A Binary Equilibrium Optimization Algorithm for 0–1 Knapsack Problems

In this paper, a binary version of equilibrium optimization (BEO) is proposed for the tackling 0–1 knapsack problem characterized as a discrete problem. Because the standard equilibrium optimizer (EO) has been proposed for solving continuous optimization problems, a discrete variant is required to solve binary problems. Hence, eight transfer functions including V-Shaped and S-Shaped are employed to convert continuous EO to Binary EO (BEO). Among those transfer functions, this study demonstrates that V-Shaped V3 is the best one. It is also observed that the sigmoid S3 transfer function can be more beneficial than V3 for improving the performance of other algorithms employed in this paper. We conclude that the performance of any binary algorithm relies on the good choice of the transfer function. In addition, we use the penalty function to sift the infeasible solution from the solutions of the problem and apply a repair algorithm (RA) for converting them to feasible solutions. The performance of the proposed algorithm is evaluated on three benchmark datasets with 63 instances of small-, medium-, and large-scale and compared with a number of the other algorithm proposed for solving 0–1 knapsack under different statistical analyses. The experimental results demonstrate that the BEOV3 algorithm is superior on all the small-, medium-scale case studies. Regarding the large-scale test cases, the proposed method achieves the optimal value for 13 out of 18 instances.²