Non-Convex Multi-Objective Optimization

Description

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.   Front Matter ....Pages i-xi Front Matter ....Pages 1-1 Definitions and Examples (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 3-12 Scalarization (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 13-18 Approximation and Complexity (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 19-31 A Brief Review of Non-convex Single-Objective Optimization (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 33-42 Front Matter ....Pages 43-43 Multi-Objective Branch and Bound (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 45-56 Worst-Case Optimal Algorithms (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 57-95 Statistical Models Based Algorithms (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 97-120 Probabilistic Bounds in Multi-Objective Optimization (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 121-135 Front Matter ....Pages 137-138 Visualization of a Set of Pareto Optimal Decisions (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 139-145 Multi-Objective Optimization Aided Visualization of Business Process Diagrams (Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas)....Pages 147-178 Back Matter ....Pages 179-192