Heuristics for the bandwidth colouring problem

The bandwidth coloring problem consists of assigning a color to each vertex of a graph, so that the absolute value of the difference between the colors of adjacent vertices is at least the value of the weight of the associated edge. This problem generalizes the classical vertex coloring problem and different heuristics have recently been proposed to obtain high quality solutions. In this paper we describe both memory-based and memory-less methods to solve the bandwidth coloring problem. In particular we propose new constructive and improvement methods based on tabu search and GRASP. Comparison of our results with previously reported instances and existing heuristics indicate that the methods we propose are competitive and require short computational times. Our findings also disclose that memory appears to play a more important role during improvement phases of search than during constructive phases.