An efficient local search for large-scale set-union knapsack problem

Abstract

Purpose

The set-union knapsack problem is one of the most significant generalizations of the Non-deterministic Polynomial (NP)-hard 0-1 knapsack problem in combinatorial optimization, which has rich application scenarios. Although some researchers performed effective algorithms on normal-sized instances, the authors found these methods deteriorated rapidly as the scale became larger. Therefore, the authors design an efficient yet effective algorithm to solve this large-scale optimization problem, making it applicable to real-world cases under the era of big data.

Design/methodology/approach

The authors develop three targeted strategies and adjust them into the adaptive tabu search framework. Specifically, the dynamic item scoring tries to select proper items into the knapsack dynamically to enhance the intensification, while the age-guided perturbation places more emphasis on the diversification of the algorithm. The lightweight neighborhood updating simplifies the neighborhood operators to reduce the algorithm complexity distinctly as well as maintains potential solutions. The authors conduct comparative experiments against currently best solvers to show the performance of the proposed algorithm.

Findings

Statistical experiments show that the proposed algorithm can find 18 out of 24 better solutions than other algorithms. For the remaining six instances on which the competitor also achieves the same solutions, ours performs more stably due to its narrow gap between best and mean value. Besides, the convergence time is also verified efficiency against other algorithms.

Originality/value

The authors present the first implementation of heuristic algorithm for solving large-scale set-union knapsack problem and achieve the best results. Also, the authors provide the benchmarks on the website for the first time.

Citation

Zhou, Y., Zhao, M., Fan, M., Wang, Y. and Wang, J. (2021), "An efficient local search for large-scale set-union knapsack problem", Data Technologies and Applications, Vol. 55 No. 2, pp. 233-250. https://doi.org/10.1108/DTA-05-2020-0120