New variable neighborhood search method for minimum sum coloring problem on simple graphs

The minimum sum coloring problem (MSCP) is to find a legal vertex coloring for G using colors represented by natural numbers (1,2, . . .) such that the total sum of the colors assigned to the vertices is minimized. The aim of this paper is to present the skewed variable neighborhood search (SVNS) for this problem based on a new structure of neighborhoods. To increase the speed of the neighborhood search process, we present the new concepts of holder vertex and set. Tested on 23 commonly used benchmark instances, our algorithm shows acceptable competitive performance with respect to recently proposed heuristics.