A Fast and Robust Heuristic Algorithm for the Minimum Weight Vertex Cover Problem

Abstract

The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications. The MWVCP seeks a vertex cover of an undirected graph such that the sum of the weights of the selected vertices is as small as possible. In this paper, we present an effective algorithm to solve the MWVCP. First, a master-apprentice evolutionary algorithm based on two individuals is conducted to enhance the diversity of solutions. Second, a hybrid tabu search combined configuration checking and solution-based tabu search is introduced to intensify local search procedure. Harnessing the power of the evolutionary strategy and a novel variant of hybrid tabu search, Master-Apprentice Evolutionary Algorithm with Hybrid Tabu Search, MAE-HTS, is presented. Results of extensive computational experiments using standard benchmark instances and other large-scale instances demonstrate the efficacy of our algorithm in terms of solution quality, running time, and robustness compared to state-of-the-art heuristics from the literature and the commercial MIP solver Gurobi. We also systematically analyze the role of each individual component of the algorithm which when worked in unison produced superior outcomes. In particular, MAE-HTS produced improved solutions for 2 out of 126 public benchmark instances with better running time. In addition, our MAE-HTS outperforms other state-of-the-art algorithms DLSWCC and NuMWVC for 72 large scale MWVCP instances by obtaining the best results for 64 ones, while other two reference algorithms can only obtain 27 best results at most.

Keywords

• Hybrid evolutionary algorithm
• metaheuristics
• minimum weight vertex cover problem
• solution-based tabu search