Bayesian heuristic approach to discrete and global optimization. Algorithms, visualization, software, and applications. Incl. 2 disks
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 application areas which are discussed include scheduling and visualization problems in chemical engineering, manufacturing process control, and epidemiology. Computational results and comparisons with a broad range of test examples are presented.
interactive dynamic visualization strategy
scientific article; zbMATH DE number 976406