A cooperative co-evolutionary algorithm with core-based grouping strategy for large-scale 0–1 knapsack problems

• Published in: Expert systems with applications Vol. 298; p. 129364
• Main Authors: Li, Xiaotong, Zhu, Shuwei, Fang, Wei, Deb, Kalyanmoy
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2026
• Subjects: Binary particle swarm optimization; Cooperative co-evolution; Divide-and-conquer strategy; Large-scale 0–1 KPs; Repair operator; Cooperative co-evolution; Binary particle swarm optimization; Repair operator; Divide-and-conquer strategy; Large-scale 0–1 KPs
• ISSN: 0957-4174
• DOI: 10.1016/j.eswa.2025.129364

•A cooperative co-evolutionary algorithm for large-scale 0–1 KP is proposed.•A core-based grouping strategy utilizing break item information is designed.•A three-phase repair operator is introduced to ensure solution quality.•A subgroup merging method considering KP characteristics is developed.•Experimental results exhibit superiority over eight state-of-the-art algorithms. The 0–1 knapsack problem (KP) is a well-known combinatorial optimization problem with wide real-world applications. While evolutionary algorithms have demonstrated promise in solving 0–1 KPs, their performance deteriorates as the problem dimension increases. Cooperative co-evolution (CC) is an algorithmic framework based on a divide-and-conquer strategy, which has been used in solving large-scale optimization problems. Inspired by the similarity between item grouping in the 0–1 KP and decomposition strategies in CC, this paper proposes a novel grouping strategy that uses the position information of break items and profit-to-weight ratio to solve large-scale 0–1 KP. The strategy aims to divide the large-scale 0–1 KP into multiple subproblems, thus having a reduced search space for each subproblem. To enhance population diversity and search efficiency, the profit-to-weight ratio is used to generate an initial elite population. Additionally, to obtain the complete solution for the original large-scale KP, a subgroup merging method is designed to accelerate convergence and further improve population diversity. A three-phase repair operator is developed to fix infeasible solutions directly to create more feasible solutions. The resulting cooperative co-evolutionary algorithm is compared with ten state-of-the-art algorithms for solving 0–1 KPs with variables ranging from 100 to 5,000, including EAs, CC-based approaches, and a deep reinforcement learning method. Experimental results show that the proposed algorithm exhibits higher solution accuracy and faster convergence than other competing algorithms. The CC framework takes considerably less running time than high-performing algorithms, providing an overall novel approach for solving large-scale 0–1 KPs.