Bayesian heuristic approach to discrete and global optimization. Algorithms, visualization, software, and applications. Incl. 2 disks
type: Item
instance of: scholarly article
title: Bayesian heuristic approach to discrete and global optimization. Algorithms, visualization, software, and applications. Incl. 2 disks
zbMATH Open document ID: 0864.65036
author: Jonas Mockus
author: Audris Mockus
author: William F. Eddy
author: L. J. Mockus
author: Gintaras V. Reklaitis
published in: Nonconvex Optimization and Its Applications
publication date: 1997-02-05T00:00:00Z
review text: Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. The book covers all aspects ranging from the formal presentation of the Bayesian approach, to its extension to the Bayesian heuristic stragety, and its utilization within the informal, interactive dynamic visualization strategy. In the introductory Part I, Bayesian approach, the results are discussed at several levels in order to facilitate understanding of what the book is about. At the first level (Chapter 1), only the general ideas are outlined. At the second level (Chapter 2), the Bayesian heuristic approach (BHA) is discussed using the terms of the well-known complexity theory. In Chapter 3 mathematical justification of BHA is considered. In Part II, Global optimization, the theory and some application examples of the Bayesian approach to continuous global optimization are described. In Part III, Network optimization, useful heuristics are considered and the power of BHA is discussed for network problems. In Part IV, Discrete optimization, it is shown how to reduce discrete optimization problems to continuous stochastic ones, using the Bayesian heuristic approach. The traditional knapsack, traveling salesman, and flow-shop problems are considered as test problems. The application of BHA to mixed integer nonlinear programming (MINLP) is discussed. In Part V, Batch process scheduling, the real scheduling problem is considered as an example of BHA application, using various heuristics. In Part VI, Software for global optimization, the global optimization software is described for both UNIX and MS-DOS environments. In Part VII, Visualization, the dynamic visualization approach is considered as a promising technique for solving ill-defined optimization problems. The developed framework is applied in forecasting, in neural network optimization, and in a large number of discrete and continuous optimization problems. Specific a…
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90Cxx
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 90-02
zbMATH DE Number: 976406
zbMATH Keywords: monograph
zbMATH Keywords: network optimization
zbMATH Keywords: discrete optimization
zbMATH Keywords: batch process scheduling
zbMATH Keywords: software
zbMATH Keywords: computational results
zbMATH Keywords: Bayesian decision theory
zbMATH Keywords: nonconvex optimization
zbMATH Keywords: Bayesian approach
zbMATH Keywords: Bayesian heuristic stragety
zbMATH Keywords: interactive dynamic visualization strategy
zbMATH Keywords: global optimization
zbMATH Keywords: knapsack
zbMATH Keywords: traveling salesman
zbMATH Keywords: flow-shop problems
zbMATH Keywords: mixed integer nonlinear programming
zbMATH Keywords: neural network optimization
reviewed by: George S. Stavrakakis
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 976406