An Efficient EA with Multipoint Guided Crossover for Bi-objective Graph Coloring Problem

Abstract

Graph Coloring Problem is a well-studied classical NP-hard combinatorial problem. Several well-known heuristics and evolutionary approaches exist to solve single-objective graph coloring problem. We have considered a bi-objective variant of graph coloring problem, in which the number of colors used and the corresponding penalty which is incurred due to coloring the end-points of an edge with same color, are simultaneously minimized. In this paper, we have presented an evolutionary approach with Multipoint Guided Crossover (MPGX) to minimize both objectives simultaneously. On applying proposed evolutionary algorithm over standard graph coloring problem instances, a guaranteed solution to the single-objective graph coloring problem is achieved. We have adapted a few well-known heuristics which are evolved for single-objective graph coloring problem to generate set of solutions for bi-objective graph coloring problem and obtained Pareto fronts. Empirical results show that proposed evolutionary algorithm with simple Multipoint Guided Crossover generates superior or (near-) equal solutions in comparison with the adapted heuristic solutions as well as with evolutionary algorithm solutions using a few crossover (Penalty-based Color Partitioning Crossover (PCPX) and Degree Based Crossover (DBX)) operators across entire Pareto front for considered bi-objective variant of graph coloring problem.