Non-Convex Multi-Objective Optimization

1. Front Matter

   Pages i-xi

   PDF

2. Basic Concepts

   1. Front Matter

      Pages 1-1

      PDF

   2. Definitions and Examples

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 3-12

   3. Scalarization

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 13-18

   4. Approximation and Complexity

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 19-31

   5. A Brief Review of Non-convex Single-Objective Optimization

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 33-42

3. Theory and Algorithms

   1. Front Matter

      Pages 43-43

      PDF

   2. Multi-Objective Branch and Bound

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 45-56

   3. Worst-Case Optimal Algorithms

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 57-95

   4. Statistical Models Based Algorithms

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 97-120

   5. Probabilistic Bounds in Multi-Objective Optimization

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 121-135

4. Applications

   1. Front Matter

      Pages 137-138

      PDF

   2. Visualization of a Set of Pareto Optimal Decisions

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 139-145

   3. Multi-Objective Optimization Aided Visualization of Business Process Diagrams

      • Panos M. Pardalos, Antanas Žilinskas, Julius Žilinskas

      Pages 147-178

5. Back Matter

   Pages 179-192

   PDF

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.  

• Branch-and-Bound approach
• Lipschitz optimization
• applications in engineering
• non-convex multi-objective optimization
• randomized algorithms
• software and applications
• Scalarization
• Tchebycheff Method
• Pareto Sets
• Normal Boundary Intersection
• Statistical Models for Global Optimization
• Optimal Algorithms for Lipschitz Functions
• Optimal Passive Algorithm
• Optimal Sequential Algorithm
• Multidimensional Bi-Objective Lipschitz Optimization
• Pareto Frontier
• Trisection of a Hyper-rectangle
• Pareto Optimal Decisions
• Binary-Linear Model
• continuous problems

“Readers will definitely enjoy this book, because all surveyed topics are rigorously exposed. Moreover, since the main prerequisites are provided, the book is essentially self-contained and easy to read. The authors have also included many illustrative pictures that ensure a good understanding of technical concepts and results. … this book is an excellent reference for researchers and graduate students in both pure and applied mathematics, as well as other disciplines.” (Nicolae Popovici, Mathematical Reviews, August, 2018)​

• Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

  Panos M. Pardalos

• Institute of Mathematics & Informatics, Vilnius University, Vilnius, Lithuania

  Antanas Žilinskas, Julius Žilinskas

Policies and ethics