Stagnation-aware breakout tabu search for the minimum conductance graph partitioning problem

The minimum conductance graph partitioning problem (MC-GPP) is to partition the vertex set of a graph into two disjoint subsets while minimizing the ratio between the number of the edges crossing the two subsets and the smallest volume of the two subsets, the volume of a vertex set being the sum of degrees of its vertices. MC-GPP has a variety of relevant applications, and however, is known to be NP-hard. In this work, we present a novel metaheuristic algorithm called “stagnation-aware breakout tabu search” for approximating MC-GPP. The algorithm combines a dedicated tabu search procedure to discover high-quality solutions and a self-adaptive perturbation procedure to overcome hard-to-escape local optimum traps. We perform extensive evaluations of the algorithm on five datasets of 110 benchmark instances in the literature. The key components of the proposed algorithm are analyzed to illustrate their influences on the performance of the algorithm

Approches d’optimisation pour le partitionnement de graphe de conductance minimale

The minimum conductance graph partitioning problem (MC-GPP) is an important NP-hard combinatorial optimization problem with numerous practical applications in various areas such as community detection, bioinformatics, and computer vision. Due to its high computational complexity, heuristic and metaheuristic approaches constitute a highly useful tool for approximating this challenging problem. This thesis is devoted to developing effective metaheuristic algorithms for the MC-GPP. Specifically, we propose a stagnation-aware breakout tabu search algorithm (SaBTS), a hybrid evolutionary algorithm (MAMC), and an iterated multilevel simulated annealing algorithm (IMSA). Extensive computational experiments and comparisons on large and massive benchmark instances (with more than 23 million vertices) demonstrate that the proposed algorithms compete very favorably with stateof- the-art algorithms in the literature. Furthermore, the key issues of these algorithms are analyzed to shed light on their influences over the performance of the proposed algorithms.Le problème de partitionnement de graphe de conductance minimale (MCGPP) est un problème d’optimisation combinatoire NP-difficile avec de nombreuses applications pratiques dans divers domaines tels que la détection communautaire, la bioinformatique et la vision par ordinateur. Etant donnée sa complexité intrinsèque, des approches heuristiques et métaheuristiques constituent un moyen convenable pour résoudre des instances de grande taille. Cette thèse est consacrée au développement d’algorithmes métaheuristiques performants pour le MC-GPP. Plus précisément, nous proposons un algorithme «Stagnation aware Breakout Tabu Search», un algorithme évolutif hybride (MAMC) et un algorithme multiniveaubasé sur le recuit simulé (IMSA). Nous présentons des résultats expérimentaux sur de nombreux graphes de grande dimension de la littérature ayant jusqu’à 23 millions de sommets. Nous montrons la haute performance de nos algorithmes par rapport à l’état de l’art. Nous analysons les éléments algorithmiques et stratégies de recherche pour mettre en lumière leur influence sur la performance des algorithmes proposés