Graph coloring using Intelligent Water Drops algorithm

Abstract

Graph coloring is a NP-Hard problem and there is not any polynomial algorithm for solving it yet. Different algorithmic approaches have been applied to find the near optimal solution where two issues always were extremely important; proximity of the solution to the optimal one as well as algorithm speed. Swarm based algorithm is one of the approaches that has been considered. Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) are some examples. In this paper, we applied another swarm based algorithm to tackle the graph coloring problem (GCP). Intelligent Water Drops (IWD) algorithm, which is used here, has some pre-requirements to be able to solve a problem. According to these pre-requirements, we customized GCP for IWD. The most important issue raised here is that IWD compounds both heuristic desirability and past experience in one concept which is called the soil, whereas in the case of algorithms like ACO, these concepts are separate (pheromone corresponds to past experience and heuristic desirability has its own separate amount). We utilized a simple interpreter to overcome this restriction of IWD. The proposed algorithm which is called IWDCOL has been evaluated against the random graphs and numerical results show that the IWD algorithm can be one of candidates to tackle the GCP by satisfactory solutions.