An adaptive evolutionary search-based method for efficiently tackling the set-union knapsack problem

Abstract

This paper tackles the NP-hard set-union knapsack problem using a novel adaptive evolutionary algorithm. Such a problem has applications in database query optimization, network design, and project portfolio management. The method starts by creating an archive set with elite and diversified solutions, employing a customized procedure based on item scores and Hamming max-min distance for diversity. Various operators are added to enhance solution quality in the elite set and refine the search process. To counteract premature convergence, combination and subset reference update methods are used. The fusion strategy serves as an exploration mechanism, generating new solutions and preventing premature convergence. Finally, the effectiveness and performance of the proposed method is evaluated on a set of benchmark instances taken from existing literature and by conducting a thorough statistical analysis of all achieved results. All obtained results are systematically compared against those achieved by state-of-the-art methods, indicating a substantial improvement of 50% for the large-sized instances, outperforming those published in the literature.