A Generalized Variable Neighborhood Search For Combinatorial Optimization Problems

• Published in: Electronic notes in discrete mathematics Vol. 47; pp. 45 - 52
• Main Authors: Bouhmala, Noureddine, Hjelmervik, Karina, Øvergaard, Kjell Ivar
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2015
• Subjects: combinatorial optimization problem; maximum satisfiability problem; Variable neighborhood search; Variable neighborhood search; maximum satisfiability problem; combinatorial optimization problem
• ISSN: 1571-0653; 1571-0653
• DOI: 10.1016/j.endm.2014.11.007

The VNS is a simple meta-heuristic that systematically changes the size and type of neighborhood during the search process in order to escape from local optima. In this paper, a generalized variable neighborhood search is proposed for combinatorial optimization problems. The set of constructed neighborhoods satisfies the property that each small neighborhood is a subset of a larger one. Most of the work published earlier on VNS starts from the first neighborhood and moves on to higher neighborhoods without controlling and adapting the ordering of neighborhood structures. The order in which the neighborhood structures have been selected in this paper during the search process offers a better mechanism for performing diversification and intensification. A set of industrial benchmark problem instances is used to test the effectiveness of the new variant of VNS using the maximum satisfying problem as a test case.