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.

Provides reader with a methodological and theoretical basis for developing and investigating optimization heuristics Summarizes basic ideas and presents recent progress and new results Includes an extensive bibliography with old Russian articles as well as new English papers Includes an extensive discussion on probabilistic and statistical models used in the global random search Expands upon more sophisticated techniques including random and semi-random coverings, stratified sampling schemes, Markovian algorithms and populations based algorithms Includes supplementary material: sn.pub/extras

Autorentext

Nina Golyandina received her MSc and PhD degrees in mathematics at St.Petersburg State University, Russia, in 1985 and 1998, respectively. She started to work at St.Petersburg State University in 1985, where she is currently an Associate Professor of Statistical Modelling Department, Faculty of Mathematics and Mechanics. Her main areas of research interest are statistical modeling and applied statistics, especially time series investigation by means of singular spectrum analysis. Dr. Golyandina is the coauthor of three monographs on singular spectrum analysis and of more than 30 research papers in refereed journals related to applied probability and statistics. During last twenty years, she was involved in different projects related to singular spectrum analysis. Anatoly Zhigljavsky has received his BSc, MSc and PhD degrees in mathematics and statistics at Faculty of Mathematics, St.Petersburg State University. He became professor of statistics at the St.Petersburg StateUniversity in 1989. Since 1997 he is a professor, Chair in Statistics at Cardiff University. Anatoly Zhigljavsky is the author or co-author of 10 monographs on the topics of time series analysis, stochastic global optimization, optimal experimental design and dynamical systems; he is the editor/co-editor of 9 books on various topics and the author of more than 150 research papers in refereed journals. He has organized several major conferences on time series analysis, experimental design and global optimization. In 2019, he has received a prestigious Constantine Caratheodory award by the International Society for Global Optimization for his contribution to stochastic optimization.

Klappentext

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.

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