Solving the Graph Coloring Problem Using Adaptive Artificial Bee Colony

Abstract

Recently, some discrete swarm intelligence algorithms such as particle swarm optimization with hamming distance (HDPSO), similarity artificial bee colony (S-ABC), and discrete firefly algorithm (DFA) have been proposed to solve graph 3-coloring problems (3-GCP) and obtain good results. However, these algorithms use static parameter settings that limit their performance on graphs with various sizes and topology. In this paper, we propose a discrete adaptive artificial bee colony (A-ABC) algorithm that can adjust the parameter automatically during the evolution according to the graph size and the fitness of candidates. For the convenience of comparison, we also propose a fixed ABC (F-ABC), which is identical to A-ABC but using fixed parameter setting during the evolution. A-ABC is simple and high performance. Experiments on 3-GCP show that A-ABC dramatically outperforms its competitors F-ABC, HDPSO, S-ABC, and DFA. We also study the scout bee phase and report that the scout bee phase is not required in solving 3-GCP