Binary team game algorithm based on modulo operation for knapsack problem with a single continuous variable

Abstract

For solving the knapsack problem with a single continuous variable (KPC), a binary team game algorithm (TGA) with one-way mutation strategy is proposed. Firstly, without changing the evolution mode of TGA, three basic operations are reconstructed based on modulo 2 operation. Then, a binary TGA (BTGA) suitable for solving binary optimization problem is proposed. In order to use BTGA to solve KPC problem effectively, a one-way mutation strategy to improve individual quality is subsequently developed. Finally, based on BTGA and the existing repair and optimization algorithm of eliminating infeasible solutions, a novel algorithm MOBTGA for solving KPC problem is proposed. For validating the performance of MOBTGA, Kruskal–Wallis test is used to determine the reasonable values of its parameters. The comparison of experimental results obtained by different algorithms for two sets of KPC instances is subsequently executed. The comparison results show that MOBTGA has better performance than the existing heuristic algorithms ETDE, S-HBDE and B-HBDE in terms of solution accuracy and stability for solving KPC. The same time, the solving speed of MOBTGA also has a certain degree of competitiveness. Thus, MOBTGA is a quick and efficient heuristic algorithm for solving large-scale KPC instances.