait till there is enough feedback from students and teachers before I wassitting down to revise the first edition. The optimization algorithms laidout in this book do not change with time, although their explanations andpresentations could have been made better. But the feedback I received fromseveral of my students and a large number of instructors has been positiveand I had not much motivation to revise the book in a major way. Thesimplified presentation of optimization algorithms remains as a hallmarkfeature of this book. Purposefully, a few topics of optimization were left outin the first edition, which I have now included in this edition. Specifically, asection on quadratic programming and its extension to sequential quadraticprogramming have been added. Genetic algorithms (GAs) for optimizationhave been significantly modified in the past 17 years, but if I have toprovide an account of all the current methods of GAs, it will be a book ofits own. But I could not resist to include some details on real-parameterGAs and multi-objective optimization. Readers interested in knowing moreabout GAs are encouraged to refer to most recent books and conferenceproceedings on the topic.A major modification has been made to the Linear Programming (LP)chapter in the Appendix. Several methods including sensitivity analysisprocedures have been added so that students can get a comprehensive ideaof different LP methods. While making the modifications, the simplicityof the algorithms, as it was presented in the first edition, has been kept.Finally, more exercise problems are added not only to this chapter, but toall previous chapters of this revised book.xi
xiiPrefaceI sincerely hope the second edition becomes more useful in getting aproper understanding of different optimization algorithms discussed in thisbook. I would appreciate very much if any typing error or comments canbe directly sent to my email address: deb@iitk.ac.in or kalyanmoy.deb@gmail.com.Kalyanmoy Deb
Preface to the First EditionMany engineers and researchers in industries and academics face difficultyin understanding the role of optimization in engineering design. To manyof them, optimization is an esoteric technique used only in mathematicsand operations research related activities. With the advent of computers,optimization has become a part of computer-aided design activities. Itis primarily being used in those design activities in which the goal isnot only to achieve just a feasible design, but also a design objective. Inmost engineering design activities, the design objective could be simply tominimize the cost of production or to maximize the efficiency of production.An optimization algorithm is a procedure which is executed iteratively bycomparing various solutions till the optimum or a satisfactory solutionis found. In many industrial design activities, optimization is achievedindirectly by comparing a few chosen design solutions and acceptingthe best solution. This simplistic approach never guarantees an optimalsolution. On the contrary, optimization algorithms begin with one or moredesign solutions supplied by the user and then iteratively check new designsolutions in order to achieve the true optimum solution. In this book, Ihave put together and discussed a few popular optimization algorithms anddemonstrated their working principles by hand-simulating on a simpleexample problem. Some working computer codes are also appended forlimited use.There are two distinct types of optimization algorithms which are inuse today. First, there are algorithms which are deterministic, with specificrules for moving from one solution to the other. These algorithms havebeen in use for quite some time and have been successfully applied tomany engineering design problems. Secondly, there are algorithms which arestochastic in nature, with probabilistic transition rules. These algorithmsare comparatively new and are gaining popularity due to certain propertieswhich the deterministic algorithms do not have. In this book, probablyfor the first time, an attempt has been made to present both these typesxiii
xivPreface to the First Editionof algorithms in a single volume. Because of the growing complexity inengineering design problems, the designer can no longer afford to rely on aparticular method. The designer must know the advantages and limitationsof various methods and choose the one that is more efficient to the problemat hand.An important aspect of the optimal design process is the formulationof the design problem in a mathematical format which is acceptable to anoptimization algorithm. However, there is no unique way of formulatingevery engineering design problem. To illustrate the variations encounteredin the formulation process, I have presented four different engineeringdesign problems in Chapter 1. Optimization problems usually containmultiple design variables, but I have begun by first presenting a numberof single-variable function optimization algorithms in Chapter 2. Theworking principles of these algorithms are simpler and, therefore, easier tounderstand. Besides, these algorithms are used in multivariable optimizationalgorithms as unidirectional search methods. Chapter 3 presents a numberof algorithms for optimizing unconstrained objective functions havingmultiple variables. Chapter 4 is an important one in that it discusses anumber of algorithms for solving constrained optimization problems—mostengineering design optimization problems are constrained. Chapter 5 dealswith two specialized algorithms for solving integer programming problemsand geometric programming problems. Two nontraditional optimizationalgorithms, which are very different in principle than the above algorithms,are covered in Chapter 6. Genetic algorithms—search and optimizationalgorithms that mimic natural evolution and genetics—are potentialoptimization algorithms and have been applied to many engineering designproblems in the recent past. Due to their population approach and parallelprocessing, these algorithms have been able to obtain global optimalsolutions in complex optimization problems. Simulated annealing methodmimics the cooling phenomenon of molten metals. Due to its inherentstochastic approach and availability of a convergence proof, this techniquehas also been used in many engineering design problems. Chapter 6 alsodiscusses the issue of finding the global optimal solution in a multioptimalproblem, where the problem contains a number of local and global optimalsolutions and the objective is to find the global optimal solution. Tocompare the power of various algorithms, one of the traditional constrainedoptimization techniques is compared with both the nontraditionaloptimization techniques in a multioptimal problem.Some algorithms in Chapter 4 use linear programming methods, whichare usually taught in operations research and transportation engineeringrelated courses. Sometimes, linear programming methods are also taughtin first or second-year undergraduate engineering courses. Thus, a detaileddiscussion of linear programming methods is avoided in this book. Instead,a brief analysis of the simplex search technique of the linear programmingmethod is given in Appendix A.
Optimization For Engineering DesignAlgorithms And Examples25%OFFPublisher : PHI LearningISBN : 9788120346789Author : Deb AndKalyanmoyType the URL : http://www.kopykitab.com/product/10271Get this eBook
algorithms, which are very different in principle than the above algorithms, are covered in Chapter 6. Genetic algorithms—search and optimization algorithms that mimic natural evolution and genetics—are potential optimization algorithms and have been applied to many engineering design problems in the recent past.
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