Analysis and improvement of the binary particle swarm optimization

Solving binary-real problems with bio-inspired algorithms is an active research matter. However, the efficiency of the employed algorithm varies drastically by tailoring the governing equations or just by adopting "more adequate" parameter setting. Within this framework, we aim to improve the parameter setting of the binary particle swarm optimization (BPSO). We derive a Markov chain model of BPSO. The transition probabilities reveal that the acceleration coefficients control the transition speed between the exploitation and exploration phases. The transition probabilities also depict a poor exploration ratio in high-dimensional search spaces. Increasing the values of the acceleration coefficients may enhance the exploration ratio. Nevertheless, overly high values for these coefficients present some shortcomings. Numerical experiments realized on three different problem sets (e.g. multidimensional knapsack problem) further prove the need to increase the acceleration coefficients as the search space dimension rises. We recommend a set of equations governing the best setting for acceleration coefficients. Finally, a comparison with other BPSO variants reveals the merits of the suggested setting over the conventional ones.