Solving 0 –1 knapsack problem by an improved binary monarch butterfly algorithm

The binary monarch butterfly optimization algorithm (BMBOA) is a meta-heuristic algorithm that has been applied widely in combinational optimization problems. Binary knapsack problem has received considerable attention in the combinational optimization. In this paper, a new time-varying transfer function is proposed to improve the exploration and exploitation capability of the BMBOA with the best solution and short computing time. Based on small, medium, and high-dimensional sizes of the knapsack problem, the computational results reveal that the proposed time-varying transfer functions obtain the best results not only by finding the best possible solutions but also by yielding short computational times. Compared to the standard transfer functions, the efficiency of the proposed time-varying transfer functions is superior, especially in the high-dimensional sizes.