N o d’ordre: 2 4 5 ÉCOLE CENTRALE DE LILLE THÈSE présentée en vue d’obtenir le grade de Docteur en Automatique, Génie Informatique, Traitement du Signal et Image par Rahma Lahyani Doctorat délivré simultanément par l’École Centrale de Lille et la Facultée Des Sciences Économiques et de Gestion de Sfax dans le cadre d’une cotutelle internationale de thèse Une matheuristique unifiée pour résoudre des problèmes de tournées de véhicules riches Unified matheuristic for solving rich vehicle routing problems Soutenue le 13 juin 2014 devant le jury d’examen: Rapporteur Bernard Gendron Université de Montréal Rapporteur Saoussen Krichen Université de Jendouba Président Saïd Hanafi Université de Valenciennes Examinateur Jorge E. Mendoza Université Catholique de l’Ouest Examinateur Nenad Mladenovic Brunel University Directeurs Habib Chabchoub Université de Sfax Mahdi Khemakhem Université de Sfax Frédéric Semet Ecole Centrale de Lille Thèse préparée au sein des laboratoires LAGIS et LOGIQ École Doctorale SPI 072 (EC Lille) PRES Université Lille Nord-de-France for me, for my parents, and for my brother and sisters. ii Acknowledgments This research project would not have been possible without the help and support of many people, in particular my three very complimentary advisers. I would like to express my gratitude to Pr. Frédéric Semet. He taught me to define clear research objectives, to mark the boundaries of what can be achieved in limited time, and to keep trying until things are perfect. I am also thankful to him for opening the doors of the Ecole Centrale de Lille, and giving me the opportunity to join the LAGIS team. I would like also to thank Dr. Mahdi Khemakhem for giving me the taste of operations research in his excellent master degree course on linear programming and metaheuristics. With him I learned that research was not exclusively about brilliant ideas, but also about methodology, attention to details, and perseverance. A special thank goes to him for his training lessons in the programming language C, for his patience and for introducing me to the world of researchers and showing me that fun and science can go well together, but most importantly for the simple fact of being a friend and believing in me. I would also like to thank Pr. Habib Chabchoub for believing in me from the first months, for his valuable advice before taking the decision to start this dissertation, and for his support during the moments of doubts. I would like to thank Pr. Saoussen Krichen for being part of my committee, for reviewing the present dissertation and for her valuable advice on research and life. I also would like to thank Pr. Bernard Gendron for accepting the invitation to be part of my committee and reviewing the present dissertation, and also for offer- ing me the opportunity to pursue my investigation with his team. I would thank him for receiving me in CIRRELT and for the fruitful (and fun) discussions we have made. In addition, I would like to thank Pr. Saïd Hanafi for his participation in the jury, his advices along the way and our always interesting discussions in congresses and conferences. I also thank Dr. Jorge Mendoza for being part of the jury and for his inspiring determination. Finally, I would like to thank Pr. Nenad Mladenovic not only for being part of my jury but also for sharing his experience in different research areas, which gave me a broader vision for my research career choices. I would like to thank Pr. Lenadro C. Coelho and Pr. Gilbert Laporte whom I visited in Montreal, and had the opportunity to continue working with after I returned to France. I thank Leandro for sharing his expertise on routing and metaheuristics, for always being here to discuss ideas even when he was busy and also for offering me the opportunity to pursue my investigation with his team. iii Acknowledgments Going through this three years journey would not have been possible without the help and support of friends and colleagues on both sides of the Mediterranean. A special thank goes to Yang, Julie, Baisi, Henri, Fanny who kindly accepted me in their office and with whom I share a good meal and a good laugh. All my grat- itude goes to Ramla, Manel, Manel, Maissa, Ryma, Abir, Fattoum who made me feel at home when missing Tunisia and for their good friendship inside and outside the University. Life would not have been possible without the support of my fam- ily, my sisters Fatma, Amina, Hanen, my brother Mohamed, my nephews Abdou, Doudi and Maymou who bring me much joy and happiness in my life. Finally, I would like to dedicate this thesis to my parents Wassila and Abdelkarim for their love, confidence, parayers and support throughout my studies and life. iv Contents Acknowledgments iii Introduction1 1 Rich vehicle routing problems: from a taxonomy to a definition 11 1.1 Introduction................................ 12 1.2 RVRP Taxonomy............................. 13 1.2.1 Taxonomy............................. 14 1.2.1.1 Scenario characteristics (SCs)............. 16 1.2.1.2 Problem physical characteristics (PPCs)....... 20 1.3 Taxonomy analysis............................ 26 1.4 Conclusions................................ 35 2 Models for a rich vehicle routing problem with compartments 37 2.1 Introduction................................ 38 2.2 Mixed integer linear program for the MDMC MCm-VRPTW..... 39 2.2.1 Problem description....................... 39 2.2.2 Mathematical model....................... 44 2.3 Reformulation based on Dantzig-Wolfe decomposition......... 49 2.3.1 Decomposition principle..................... 49 2.3.2 DW reformulation for the MDMCMCm-VRPTW....... 52 2.4 Pricing subproblem formulation..................... 55 2.5 Conclusions................................ 57 3 Matheuristic design for a multi-constrained TSP with profits 59 3.1 Introduction................................ 60 3.2 Describing available unified methods for VRPs............. 61 3.3 Matheuristic approach.......................... 62 3.3.1 Perturbation phase........................ 64 3.3.2 Improvement phase........................ 66 3.4 Main features of the matheuristic approach............... 68 3.4.1 Multi-start constructive heuristic................ 68 3.4.2 Neighborhoods.......................... 69 3.4.2.1 Routing neighborhoods................. 70 3.4.2.2 Loading neighborhoods................. 77 v CONTENTS 3.4.3 Route feasibility check...................... 79 3.4.3.1 Loading feasibility check................ 79 3.4.3.2 Temporal feasibility check and optimization..... 80 3.5 Conclusions................................ 81 4 From methods to implementation and results 83 4.1 Design of data structure classes..................... 84 4.1.1 Challenges............................. 84 4.1.2 Data structures classes...................... 85 4.2 Computational experiments....................... 89 4.2.1 OP instances........................... 90 4.2.2 OPTW instances......................... 91 4.2.3 Experimental results for the RPTP............... 96 4.2.3.1 New testbed....................... 96 4.2.3.2 Sensitivity analysis................... 101 4.3 Conclusions................................ 103 5 Column generation heuristic 105 5.1 Introduction................................ 105 5.2 Column generation heuristic components................ 106 5.2.1 Initial solution heuristic..................... 106 5.2.2 Accelerating strategies for solving the pricing problem..... 109 5.2.3 Post-processing procedure.................... 110 5.3 Computational experiments....................... 111 5.3.1 CVRP instances.......................... 111 5.3.2 MCMCm-VRPTW instances................... 113 5.4 Conclusions................................ 115 6 Real case study: The collection of olive oil in Tunisia 117 6.1 Introduction................................ 118 6.2 Mathematical description of the problem................ 120 6.2.1 Notation.............................. 120 6.2.2 Mathematical model....................... 121 6.2.3 Valid inequalities......................... 122 6.3 Branch-and-cut algorithm........................ 124 6.4 Computational experiments....................... 125 6.4.1 Instance generation........................ 125 6.4.2 Computational results...................... 128 6.5 Conclusions................................ 131 Conclusions 133 References 137 Résumé 167 vi Abstract 171 Electronic appendix 173 vii List of Figures 1 Operations research cycle (Rardin, 1998)................2 2 Contributions summary.........................7 1.1 Cluster analysis.............................. 31 2.1 The MDMCMCm-VRPTW assumptions................ 41 2.2 The related problems to the MDMCMCm-VRPTW and their inter- connections................................ 42 2.3 Example of solution for the MDMCMCm-VRPTW.......... 44 2.4 Block-angular matrices for K blocks................... 50 3.1 Transformation process for solving rich and basic VRPs with a unified matheurisric, adapted from Røpke and Pisinger(2006a)....... 63 3.2 Representing the VNS* general behavior................ 66 3.3 Similarity removal heuristic....................... 72 3.4 Spatio-temporal insertion heuristic................... 76 3.5 Example of a solution based on the Quadratic Multiple Knapsack Problem with Conflicts.......................... 78 4.1 Solution representation using the order class and the compartment class.................................... 88 5.1 Column generation based heuristic................... 107 6.1 Map of Tunisia pinpointing producers and regional offices locations (Source: Google Maps, accessed