A memetic approach for the unicost set covering problem

Abstract

The Unicost Set Covering Problem (USCP) is a well-known $$\mathcal {NP}$$-hard combinatorial optimization problem. This paper presents a memetic algorithm that combines and adapts the Hybrid Evolutionary Algorithm in Duet (HEAD) and the Row Weighting Local Search (RWLS) to solve the USCP. The former is a memetic approach with a population of only two individuals which was originally developed to tackle the graph coloring problem. The latter is a heuristic algorithm designed to solve the USCP by using a smart weighting scheme that prevents early convergence and guides the algorithm toward interesting sets. RWLS has been shown to be one of the most effective algorithm for the USCP. In the proposed approach, RWLS is modified to be efficiently used as the local search of HEAD (for exploitation purpose) on the one hand, and also to be used as the crossover (for exploration purpose) on the other hand. The HEAD framework is also adapted to take advantage of the information provided by the weighting scheme of RWLS. The proposed memetic algorithm is compared to RWLS on 98 widely-used benchmark instances (87 from the OR-Library and 11 derived from Steiner triple systems). The experimental study reports competitive results and the proposed algorithm improves the best known solutions for 8 instances.