Stochastic Adaptive Search for Global Optimization
The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these othe
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N onconvex Optimization and Its Applications Volume72 Managing Editor:
Panos Pardalos University ofFlorida, U.SA. Advisory Board: J. R. Birge University ofMichigan, U.SA.
Ding-ZhuDu University ofMinnesota, U.SA. C. A Floudas Princeton University, U.SA. J. Moclcus Lithuanian Academy ofSciences, Lithuania H. D. Sherali Virginia Polytechnic Institute and State University, U.SA.
G. Stavroulakis Technical University Braunschweig, Germany
STOCHASTIC ADAPTIVE SEARCH FOR GLOBAL OPTIMIZATION
ZELDA B. ZABINSKY
University of Washington Seattle, Washington, USA
Springer Science+Business Media, LLC
Library of Congress Cataloging-in-Publication
Zabinsky, Zelda B. Stochastic Adaptive Search for Global Optimization ISBN 978-1-4613-4826-9 DOI 10.1007/978-1-4419-9182-9
ISBN 978-1-4419-9182-9 (eBook)
Copyright © 2003 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1st edition 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. PermissionsforbookspublishedintheUSA:permi ssj ons@wkap com Permissions for books published in Europe: [email protected] Printed on acid-free paper.
I dedicate this book to my parents, Joe and Helen Zabinsky, to show my love and appreciation.
Contents
List of Figures List of Tables Preface 1. INTRODUCTION Classification of Optimization Problems 1 2 Types of Algorithms Definitions and Assumptions 3 3.1 Assumptions for Continuous Problems 3.2 Assumptions for Discrete Problems 3.3 Mixed Continuous-discrete Problems Overview of Random Search Methods 4 4.1 Enumeration or Exhaustive Search Grid Search Pure Random Search Other Covering Methods 4.2 Sequential Random Search Simulated Annealing Step Size Algorithms Convergence 4.3 Two-Phase Methods Genetic Algorithms 4.4 4.5 Other Stochastic Methods Overview of this Book 5 Summary 6
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viii STOCHASTIC ADAPTIVE SEARCH FOR GLOBAL OPTIMIZATION
2. PURE RANDOM SEARCH AND
PURE ADAPTIVE SEARCH 1 Pure Random Search (PRS) 2 Pure Adaptive Search (PAS) Comparison of PRS and PAS 3 Distribution of Improvement for PAS 4 Continuous PAS Distribution 4.1 4.2 Finite PAS Distribution Linearity Result for PAS 5 Summary 6
3. HESITANT ADAPTIVE SEARCH 1 Hesitant Adaptive Search (HAS) 2 Number of HAS Iterations to Convergence 2.1 Continuous HAS Distribution 2.2 Discrete HAS Distribution General HAS Distribution 2.3 Numerical Examples of HAS 3 4 Combination of PRS and PAS, {1-p)PRS+pPAS 4.1 Continuous PRS and PAS Combination 4.2 Discrete PRS and PAS Combination 5 ·Summary
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