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Optimization Algorithms for Clique Problems

Abstract : This thesis considers four clique problems: the maximum vertex weight clique problem (MVWCP), the maximum s-plex problem (MsPlex), the maximum balanced biclique problem (MBBP) and the clique partitioning problem (CPP). The first three are generalization and relaxation of the classic maximum clique problem (MCP), while the last problem belongs to a clique grouping problem. These combinatorial problems have numerous practical applications. Given that they all belong to the NP-Hard family, it is computationally difficult to solve them in the general case. For this reason, this thesis is devoted to develop effective algorithms to tackle these challenging problems. Specifically, we propose two restart tabu search algorithms based on a generalized PUSH operator for MVWCP, a frequency driven local search algorithms for MsPlex, a graph reduction based tabu search as well as effective exact branch and bound algorithms for MBBP and lastly, a three phase local search algorithm for CPP. In addition to the design of efficient move operators for local search algorithms, we also integrate components like graph reduction or upper bound propagation in order to deal deal with very large real-life networks. The experimental tests on a wide range of instances show that our algorithms compete favorably with the main state-of-the-art algorithms.
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Submitted on : Monday, February 12, 2018 - 2:48:07 PM
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  • HAL Id : tel-01707043, version 1


Yi Zhou. Optimization Algorithms for Clique Problems. Optimization and Control [math.OC]. Université d'Angers, 2017. English. ⟨NNT : 2017ANGE0013⟩. ⟨tel-01707043⟩



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