Bayesian Heuristic Approach to Discrete and Global Optimization

1. Front Matter

   Pages i-xv

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2. Bayesian Approach

   1. Front Matter

      Pages 1-1

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   2. Different Approaches to Numerical Techniques and Different Ways of Regarding Heuristics: Possibilities and Limitations

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 3-29

   3. Information-Based Complexity (IBC) and the Bayesian Heuristic Approach

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 31-46

   4. Mathematical Justification of the Bayesian Heuristics Approach

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 47-59

3. Global Optimization

   1. Front Matter

      Pages 61-61

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   2. Bayesian Approach to Continuous Global and Stochastic Optimization

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 63-69

   3. Examples of Continuous Optimization

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 71-82

   4. Long-Memory Processes and Exchange Rate Forecasting

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 83-117

   5. Optimization Problems in Simple Competitive Model

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 119-127

4. Networks Optimization

   1. Front Matter

      Pages 129-129

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   2. Application of Global Line-Search in the Optimization of Networks

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 131-138

   3. Solving Differential Equations by Event- Driven Techniques for Parameter Optimization

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 139-151

   4. Optimization in Neural Networks

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 153-174

5. Discrete Optimization

   1. Front Matter

      Pages 175-175

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   2. Bayesian Approach to Discrete Optimization

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 177-194

   3. Examples of Discrete Optimization

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 195-219

   4. Application of BHA to Mixed Integer Nonlinear Programming (MINLP)

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 221-230

6. Batch Process Scheduling

   1. Front Matter

      Pages 231-231

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   2. Batch/Semi-Continuous Process Scheduling Using MRP Heuristics

      • Jonas Mockus, William Eddy, Audris Mockus, Linas Mockus, Gintaras Reklaitis

      Pages 233-244

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.

• Fathom
• algorithm
• algorithms
• chemical engineering
• decision theory
• genetic algorithms
• global optimization
• linear optimization
• mathematical statistics
• network
• nonlinear optimization
• operations research
• optimization
• scheduling
• statistics
• combinatorics

• Institute of Mathematics and Informatics, Kaunas Technological University, Vilnius, Lithuania

  Jonas Mockus

• Vytautas Magnus University, Vilnius, Lithuania

  Jonas Mockus

• Vilnius Technical University, Vilnius, Lithuania

  Jonas Mockus

• Department of Statistics, Carnegie-Mellon University, Pittsburgh, USA

  William Eddy

• Lucent Technologies AT&T Bell Laboratories, Pittsburgh, USA

  Audris Mockus

• School of Chemical Engineering, Purdue University, W. Lafayette, USA

  Linas Mockus, Gintaras Reklaitis

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