Stochastic Adaptive Search for Global Optimization, 2003 Nonconvex Optimization and Its Applications Series, Vol. 72

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 other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo­ rithms, are gaining in popularity among practitioners and engineers be­ they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these stochastic methods is not well under­ stood. In this book, an attempt is made to describe the theoretical prop­ erties of several stochastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and de­ velopment of stochastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical anal­ ysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use stochastic adaptive search methods.

Preface. Part I: Theory. Some History Leading to Design Criteria for Bayesian Prediction, A.C. Atkinson, V.V. Fedorov. Optimal Designs for the Evaluation of an Extremum Point, R.C.H. Cheng, et al. On Regression Experiment Design in the Presence of Systematic Error, S.M. Ermakov. Gröbner Basis Methods in Mixture Experiments and Generalisations, B. Giglio, et al. Efficient Designs for Paired Comparisons with a Polynomial Factor, H. Großmann, et al. On Generating and Classifying All qn-m Regular Designs for Square-Free q, P.J. Laycock, P.J. Rowley. Second-Order Optimal Sequential Tests, M.B. Malyutov, I.I. Tsitovich. Variational Calculus in the Space of Measures and Optimal Design, I. Molchanov, S. Zuyev. On the Efficiency of Generally Balanced Designs Analysed by Restricted Maximum Likelihood, H. Monod. Concentration Sets, Elfving Sets and Norms in Optimum Design, A. Pázman. Sequential Construction of an Experimental Design from an I.I.D. Sequence of Experiments without Replacement, L. Pronzato. Optimal Characteristic Designs for Polynomial Models, J.M. Rodríguez-Díaz, J. López-Fidalgo. A Note on Optimal Bounded Designs, M. Sahm, R. Schwabe. Construction of Constrained Optimal Designs, B. Torsney, S. Mandal. Part II: Applications. Pharmaceutical Applications of a Multi-Stage Group Testing Method, B. Bond, et al. Block Designs for Comparison of Two Test Treatments with a Control, S.M. Bortnick, et al. Optimal Sampling Design with Random Size Clusters for a Mixed Model with Measurement Errors, A. Giovagnoli, L. Martino. Optimizing a Unimodal Response Function for Binary Variables, J. Hardwick, Q.F. Stout. An Optimizing Up-And-Down Design, E.E. Kpamegan, N. Flournoy. Further Results on Optimal and Efficient Designs for Constrained Mixture Experiments, R.J. Martin, et al. Coffee-House Designs, W.G. Mü,ller. (D,t, C)-Optimal Run Orders, L. Tack, M. Vandebroek. Optimal Design in Flexible Models, including Feed-Forward Networks and Nonparametric Regression, D.M. Titterington. On Optimal Designs for High Dimensional Binary Regression Models, B. Torsney, N. Gunduz. Planning Herbicide Dose-Response Bioassays Using the Bootstrap, S.S. Zocchi, C.G. Borges Demé,trio. Photo Gallery. Optimum Design 2000: List of Participants.