A Binary Particle Swarm Optimization for the Minimum Weight Dominating Set Problem

The minimum weight dominating set problem (MWDSP) is an NP-hard problem with a lot of real-world applications. Several heuristic algorithms have been presented to produce good quality solutions. However, the solution time of them grows very quickly as the size of the instance increases. In this paper, we propose a binary particle swarm optimization (FBPSO) for solving the MWDSP approximately. Based on the characteristic of MWDSP, this approach designs a new position updating rule to guide the search to a promising area. An iterated greedy tabu search is used to enhance the solution quality quickly. In addition, several stochastic strategies are employed to diversify the search and prevent premature convergence. These methods maintain a good balance between the exploration and the exploitation. Experimental studies on 106 groups of 1 060 instances show that FBPSO is able to identify near optimal solutions in a short running time. The average deviation between the solutions obtained by FBPSO and the best known solutions is 0.441%. Moreover, the average solution time of FBPSO is much less than that of other existing algorithms. In particular, with the increasing of instance size, the solution time of FBPSO grows much more slowly than that of other existing algorithms.