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

Abstract

PurposeThe 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/approachThe 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.FindingsStatistical 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/valueThe 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.

Efficient and Effective Local Search for the Set-Union Knapsack Problem and Budgeted Maximum Coverage Problem

“…Wei and Hao (Wei and Hao, 2021b) tested these tabu search algorithms on SUKP instances with no more than 1,000 items and elements. Recently, Zhou et al (Zhou et al, 2021) proposed an efficient local search algorithm called ATS-DLA for the SUKP, and tested the algorithm on SUKP instances with up to 5,000 items and elements. For the BMCP, Li et al (Li et al, 2021) proposed the first local search method.…”

“…However, their search neighborhood contains lots of low-quality moves, which may reduce the algorithm efficiency. The search region of the ATS-DLA algorithm (Zhou et al, 2021) is small, which may make the algorithm hard to escape from some local optima. The VDLS algorithm (Zhou et al, 2022) has a wide and deep search region.…”

“…(Value-weight Ratio) The value-weight ratio of an item to a solution is defined as ( , ) = ∕ ( , ), which is the ratio of the value of to the addition weight of to . Obviously, an item with a larger value-weight ratio to a solution is a better candidate item of (Khuller et al, 1999;Zhou et al, 2021Zhou et al, , 2022.…”

A Binary Machine Learning Cuckoo Search Algorithm Improved by a Local Search Operator for the Set-Union Knapsack Problem

“…In [26], the effectiveness of different transfer functions is studied in order to binarize the moth metaheuristics. A local search operator is designed in [35] and applied to long-scale instances of SUKP. The article proposes three strategies that conform to the adaptive tabu search framework and efficiently solve new instances of SUKP.…”

Optimization of agricultural product storage using real-coded genetic algorithm based on sub-population determination

“…Various methods have been developed to solve knapsack problems such as local search, heuristics, meta-heuristic, and hybridization methods. For example, a local search is modified to efficiently solve a large scale knapsack problem [8]. An evolutionary algorithm based approach is developed to solve hardware/software partitioning that is considered as a variant of knapsack problem [9].…”