Multiparent path relinking. An application to the power dominating set problem

Abstract We propose a reference framework to apply the multiparent path relinking (MPR) methodology. MPR is an extension of path relinking (PR) that has been proposed and described but, to the best of our knowledge, it has never been applied. PR is a trajectory-based neighborhood search strategy that explores paths that traverse pairs of solutions. PR has been widely used for search intensification purposes within metaheuristic implementations. To show how MPR can be embedded in more than one setting, our proposal consists of both employing MPR as a post-processing step in a greedy randomized adaptive search procedure (GRASP) and as the combination method in a scatter search (SS). We use the power dominating set problem (PDSP) as our testing platform because its difficulty and structure enable the design and assessment of various strategies. The PDSP seeks to find the minimum placement of measurement devices in an electrical network to monitor the entire system. Our computational experiments are designed to identify the contribution of each element of our proposed MRP implementations.