Constructive Genetic Algorithm for Graph Coloring

This work presents a new constructive heuristic for graph coloring based on Genetic Algorithms. The Constructive Genetic Algorithm (CGA) begins with an initial population formed only of schemas (partial colorings), and iterates (re)combining two schemas. The new schemas present more colored nodes. At each iteration, is performed an elimination of schemas from the population and the process finishes with an empty population or an iteration limit reached. The permanence criterion is based on proportional adaptation of the schema to the population. The same CGA is adapted to find the maximum independent node set of a given graph. The identified set is removed from the graph and the process is repeated for the reduced graph. Successive reductions result in the node coloring of the original graph. This approach is used for large, or high density graphs. Computational results are shown for instances from the literature using microcomputer implementation.