Optimization Algorithms for Clique Problems Yi Zhou To cite this version: Yi Zhou. Optimization Algorithms for Clique Problems. Optimization and Control [math.OC]. Uni- versité d’Angers, 2017. English. NNT : 2017ANGE0013. tel-01707043 HAL Id: tel-01707043 https://tel.archives-ouvertes.fr/tel-01707043 Submitted on 12 Feb 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Thèse de Doctorat Yi ZHOU Mémoire présenté en vue de l’obtention du grade de Docteur de l’Université d’Angers Label européen sous le sceau de l’Université Bretagne Loire École doctorale : 503 (STIM) Discipline : Informatique, section CNU 27 Unité de recherche : Laboratoire d’Étude et de Recherche en Informatique d’Angers (LERIA) Soutenue le 29 Juin 2017 Thèse n° : 1 Optimization Algorithms for Clique Problems JURY Rapporteurs : M. Christian BLUM, Directeur de recherche, Spanish National Research Council (CSIC) M. Sébastien VÉREL, Maître de conférences HDR, Université du Littoral Côte d’Opale Examinateurs : M. André ROSSI, Professeur, Université d’Angers M. Marc SEVAUX, Professeur, Université de Bretagne-Sud Mme Yang WANG, Professeur, Northwestern Polytechnic University Directeur de thèse : M. Jin-Kao HAO, Professeur, Université d’Angers Co-directeur de thèse : M. Adrien GOËFFON, Maître de conférences HDR, Université d’Angers Acknowledgement Four years ago, I started my journey in the joint area of computer science, combinatorial optimization and artificial intelligence in LERIA, University of Angers. From a foreign beginner who hardly knows anything around to a final year PhD student who enjoys very much the research and daily life in France, I feel that a few lines are not enough to thank everyone who has helped me adapting the work and life. I would like firstly thank my supervisor Prof. Jin-Kao Hao, who introduced me the interesting clique problems. In order to achieve an efficient algorithm, one may do many unfruitful experiments and try a lot unnecessary techniques. Thanks to him, I got many valuable advises and avoid some detours. Prof. Hao is also very kind and always be patient with my questions. I also appreciate my associate supervisor, Prof. Adrien Goëffon, who I cooperated a lot during the four years. He not only proposed some interesting ideas, but also proofread some of my manuscripts. My thanks also go to another professor, Prof. André Rossi who had a lot of interesting talk with me. His rich experience in integer programming gave me another key to solve the combinatorial problems. I also thank my office mates Arthur Chambon, Marc Legeay who spent a great deal of time solving my daily-life problems since I spoke french poorly. We also have a lot of interesting non-work related discussions. Ad- ditionally, I want to thank our technicians Eric Girardeau and Jean-Mathieu Chantrein, our nice secretaries Catherine Pawlonski and Christine Bardarine, my new office mate Hugo Traverson and all the other lab members. Thanks to their supports, the research work becomes much more easier and enjoyable in LERIA. Also, I would like to thank the Center of French Language for Foreigners (CeLFE) in University of Angers. After following their free courses, I am able to speak french in daily life and also make some foreign friends. I am particularly grateful to my parents, my elder sister Zhifang Zhou as well as her husband Min Zhu. Thanks for all their love and selfless support! Without them, this work would not be possible. I also thank my Chinese friends Yuning Chen, Zhanghua Fu, Yan Jin, Fuda Ma, Xiangjin Lai, Le Li, Wen Sun, Yangming Zhou, Zhi Lu, Jintong Ren in Angers for their accompanies. I also appreciate my best friends in Chengdu – thanks for being there for me. I also thank all the jury members, for their efforts in reviewing and improving this thesis. This research has been financially supported by China Scholarship Council (CSC). 3 Contents General Introduction 1 1 Introduction 5 1.1 Clique problems........................................6 1.2 Applications..........................................8 1.3 Evolution of maximum clique algorithms..........................9 1.4 Algorithm assessment..................................... 10 1.4.1 Benchmarks...................................... 11 1.4.2 Metaheuristic algorithms evaluation......................... 12 1.4.3 Exact algorithms Evaluation............................. 13 2 A Generalized Operator “PUSH” for MVWCP 15 2.1 Introduction.......................................... 17 2.2 PUSH: a generalized operator for MVWCP......................... 18 2.2.1 Preliminary definitions................................ 18 2.2.2 Motivations for the PUSH operator......................... 19 2.2.3 Definition of the PUSH Operator........................... 20 2.2.4 Special cases of PUSH................................ 20 2.3 PUSH-based tabu search................................... 21 2.3.1 Random initial solution................................ 22 2.3.2 Solution reconstruction................................ 22 2.3.3 ReTS-I: Tabu search with the largest candidate push set............... 23 2.3.4 ReTS-II: Tabu search with three decomposed candidate push sets......... 23 2.3.5 Fast evaluation of move gains............................ 24 2.4 Computational experiments.................................. 25 2.4.1 Benchmarks...................................... 26 2.4.2 Experimental protocol................................ 26 2.4.3 Computational results................................ 26 2.4.4 Comparisons with state-of-the-art algorithms.................... 27 2.5 Effectiveness of restart strategy................................ 31 2.6 Conclusion.......................................... 34 3 Frequency-driven tabu search for MsPlex 35 3.1 Introduction.......................................... 36 3.2 FD-TS algorithm for the maximum s-plex problem..................... 37 3.2.1 General procedure.................................. 37 3.2.2 Preliminary definitions................................ 37 3.2.3 Move operators.................................... 38 3.2.4 Constructing the initial solutions........................... 40 3.2.5 FD-TS........................................ 41 3.2.6 Reducing large (sparse) graphs............................ 43 5 6 CONTENTS 3.3 Implementation and time complexity............................. 43 3.4 Computational assessment.................................. 44 3.4.1 Benchmarks...................................... 44 3.4.2 Experimental protocol and parameter tuning..................... 44 3.4.3 Computational results for very large networks from SNAP and the 10th DIMACS Challenge....................................... 45 3.4.4 Computation results for graphs from the 2nd DIMACS Challenge......... 48 3.4.5 Impact of frequency information........................... 51 3.5 Conclusions.......................................... 53 4 Heuristic and exact algorithms for MBBP 55 4.1 Introduction.......................................... 57 4.2 Heurisitc algorithm with graph reduction........................... 58 4.2.1 Preliminary definitions................................ 58 4.2.2 Rationale of the proposed approach......................... 59 4.2.3 General procedure of TSGR-MBBP......................... 60 4.2.4 Computational experiments............................. 65 4.2.5 Analysis....................................... 70 4.3 Exact algorithms....................................... 72 4.3.1 Preliminary definitions................................ 72 4.3.2 Review of the BBClq algorithm........................... 73 4.3.3 Upper bound propagation and its use to improve BBClq.............. 73 4.3.4 The upper bound propagation procedure....................... 74 4.3.5 A tighter mathematical formulation......................... 76 4.3.6 A novel MBBP algorithm ExtUniBBClq...................... 77 4.3.7 Computational experiments............................. 78 4.3.8 Analysis....................................... 81 4.4 Conclusion.......................................... 83 5 A Three-Phased Local Search Approach for CPP 85 5.1 Introduction.......................................... 87 5.2 General procedure....................................... 88 5.2.1 Search space and evaluation function........................ 88 5.2.2 Top Move and restricted neighborhood....................... 88 5.2.3 Heap structure.................................... 90 5.2.4 Generation of initial solution............................. 90 5.2.5 Descent search phase................................. 90 5.2.6 Exploration search phase............................... 91 5.2.7 Directed perturbation phase............................. 91 5.2.8 Singularity of CPP-P3 ................................ 92 5.3 Computational experiments.................................. 92 5.3.1 Benchmark instances and parameter settings.................... 93 5.3.2 Experiments and comparison............................. 93 5.4 Analysis............................................ 99 5.4.1 The effectiveness of Top Move based neighborhood................. 99 5.4.2 Landscape analysis.................................