Evolutionary Graph Coloring

The Graph Coloring Problem (GCP) asks for the minimum number of colors required to color the vertices of a graph such that no two adjacent vertices have the same color. In this thesis we present an evolutionary algorithm for the GCP with novel crossover operations using graph partitioning. Our population contains only legal colorings and we use various greedy coloring algorithms to initialize it. In each generation, two colorings of the population function as parents. We combine them using one of the proposed crossover operations. Our first crossover uses a graph partitioning as the crossing point and generates a new coloring by selecting a different coloring for each block. The second crossover works in a similar fashion but uses a vertex separator instead of a partitioning. Our third crossover computes a new coloring from the overlap of the parents. Finally, we improve the new coloring with a local search algorithm. As the goal for our algorithm is to perform well on large graphs, we use a simple tabu search as well as fast crossovers. We evaluate our proposed algorithm by comparing it to the state-of-the-art algorithm PASS by San Segundo [36] on graph instances found in the literature. We are able to outperform PASS on almost 50 % of the graph instances.