Metaheuristic algorithms for computing capacitated dominating set with uniform and variable capacities

The minimum capacitated dominating set (CAPMDS) problem is the problem of finding a dominating set of minimum cardinality with the additional constraint that the nodes dominated do not exceed the capacity of the respective dominating nodes. Being a generalization of the dominating set problem, CAPMDS is also NP-hardNP-hard. In this paper, we study the use of metaheuristic techniques like genetic algorithms (GA) and ant colony optimization (ACO) for solving the CAPMDS problem in graphs with uniform and variable capacity for the nodes. To our knowledge, this is the first attempt at applying the metaheuristic techniques to this problem. We show that the standard GA needs to be seeded with solutions using a heuristic we designed, for the GA to perform well. Similarly, we show that using a pre-processing step for the ACO algorithm improves its performance. When the capacity of the nodes is small, the metaheuristics return a much better solution than the heuristic. However, as the capacity increases or average degree of the graph increases, the solution returned by them does not improve significantly.