Constraint Satisfaction Problems: CSP Formalisms and Techniques

A Constraint Satisfaction Problem (CSP) consists of a set of variables, a domain of values for each variable and a set of constraints. The objective is to assign a value for each variable such that all constraints are satisfied. CSPs continue to receive increased attention because of both their high complexity and their omnipresence in academic, industrial and even real-life problems. This is why they are the subject of intense research in both artificial intelligence and operations research. This book introduces the classic CSP and details several extensions/improvements of both formalisms and techniques in order to tackle a large variety of problems. Consistency, flexible, dynamic, distributed and learning aspects are discussed and illustrated using simple examples such as the n-queen problem. Contents 1. Foundations of CSP. 2. Consistency Reinforcement Techniques. 3. CSP Solving Algorithms. 4. Search Heuristics. 5. Learning Techniques. 6. Maximal Constraint Satisfaction Problems. 7. Constraint Satisfaction and Optimization Problems. 8. Distibuted Constraint Satisfaction Problems. About the Authors Khaled Ghedira is the general managing director of the Tunis Science City in Tunisia, Professor at the University of Tunis, as well as the founding president of the Tunisian Association of Artificial Intelligence and the founding director of the SOIE research laboratory. His research areas include MAS, CSP, transport and production logistics, metaheuristics and security in M/E-government. He has led several national and international research projects, supervised 30 PhD theses and more than 50 Master’s theses, co-authored about 300 journal, conference and book research papers, written two text books on metaheuristics and production logistics and co-authored three others.

Table of Contents:
Preface ix Introduction xi Chapter 1. Foundations of CSP 1 1.1. Basic concepts 1 1.2. CSP framework 3 1.2.1. Formalism 4 1.2.2. Areas of application 6 1.2.3. Extensions 17 1.3. Bibliography 22 Chapter 2. Consistency Reinforcement Techniques 29 2.1. Basic notions 29 2.1.1. Equivalence 29 2.1.2. K-consistency 30 2.2. Arc consistency reinforcement algorithms 32 2.2.1. AC-1 33 2.2.2. AC-2 36 2.2.3. AC-3 38 2.2.4. AC-4 41 2.2.5. AC-5 44 2.2.6. AC-6 50 2.2.7. AC-7 54 2.2.8. AC2000 61 2.2.9. AC2001 65 2.3. Bibliography 69 Chapter 3. CSP Solving Algorithms 73 3.1. Complete resolution methods 73 3.1.1. The backtracking algorithm 74 3.1.2. Look-back algorithms 76 3.1.3. Look-ahead algorithms 86 3.2. Experimental validation 92 3.2.1. Random generation of problems 92 3.2.2. Phase transition 94 3.3. Bibliography 96 Chapter 4. Search Heuristics 99 4.1. Organization of the search space 99 4.1.1. Parallel approaches 99 4.1.2. Distributed approaches 100 4.1.3. Collaborative approaches 102 4.2. Ordering heuristics 102 4.2.1. Illustrative example 102 4.2.2. Variable ordering 109 4.2.3. Value ordering 115 4.2.4. Constraints-based ordering 116 4.3. Bibliography 117 Chapter 5. Learning Techniques 121 5.1. The “nogood” concept 122 5.1.1. Example of union and projection 123 5.1.2. Use of nogoods 125 5.1.3. Nogood handling 125 5.2. Nogood-recording algorithm 126 5.3. The nogood-recording-forward-checking algorithm 129 5.4. The weak-commitment-nogood-recording algorithm 132 5.5. Bibliography 133 Chapter 6. Maximal Constraint Satisfaction Problems 135 6.1. Branch and bound algorithm 136 6.2. Partial Forward-Checking algorithm 138 6.3. Weak-commitment search 142 6.4. GENET method 144 6.5. Distributed simulated annealing 146 6.6. Distributed and guided genetic algorithm 147 6.6.1. Basic principles 148 6.6.2. The multi-agent model 150 6.6.3. Genetic process 152 6.6.4. Extensions 158 6.7. Bibliography 162 Chapter 7. Constraint Satisfaction and Optimization Problems 165 7.1. Formalism 166 7.2. Resolution methods 166 7.2.1. Branch-and-bound algorithm 167 7.2.2. Tunneling algorithm 170 7.3. Bibliography 178 Chapter 8. Distributed Constraint Satisfaction Problems 181 8.1. DisCSP framework 183 8.1.1. Formalism 183 8.1.2. Distribution modes 185 8.1.3. Communication models 191 8.1.4. Convergence properties 193 8.2. Distributed consistency reinforcement 195 8.2.1. The DisAC-4 algorithm 196 8.2.2. The DisAC-6 algorithm 197 8.2.3. The DisAC-9 algorithm 198 8.2.4. The DRAC algorithm 199 8.3. Distributed resolution 200 8.3.1. Asynchronous backtracking algorithm 201 8.3.2. Asynchronous weak-commitment search 204 8.3.3. Asynchronous aggregation search 205 8.3.4. Approaches based on canonical distribution 207 8.3.5. DOC approach 208 8.3.6. Generalization of DisCSP algorithms to several variables 214 8.4. Bibliography 215 Index 221

About the Author :
Khaled Ghedira is Professor at the University of Tunis, Tunisia.