Characterization of graph properties for improved Pareto fronts using heuristics and EA for bi-objective graph coloring problem

Abstract

Bi-objective graph coloring problem (BOGCP) is a generalized version in which the number of colors used to color the vertices of a graph and the corresponding penalty which incurs due to coloring the end-points of an edge with the same color are simultaneously minimized. In this paper, we have analyzed the graph density, the interconnection between high degree nodes of a graph, the rank exponent of the standard benchmark input graph instances and observed that the characterization of graph instances affects on the behavioral quality of the solution sets generated by existing heuristics across the entire range of the obtained Pareto fronts. We have used multi-objective evolutionary algorithm (MOEA) to obtain improved quality solution sets with the problem specific knowledge as well as with the embedded heuristics knowledge. To establish this fact for BOGCP, hybridization approach is used to construct recombination operators and mutation operators and it is observed from empirical results that the embedded problem specific knowledge in evolutionary operators helps to improve the quality of solution sets across the entire Pareto front; the nature of problem specific knowledge differentiates the quality of solution sets.