A New Hybrid Genetic Algorithm for the Robust Graph Coloring Problem

Abstract

The RGCP (Robust Graph Coloring problem) is a new variant of the traditional graph coloring problem. It has numerous practical applications in real world like timetabling and crew scheduling. The traditional graph coloring problem focuses on minimizing the number of colors used in the graph. RGCP focuses on the robustness of the coloring so that the coloring is able to handle uncertainty that often occurs in the real world. By that, we mean that given a fixed number of colors we would like to color the graph so that adjacent vertices are assigned different colors with the consideration of the possible appearance of the missing edges. In this paper, we present a new hybrid genetic algorithm (GA), which embeds two kinds of local search algorithms – enumerative search and random search within the GA framework. In addition, we integrate a partition based encoding scheme with a specialized crossover operator into our GA method. We also propose an adaptive scheme that alternates between two local search methods to increase performance. Experimental results show that our new algorithm outperforms the best published results in terms of the quality of solutions and the computing time needed.