Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.
Abstract. The p-median problem, like most location problems, is classified as N P -hard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the p-median, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.
Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds de recherche du Québec -Nature et technologies. G-2013-98 Les Cahiers du GERAD Abstract: The analysis of networks and in particular the identification of communities, or clusters, is a topic of active research with application arising in many domains. Several models were proposed for its solution. In [Cafieri et al., Phys. Rev. E 81(2):026105, 2010], a criterion is proposed for a graph bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges (edge ratio), and it is used in a hierarchical divisive algorithm for community identification in networks. In this paper, we develop a VNS-based heuristic for hierarchical divisive edge ratio network clustering. A k-neighborhood is defined as move of k entities, i.e., k entities change their membership from one to another cluster. A local search is based on 1-changes and k-changes are used for shaking the incumbent solution. Computational results on datasets from the literature validate the proposed approach.Résumé : L'analyse de réseaux et en particulier l'identification de communautés, ou classes, est un sujet de recherche très actif dont les applications sont nombreuses dans de multiples domaines. Plusieurs modèles ontété proposés pour sa résolution. Dans [Cafieri et al., Phys. Rev. E 81(2):026105, 2010], on propose un critère pour que la bipartition d'un graphe soit optimale : on chercheà maximiser le minimum pour les deux classes de la bipartition du rapport du nombre d'arêtes internes au nombre d'arêtes coupées (edgeratio). Ce critère est utilisé dans un algorithme hiérarchique divisif pour l'identification de communautés dans les réseaux. Dans le présent article, nous développons une heuristique pour la classification hiérarchique descendante basée sur la métaheuristique de rechercheà voisinage variable. Un k-voisinage est défini comme le mouvement de k entités, c'est-à-dire que k entités changent leur appartenance d'une classeà l'autre. Une recherche locale est basée sur les 1-échanges et les k-échanges sont utilisés pour perturber la meilleure solution connue. Les résultats de calcul sur des données de la littérature valident l'approche proposée.
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