Enhanced Moth Search Algorithm for the Set-Union Knapsack Problems

As an important and novel model with multitudinous practical applications, the set-union knapsack problem (SUKP) is a challenging issue in combinatorial optimization. In this paper, we present an enhanced moth search algorithm (EMS) for solving SUKP, which introduces an enhanced interaction operator (EIO) by integrating differential mutation into the global harmony search and then Lévy flight is replaced by EIO. Comparative experimental results, which were conducted on three types of 30 popular SUKP benchmark instances, demonstrate that EMS algorithm is superior to or competitive with the other state-of-the-art metaheuristic algorithm. In particular, EMS reaches the best-known solutions for the great majority of test instances and improves the best-known solutions for six instances. Two critical ingredients of EIO is investigated to confirm their impact on the performance of EMS. The results show that both components have an important role in improving the performance of EMS.