Constraint and Integer Programming: Toward a Unified Methodology

ISBN-13: 9781461347194 / Angielski / Miękka / 2012 / 370 str.

Michela Milano

Opis

Despite differing origins, constraint programming and mathematical programming are beginning to merge. Constraint programming has grown out of the logic programming community as part of an effort to embed constraints in a programming language. Mathematical programming, a much older field, is rooted in the mathematics of optimization. Because these two areas have complementary strengths, there are ongoing efforts to integrate the two.Constraint and Integer Programming presents some of the basic ideas of constraint programming and mathematical programming, explores approaches to integration, brings us up to date on heuristic methods, and attempts to discern future directions in this fast-moving field.
Constraint and Integer Programming is organized as follows: Chapter 1 is a high level overview of the main concepts of Constraint Programming (CP) and Integer Programming (IP) used in the book. Chapter 2 informally introduces integration methods describing and classifying the main works in the field. Chapter 3 outlines a unifying framework which involves the main concepts of CP and IP, underlining similarities and differences, and stating the basis for possible integrations. Chapter 4 describes global constraints as a vehicle for integrating IP concepts in CP in a transparent way for the user. Chapter 5 presents various ways to integrate relaxations in Constraint Programming focussing on global constraints. Chapter 6 presents hybrid solvers and Chapter 7 outlines Column Generation and its integration in Constraint Programming. Chapter 8 examines randomization and problem structure as a basis for understanding the intrinsic difficulty of the combinatorial problems. Chapter 9 studies the use of local search and meta-heuristics in CP. Chapter 10 is devoted to open perspectives and future directions.

Spis treści

List of Figures. List of Tables. Preface. Contributing Authors. Foreword; J. Hooker. 1: Constraint and Integer Programming; M. Milano, M. Trick. 1. Introduction. 2. CP(FD) Basic Concepts. 3. Integer Linear Programming Basic Concepts. 4. Incomplete search strategies. 5. Conclusion. References. 2: Two Generic Schemes for Efficient and Robust Cooperative Algorithms; E. Danna, C. Le Pape. 1. Introduction. 2. Operations Research Algorithms and Constraint Programming. 3. Operations Research Algorithms and Mixed Integer Programming. 4. Constraint Programming and Mixed Integer Programming. 5. Operations Research Algorithms and Local Search. 6. Mixed Integer Programming and Local Search. 7. Constraint Programming and Local Search. References. 3: Branch-and-Infer; A. Bockmayr, T. Kasper. 1. Introduction. 2. Modeling in CP and IP. 3. An illustrating example: discrete tomography. 4. Branch and Infer. 5. Symbolic constraints in IP. 6. Example: Symbolic constraints for supply chain planning. 7. Summary. References. 4: Global Constraints and Filtering Algorithms; J.-C. Régin. 1. Introduction. 2. Global Constraints. 3. Filtering Algorithms. 4. Two Successful Filtering Algorithms. 5. Global Constraints and Over-constrained Problems. 6. Quality of Filtering Algorithms. 7. Discussion. 8. Conclusion. References. 5:Exploiting relaxations in CP; F. Focacci, A. Lodi, M. Milano. 1. Introduction and Motivation. 2. Integer Linear Programming and Relaxations. 3. Integrating Relaxations in CP. 4. Relax to propagate. 5. Relax to guide the search. 6. A case study: global optimization constraints for a Path constraint. 6: Hybrid Problem Solving in ECLiPSe; F. Ajili, M.G. Wallace. 1. Introduction. 2. Integration of Constraints and Operations Research. 3. Language Ingredients for Hybrid Solvers. 4. ECLiPSe as a Platform for Building Hybrid Algorithms. 5. Programming a Hybrid Search in ECLiPSe. 6. Conclusion. References. 7: CP Based Branch-and-Price; K. Easton, G. Nemhauser, M. Trick. 1. Introduction. 2. Three Illustrative Examples. 3. Implementation Issues. 4. Future Directions for CP Based Branch-and-Price. References. 8: Randomized Backtrack Search; C.P. Gomes. 1. Introduction. 2. Randomization of Backtrack Search Methods. 3. Formal Models of Heavy-Tailed Behavior. 4. Heavy and Fat-Tailed Distributions. 5. Heavy and Fat-Tailed Distributions in Backtrack Search. 6. Restart Strategies. 7. Portfolio Strategies. 8. Conclusions. References. 9: Local Search and Constraint Programming: LS and CP illustrated on a transportation Problem; F. Focacci, F. Laburthe, A. Lodi. 1. Introduction. 2. A didactic transportation problem. 3. A CP approach