Adaptive Memory Programming: An Empirical Study with the Bandwidth Coloring Problem

In this article we study the use of memory structures in both constructive and improvement methods. Typical tabu search applications employ short term memory structures to overcome local optimality. However, other memory structures, such as frequency-based constructions have often been ignored or implemented in naïve ways that disregard important elements of the original proposals. In this paper we describe the adaptation of these memory programming elements to the bandwidth coloring problem. We also propose constructive and improvement methods based on GRASP, a wellknown memory-less methodology, to compare and hybridize both designs. 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. 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.