Bayesian Heuristic Approach to Discrete and Global Optimization - Gintaras Reklaitis

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Résumé :
Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems. This book is the first to demonstrate that this framework is also well suited for the exploitation of heuristic methods in the solution of such problems, especially those of large scale for which exact optimization approaches can be prohibitively costly. The book covers all aspects ranging from the formal presentation of the Bayesian Approach, to its extension to the Bayesian Heuristic Strategy, and its utilization within the informal, interactive Dynamic Visualization strategy. 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. The software required for implementation of the Bayesian Heuristic Approach is included. Although some knowledge of mathematical statistics is necessary in order to fathom the theoretical aspects of the development, no specialized mathematical knowledge is required to understand the application of the approach or to utilize the software which is provided. Audience: The book is of interest to both researchers in operations research, systems engineering, and optimization methods, as well as applications specialists concerned with the solution of large scale discrete and/or nonconvex optimization problems in a broad range of engineering and technological fields. It may be used as supplementary material for graduate level courses.

Sommaire:
Preface. Part I: Bayesian Approach. 1. Different Approaches to Numerical Techniques and Different Ways of Regarding Heuristics: Possibilities and Limitations. 2. Information-Based Complexity (IBC) and the Bayesian Heuristic Approach. 3. Mathematical Justification of the Bayesian Heuristics Approach. Part II: Global Optimization. 4. Bayesian Approach to Continuous Global and Stochastic Optimization. 5. Examples of Continuous Optimization. 6. Long-Memory Processes and Exchange Rate Forecasting. 7. Optimization Problems in Simple Competitive Model. Part III: Networks Optimization. 8. Application of Global Line-Search in the Optimization of Networks. 9. Solving Differential Equations by Event-Driven Techniques for Parameter Optimization. 10. Optimization in Neural Networks. Part IV: Discrete Optimization. 11. Bayesian Approach to Discrete Optimization. 12. Examples of Discrete Optimization. 13. Application of BHA to Mixed Integer Nonlinear Programming (MINLP) Part V: Batch Process Scheduling. 14. Batch/Semi-Continuous Process Scheduling Using MRP Heuristics. 15. Batch Process Scheduling Using Simulated Annealing. 16. Genetic Algorithms for Batch Process Scheduling Using BHA and MILP Formulation. Part VI: Software For Global Optimization. 17. Introduction to Global Optimization Software (GM). 18. Portable Fortran Library for Continuous Global Optimization. 19. Software for Continuous Global Optimization Using Unix C++. 20. Examples of Unix C++ Software Applications. Part VII: Visualization. 21. Dynamic Visualization in Modeling and Optimization of Ill Defined Problems: Case Studies and Generalizations. References. Index.