A randomized population-based iterated greedy algorithm for the minimum weight dominating set problem

Iterated greedy algorithms belong to the class of stochastic local search strategies that have been shown to be very successful for solving a considerable number of difficult optimization problems. They are based on the simple and effective principle of generating a sequence of solutions by iterating over a constructive greedy heuristic using destruction and construction phases. This paper presents an efficient randomized iterated greedy approach for the minimum weight dominating set problem, whose goal is to identify a subset of vertices in a vertex-weighted graph with minimum total weight such that each vertex of the graph is either in the subset or has a neighbor in the subset. Our proposed approach works on a population of solutions rather than on a single one. Moreover, it is based on a fast randomized construction procedure making use of two different greedy heuristics. The performance evaluation done on a commonly used set of benchmark instances shows that our proposed algorithm outperforms current state-of-the-art approaches both in term of solution quality and computational time.