Global Optimization : From Theory to Implementation

From Theory to Implementation

By: Leo Liberti (Editor), Nelson Maculan (Editor)

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Hardcover | 1 February 2006

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Most books about global optimization describe the theory of the algorithms, whereas a given implementation's quality never depends exclusively on the theoretical soundness of the algorithms that are implemented. The literature rarely discusses the tuning of algorithmic parameters, implementation tricks, software architectures, and the embedding of local solvers within global solvers. And yet, there are many good software implementations "out there" from which the entire community could learn something.

The scope of this book is moving a few steps toward the systematization of the path that goes from the invention to the implementation and testing of a global optimization algorithm. Some of the contributors to the book are famous and some are less well-known, but all are experts in the discipline of actually getting global optimization to work. Thus, the papers in this book address the following topics:

- Descriptions of new implementations of general-purpose or problem-specific global optimization algorithms

- New algorithms in global optimization (some with numerical results and a discussion of the implementation)

- Surveys discussing existing software packages.

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Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set	p. 3
Introduction	p. 3
Some basic concepts and results of monotonic optimization	p. 5
Problems with composite monotonic constraints	p. 7
Constrained optimization over the efficient set	p. 11
Solution method for problem (Q)	p. 15
Improvements for problems (OWE) and (OE)	p. 19
Problems with a composite monotonic objective function	p. 25
Illustrative examples and computational results	p. 26
References	p. 29
On a Local Search for Reverse Convex Problems	p. 33
Introduction	p. 33
Some features of RCP	p. 34
Local search methods	p. 36
Computational testing	p. 40
Conclusion	p. 42
References	p. 42
Some Transformation Techniques in Global Optimization	p. 45
Introduction	p. 45
The MINLP Problem	p. 46
The transformation approach	p. 47
Examples of transformations	p. 52
The GGPECP algorithm	p. 55
Convergence to the globally optimal solution	p. 57
A numerical example	p. 59
Some aspects on the numerical solution approach	p. 64
Conclusions	p. 70
References	p. 71
Solving Nonlinear Mixed Integer Stochastic Problems: a Global Perspective	p. 75
Introduction	p. 76
Motivations	p. 76
SMINLP: state of the art	p. 77
Problem formulation	p. 84
The two-phase solution approach	p. 86
Illustrative application: the Stochastic Trim Loss Problem	p. 98
Concluding Remarks	p. 104
References	p. 106
Application of Quasi Monte Carlo Methods in Global Optimization	p. 111
Introduction	p. 111
Analysis of Quasirandom Search methods	p. 114
Single linkage and multilevel single linkage methods	p. 117
Computational experiments	p. 120
Conclusion	p. 131
References	p. 131
GLOB - A new VNS-based Software for Global Optimization	p. 135
Introduction	p. 135
VNS methodology	p. 136
Software package GLOB	p. 137
Numerical experiments	p. 141
Conclusion	p. 147
References	p. 148
Disciplined Convex Programming	p. 155
Introduction	p. 155
Motivation	p. 156
Convex programming	p. 162
Modeling frameworks	p. 169
Disciplined convex programming	p. 171
The convexity ruleset	p. 172
The atom library	p. 183
Verification	p. 188
Creating disciplined convex programs	p. 191
Implementing atoms	p. 193
Conclusion	p. 199
References	p. 200
Writing Global Optimization Software	p. 211
Introduction	p. 211
Global Optimization algorithms	p. 214
Global Optimization software	p. 223
Optimization software framework design	p. 232
Symbolic manipulation of mathematical expressions	p. 240
Local solvers	p. 247
Global solvers	p. 248
Conclusion	p. 257
References	p. 258
MathOptimizer Professional: Key Features and Illustrative Applications	p. 263
Introduction	p. 263
Global Optimization	p. 266
LGO Solver Suite	p. 267
MathOptimizer Professional	p. 268
Illustrative applications: solving sphere packing models	p. 271
Conclusions	p. 276
References	p. 277
Variable Neighborhood Search for Extremal Graphs 14: The AutoGraphiX 2 System	p. 281
Introduction	p. 281
AGX 2 Interactive functions	p. 283
Algebraic syntax used in AutoGraphiX	p. 291
Optimization using Variable Neighborhood Search	p. 294
AutoGraphiX Tasks	p. 299
Automated proofs	p. 301
Some examples	p. 305
Conclusion	p. 308
References	p. 308
From Theory to Implementation: Applying Metaheuristics	p. 311
Introduction	p. 311
Class hierarchy	p. 316
Implementation: The p-Median Problem	p. 333
Conclusions	p. 338
References	p. 339
ooMILP - AC++ Callable Object-oriented Library and the Implementation of its Parallel Version using CORBA	p. 353
Introduction	p. 353
ooMILP Overview	p. 356
C++ objects and pre-CORBA serial implementation	p. 357
Initial CORBA Version	p. 361
Partially decomposable MILPs	p. 366
Parallel solution software architecture	p. 368
Conclusions	p. 375
References	p. 375
Global Order-Value Optimization by means of a Multistart Harmonic Oscillator Tunneling Strategy	p. 379
Introduction	p. 379
Local algorithm	p. 381
Lissajous motions	p. 382
Global algorithm	p. 384
Hidden patterns	p. 387
Numerical experiments	p. 388
Conclusions	p. 394
References	p. 397
On generating Instances for the Molecular Distance Geometry Problem	p. 405
Introduction	p. 405
Moré-Wu instances	p. 406
New instances	p. 407
Conclusion	p. 413
References	p. 414
Index	p. 415
Table of Contents provided by Publisher. All Rights Reserved.

Global Optimization : From Theory to Implementation

From Theory to Implementation

At a Glance

Hardcover

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