Fixed Set Search Applied to the Minimum Weighted Vertex Cover Problem

Abstract

Fixed set search (FSS) is a novel metaheuristic adding a learning mechanism to enhanced greedy approaches. In this paper we use FSS for solving the Minimum Weighted Vertex Cover Problem (MWVCP). First we define a Greedy Randomized Adaptive Search Procedure (GRASP) by randomizing the standard greedy constructive algorithm and combine it with a local search. The used local search is based on a simple downhill procedure. It checks if substituting a single or a pair of elements from a solution with ones that need to be added to keep the solution a vertex cover decreases the value of the objective function. The performance of the GRASP algorithm is improved by extending it towards FSS. Computational experiments performed on standard test instances from literature show that the proposed FSS algorithm for the MWVCP is highly competitive with state-of-the-art methods. Further, it is shown that the FSS manages to significantly improve the GRASP algorithm it is based on.