Stochastic Global Optimization

ISBN-13: 9781441944856 / Angielski / Miękka / 2010 / 262 str.

Anatoly Zhigljavsky; Antanasz Zilinskas

Opis

This book aims to cover major methodological and theoretical developments in the ?eld of stochastic global optimization. This ?eld includes global random search and methods based on probabilistic assumptions about the objective function. We discuss the basic ideas lying behind the main algorithmic schemes, formulate the most essential algorithms and outline the ways of their theor- ical investigation. We try to be mathematically precise and sound but at the same time we do not often delve deep into the mathematical detail, referring instead to the corresponding literature. We often do not consider the most g- eral assumptions, preferring instead simplicity of arguments. For example, we only consider continuous ?nite dimensional optimization despite the fact that some of the methods can easily be modi?ed for discrete or in?nite-dimensional optimization problems. The authors' interests and the availability of good surveys on particular topics have in uenced the choice of material in the book. For example, there are excellent surveys on simulated annealing (both on theoretical and - plementation aspects of this method) and evolutionary algorithms (including genetic algorithms). We thus devote much less attention to these topics than they merit, concentrating instead on the issues which are not that well d- umented in literature. We also spend more time discussing the most recent ideas which have been proposed in the last few years.

Recenzje

From the reviews:

"This excellent book is written for researchers interested in global optimization. ... the approach of carrying through from basic ideas to the most recent techniques will make this a valuable resource for the initiated. ... Gathering together contemporary methods and developments in stochastic global optimization, this text presents four chapters." (Tom Schulte, MathDL, February, 2008)

"For global optimization, based on former monographs and articles of the authors on (global) random search, in this book global random search methods and stochastic models for the objective function are presented. ... This well-written book contains many references on the field of (global) random search techniques." (Kurt Marti, Mathematical Reviews, Issue 2008 j)

"The aim of the book is to present the major methodological and theoretical developments in the field of stochastic global optimization including global random search and methods based on probabilistic assumptions about the objective function. The book contains four chapters. ... The book also contains an index. The book is well written and the presentation is ... self-contained." (I. M. Stancu-Minasian, Zentralblatt MATH, Vol. 1136 (14), 2008)

Spis treści

Basic Concepts and Ideas.- Global Random Search: Fundamentals and Statistical Inference.- Global Random Search: Extensions.- Methods Based on Statistical Models of Multimodal Functions.

Blurb

This book presents the main methodological and theoretical developments in stochastic global optimization. The extensive text is divided into four chapters; the topics include the basic principles and methods of global random search, statistical inference in random search, Markovian and population-based random search methods, methods based on statistical models of multimodal functions and principles of rational decisions theory.

Key features:

* Inspires readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods;

* Includes a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms;

* Expands upon more sophisticated techniques including random and semi-random coverings, stratified sampling schemes, Markovian algorithms and population based algorithms;

*Provides a thorough description of the methods based on statistical models of objective function;

*Discusses criteria for evaluating efficiency of optimization algorithms and difficulties occurring in applied global optimization.

Stochastic Global Optimization is intended for mature researchers and graduate students interested in global optimization, operations research, computer science, probability, statistics, computational and applied mathematics, mechanical and chemical engineering, and many other fields where methods of global optimization can be used.