On Sum Coloring of Graphs with Parallel Genetic Algorithms

Abstract

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.

A Study of Breakout Local Search for the Minimum Sum Coloring Problem

“…Moreover, the best result obtained with BLS is in each case either better or as good as that reported by HLS [4], MRLF [10] and PGA [9]. For TS, no results are reported on these instances in [3].…”

“…To further evaluate the performance of BLS, we show a comparison with the following approaches from the literature: a very recent heuristic EXSCOL [13]; a hybrid local search (HLS) [4]; a greedy algorithm (MRLF) based on the popular RLF graph coloring heuristic [10]; a parallel genetic algorithm (PGA) [9]; a tabu search algorithm (TS) [3]; and a recent local search combining ideas of variable neighborhood search and iterated local search (MDSLS) [6]. EXSCOL [13] is the current best-performing approach in the literature and is particularly effective on large graphs.…”

“…The time limit used by MDSLS [6] is 1 hour on a computer similar to ours. For other reference approaches [3,4,9,10], details on testing conditions are not available. Tables 2 and 3 report respectively the comparative results with these reference algorithms on the tested DIMACS and COLOR02 instances.…”

“…Over the past two decades, it has been studied mainly from a theoretical point of view. Only recently, several heuristics have been proposed for the practical solving of the general MSCP [3,4,6,9,10,13].…”

Parallel Simulated Annealing Algorithm for Graph Coloring Problem

“…At the time of this writing, the only parallel metaheuristic for GCP is parallel genetic algorithm [10,[12][13][14][15].…”