Engineering optimization : methods and applications

The classic introduction to engineering optimization theory and practice--now expanded and updated

Engineering optimization helps engineers zero in on the most effective, efficient solutions to problems. This text provides a practical, real-world understanding of engineering optimization. Rather than belaboring underlying proofs and mathematical derivations, it emphasizes optimization methodology, focusing on techniques and stratagems relevant to engineering applications in design, operations, and analysis. It surveys diverse optimization methods, ranging from those applicable to the minimization of a single-variable function to those most suitable for large-scale, nonlinear constrained problems. New material covered includes the duality theory, interior point methods for solving LP problems, the generalized Lagrange multiplier method and generalization of convex functions, and goal programming for solving multi-objective optimization problems. A practical, hands-on reference and text, Engineering Optimization, Second Edition covers:
* Practical issues, such as model formulation, implementation, starting point generation, and more
* Current, state-of-the-art optimization software
* Three engineering case studies plus numerous examples from chemical, industrial, and mechanical engineering
* Both classical methods and new techniques, such as successive quadratic programming, interior point methods, and goal programming

Excellent for self-study and as a reference for engineering professionals, this Second Edition is also ideal for senior and graduate courses on engineering optimization, including television and online instruction, as well as for in-plant training.

Author Notes

A. Ravindran, PhD, is Professor of Industrial and Manufacturing Engineering at Penn State University in University Park, Pennsylvania
K. M. Ragsdell, PhD, is Professor of Engineering Management at the University of Missouri in Rolla, Missouri
G. V. Reklaitis, PhD, is Edward W. Comings Professor of Chemical Engineering at Purdue University in West Lafayette, Indiana

Preface	p. xiii
1 Introduction to Optimization	p. 1
1.1 Requirements for the Application of Optimization Methods	p. 2
1.1.1 Defining the System Boundaries	p. 2
1.1.2 Performance Criterion	p. 3
1.1.3 Independent Variables	p. 4
1.1.4 System Model	p. 5
1.2 Applications of Optimization in Engineering	p. 6
1.2.1 Design Applications	p. 8
1.2.2 Operations and Planning Applications	p. 15
1.2.3 Analysis and Data Reduction Applications	p. 20
1.2.4 Classical Mechanics Applications	p. 26
1.2.5 Taguchi System of Quality Engineering	p. 27
1.3 Structure of Optimization Problems	p. 28
1.4 Scope of This Book	p. 29
References	p. 30
2 Functions of a Single Variable	p. 32
2.1 Properties of Single-Variable Functions	p. 32
2.2 Optimality Criteria	p. 35
2.3 Region Elimination Methods	p. 45
2.3.1 Bounding Phase	p. 46
2.3.2 Interval Refinement Phase	p. 48
2.3.3 Comparison of Region Elimination Methods	p. 53
2.4 Polynomial Approximation or Point Estimation Methods	p. 55
2.4.1 Quadratic Estimation Methods	p. 56
2.4.2 Successive Quadratic Estimation Method	p. 58
2.5 Methods Requiring Derivatives	p. 61
2.5.1 Newton-Raphson Method	p. 61
2.5.2 Bisection Method	p. 63
2.5.3 Secant Method	p. 64
2.5.4 Cubic Search Method	p. 65
2.6 Comparison of Methods	p. 69
2.7 Summary	p. 70
References	p. 71
Problems	p. 71
3 Functions of Several Variables	p. 78
3.1 Optimality Criteria	p. 80
3.2 Direct-Search Methods	p. 84
3.2.1 The S[superscript 2] (Simplex Search) Method	p. 86
3.2.2 Hooke-Jeeves Pattern Search Method	p. 92
3.2.3 Powell's Conjugate Direction Method	p. 97
3.3 Gradient-Based Methods	p. 108
3.3.1 Cauchy's Method	p. 109
3.3.2 Newton's Method	p. 111
3.3.3 Modified Newton's Method	p. 115
3.3.4 Marquardt's Method	p. 116
3.3.5 Conjugate Gradient Methods	p. 117
3.3.6 Quasi-Newton Methods	p. 123
3.3.7 Trust Regions	p. 127
3.3.8 Gradient-Based Algorithm	p. 128
3.3.9 Numerical Gradient Approximations	p. 129
3.4 Comparison of Methods and Numerical Results	p. 130
3.5 Summary	p. 137
References	p. 137
Problems	p. 141
4 Linear Programming	p. 149
4.1 Formulation of Linear Programming Models	p. 149
4.2 Graphical Solution of Linear Programs in Two Variables	p. 154
4.3 Linear Program in Standard Form	p. 158
4.3.1 Handling Inequalities	p. 159
4.3.2 Handling Unrestricted Variables	p. 159
4.4 Principles of the Simplex Method	p. 161
4.4.1 Minimization Problems	p. 172
4.4.2 Unbounded Optimum	p. 173
4.4.3 Degeneracy and Cycling	p. 174
4.4.4 Use of Artificial Variables	p. 174
4.4.5 Two-Phase Simplex Method	p. 176
4.5 Computer Solution of Linear Programs	p. 177
4.5.1 Computer Codes	p. 177
4.5.2 Computational Efficiency of the Simplex Method	p. 179
4.6 Sensitivity Analysis in Linear Programming	p. 180
4.7 Applications	p. 183
4.8 Additional Topics in Linear Programming	p. 183
4.8.1 Duality Theory	p. 184
4.8.2 Dual Simplex Method	p. 188
4.8.3 Interior Point Methods	p. 189
4.8.4 Integer Programming	p. 205
4.8.5 Goal Programming	p. 205
4.9 Summary	p. 206
References	p. 206
Problems	p. 207
5 Constrained Optimality Criteria	p. 218
5.1 Equality-Constrained Problems	p. 218
5.2 Lagrange Multipliers	p. 219
5.3 Economic Interpretation of Lagrange Multipliers	p. 224
5.4 Kuhn-Tucker Conditions	p. 225
5.4.1 Kuhn-Tucker Conditions or Kuhn-Tucker Problem	p. 226
5.4.2 Interpretation of Kuhn-Tucker Conditions	p. 228
5.5 Kuhn-Tucker Theorems	p. 229
5.6 Saddlepoint Conditions	p. 235
5.7 Second-Order Optimality Conditions	p. 238
5.8 Generalized Lagrange Multiplier Method	p. 245
5.9 Generalization of Convex Functions	p. 249
5.10 Summary	p. 254
References	p. 254
Problems	p. 255
6 Transformation Methods	p. 260
6.1 Penalty Concept	p. 261
6.1.1 Various Penalty Terms	p. 262
6.1.2 Choice of Penalty Parameter R	p. 277
6.2 Algorithms, Codes, and Other Contributions	p. 279
6.3 Method of Multipliers	p. 282
6.3.1 Penalty Function	p. 283
6.3.2 Multiplier Update Rule	p. 283
6.3.3 Penalty Function Topology	p. 284
6.3.4 Termination of the Method	p. 285
6.3.5 MOM Characteristics	p. 286
6.3.6 Choice of R-Problem Scale	p. 289
6.3.7 Variable Bounds	p. 289
6.3.8 Other MOM-Type Codes	p. 293
6.4 Summary	p. 293
References	p. 294
Problems	p. 298
7 Constrained Direct Search	p. 305
7.1 Problem Preparation	p. 306
7.1.1 Treatment of Equality Constraints	p. 306
7.1.2 Generation of Feasible Starting Points	p. 309
7.2 Adaptations of Unconstrained Search Methods	p. 309
7.2.1 Difficulties in Accommodating Constraints	p. 310
7.2.2 Complex Method	p. 312
7.2.3 Discussion	p. 320
7.3 Random-Search Methods	p. 322
7.3.1 Direct Sampling Procedures	p. 322
7.3.2 Combined Heuristic Procedures	p. 326
7.3.3 Discussion	p. 329
7.4 Summary	p. 330
References	p. 330
Problems	p. 332
8 Linearization Methods for Constrained Problems	p. 336
8.1 Direct Use of Successive Linear Programs	p. 337
8.1.1 Linearly Constrained Case	p. 337
8.1.2 General Nonlinear Programming Case	p. 346
8.1.3 Discussion and Applications	p. 355
8.2 Separable Programming	p. 359
8.2.1 Single-Variable Functions	p. 359
8.2.2 Multivariable Separable Functions	p. 362
8.2.3 Linear Programming Solutions of Separable Problems	p. 364
8.2.4 Discussion and Applications	p. 368
8.3 Summary	p. 372
References	p. 373
Problems	p. 374
9 Direction Generation Methods Based on Linearization	p. 378
9.1 Method of Feasible Directions	p. 378
9.1.1 Basic Algorithm	p. 380
9.1.2 Active Constraint Sets and Jamming	p. 383
9.1.3 Discussion	p. 387
9.2 Simplex Extensions for Linearly Constrained Problems	p. 388
9.2.1 Convex Simplex Method	p. 389
9.2.2 Reduced Gradient Method	p. 399
9.2.3 Convergence Acceleration	p. 403
9.3 Generalized Reduced Gradient Method	p. 406
9.3.1 Implicit Variable Elimination	p. 406
9.3.2 Basic GRG Algorithm	p. 410
9.3.3 Extensions of Basic Method	p. 419
9.3.4 Computational Considerations	p. 427
9.4 Design Application	p. 432
9.4.1 Problem Statement	p. 433
9.4.2 General Formulation	p. 434
9.4.3 Model Reduction and Solution	p. 437
9.5 Summary	p. 441
References	p. 441
Problems	p. 443
10 Quadratic Approximation Methods for Constrained Problems	p. 450
10.1 Direct Quadratic Approximation	p. 451
10.2 Quadratic Approximation of the Lagrangian Function	p. 456
10.3 Variable Metric Methods for Constrained Optimization	p. 464
10.4 Discussion	p. 470
10.4.1 Problem Scaling	p. 470
10.4.2 Constraint Inconsistency	p. 470
10.4.3 Modification of H[superscript (t)]	p. 471
10.4.4 Comparison of GRG with CVM	p. 471
10.5 Summary	p. 475
References	p. 476
Problems	p. 477
11 Structured Problems and Algorithms	p. 481
11.1 Integer Programming	p. 481
11.1.1 Formulation of Integer Programming Models	p. 482
11.1.2 Solution of Integer Programming Problems	p. 484
11.1.3 Guidelines on Problem Formulation and Solution	p. 492
11.2 Quadratic Programming	p. 494
11.2.1 Applications of Quadratic Programming	p. 494
11.2.2 Kuhn-Tucker Conditions	p. 498
11.3 Complementary Pivot Problems	p. 499
11.4 Goal Programming	p. 507
11.5 Summary	p. 518
References	p. 518
Problems	p. 521
12 Comparison of Constrained Optimization Methods	p. 530
12.1 Software Availability	p. 530
12.2 A Comparison Philosophy	p. 531
12.3 Brief History of Classical Comparative Experiments	p. 533
12.3.1 Preliminary and Final Results	p. 535
12.4 Summary	p. 539
References	p. 539
13 Strategies for Optimization Studies	p. 542
13.1 Model Formulation	p. 543
13.1.1 Levels of Modeling	p. 544
13.1.2 Types of Models	p. 548
13.2 Problem Implementation	p. 552
13.2.1 Model Assembly	p. 553
13.2.2 Preparation for Solution	p. 554
13.2.3 Execution Strategies	p. 580
13.3 Solution Evaluation	p. 588
13.3.1 Solution Validation	p. 589
13.3.2 Sensitivity Analysis	p. 590
13.4 Summary	p. 594
References	p. 594
Problems	p. 597
14 Engineering Case Studies	p. 603
14.1 Optimal Location of Coal-Blending Plants by Mixed-Integer Programming	p. 603
14.1.1 Problem Description	p. 604
14.1.2 Model Formulation	p. 604
14.1.3 Results	p. 609
14.2 Optimization of an Ethylene Glycol-Ethylene Oxide Process	p. 610
14.2.1 Problem Description	p. 610
14.2.2 Model Formulation	p. 612
14.2.3 Problem Preparation	p. 618
14.2.4 Discussion of Optimization Runs	p. 618
14.3 Optimal Design of a Compressed Air Energy Storage System	p. 621
14.3.1 Problem Description	p. 621
14.3.2 Model Formulation	p. 622
14.3.3 Numerical Results	p. 627
14.3.4 Discussion	p. 629
14.4 Summary	p. 630
References	p. 631
Appendix A Review of Linear Algebra	p. 633
A.1 Set Theory	p. 633
A.2 Vectors	p. 633
A.3 Matrices	p. 634
A.3.1 Matrix Operations	p. 635
A.3.2 Determinant of a Square Matrix	p. 637
A.3.3 Inverse of a Matrix	p. 637
A.3.4 Condition of a Matrix	p. 639
A.3.5 Sparse Matrix	p. 639
A.4 Quadratic Forms	p. 640
A.4.1 Principal Minor	p. 641
A.4.2 Completing the Square	p. 642
A.5 Convex Sets	p. 646
Appendix B Convex and Concave Functions	p. 648
Appendix C Gauss-Jordan Elimination Scheme	p. 651
Author Index	p. 653
Subject Index	p. 659

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