Position-Guided Tabu Search Algorithm for the Graph Coloring Problem

A very undesirable behavior of any heuristic algorithm is to be stuck in some specific parts of the search space, in particular in the basins of attraction of the local optima. While there are many wellstudied methods to help the search process escape a basin of attraction, it seems more difficult to prevent it from looping between a limited number of basins of attraction. We introduce a Position Guided Tabu Search (PGTS) heuristic that, besides avoiding local optima, also avoids re-visiting candidate solutions in previously visited regions. A learning process, based on a metric of the search space, guides the Tabu Search toward as–yet–unexplored regions. The results of PGTS for the graph coloring problem are competitive. It significantly improves the results of the basic Tabu Search for almost all tested difficult instances (from the Dimacs Challenge Benchmark) and it matches most of the results ever obtained by the best algorithms—often evolutionary—in the literature.