Sequential variable neighborhood descent variants: an empirical study on the traveling salesman problem |
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Authors: | Anis Mjirda Raca Todosijević Saïd Hanafi Pierre Hansen Nenad Mladenović |
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Affiliation: | 1. Institut de Recherche Technologique Railenium, Famars, France;2. Inria Lille‐Nord Europe, Villeneuve d'Ascq, France;3. LAMIH UMR CNRS 8201—Université de Valenciennes, France;4. GERAD & HEC Montréal, chemin de la Cote‐Sainte‐Catherine, Montréal, Québec, Canada |
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Abstract: | In a single local search algorithm, several neighborhood structures are usually explored. The simplest way is to define a single neighborhood as the union of all predefined neighborhood structures; the other possibility is to make an order (or sequence) of the predefined neighborhoods, and to use them in the first improvement or the best improvement fashion, following that order. In this work, first we classify possible variants of sequential use of neighborhoods and then, empirically analyze them in solving the classical traveling salesman problem (TSP). We explore the most commonly used TSP neighborhood structures, such as 2‐opt and insertion neighborhoods. In our empirical study, we tested 76 different such heuristics on 15,200 random test instances. Several interesting observations are derived. In addition, the two best of 76 heuristics (used as local searches within a variable neighborhood search) are tested on 23 test instances taken from the TSP library (TSPLIB). It appears that the union of neighborhoods does not perform well. |
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Keywords: | neighborhood structures variable neighborhood descent variable neighborhood search TSP empirical study |
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