Authors: Mjirda, Anis
Todosijević, Raca 
Hanafi, Saïd
Hansen, Pierre
Mladenović, Nenad 
Title: Sequential variable neighborhood descent variants: an empirical study on the traveling salesman problem
Journal: International Transactions in Operational Research
Volume: 24
Issue: 3
First page: 615
Last page: 633
Issue Date: 1-May-2017
Rank: M21
ISSN: 0969-6016
DOI: 10.1111/itor.12282
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.
Keywords: empirical study | neighborhood structures | TSP | variable neighborhood descent | variable neighborhood search
Publisher: Wiley

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