Abstract. Chromatic number, chromatic sum and chromatic sum number are important graph coloring characteristics. The paper proves that a parallel metaheuristic like the parallel genetic algorithm (PGA) can be efficiently used for computing approximate sum colorings and finding upper bounds for chromatic sums and chromatic sum numbers for hardto-color graphs. Suboptimal sum coloring with PGA gives usually much closer upper bounds then theoretical formulas known from the literature.

Abstract. In this paper a new parallel genetic algorithm for coloring graph vertices is presented. In the algorithm we apply a migration model of parallelism and de ne two new recombination operators: SPPX and CEX. For comparison two recently proposed crossover operators: UISX and GPX are selected. The performance of the algorithm is veri ed by computer experiments on a set of standard graph coloring instances.