Hierarchical bare bones particle swarm for solving constrained optimization problems

Bare bones particle swarm optimization (BBPSO) is a well-known swarm algorithm which has shown potential for solving single-objective unconstrained optimization problems. In this paper, firstly, we propose a generalization of the BBPSO, named by us as hierarchical BBPSO, HBBPSO for short. Next a hybrid approach is introduced combining the constraint-handling method based on sum of ranks with the HBBPSO algorithm for solving single-objective constrained optimization problems. In the HBBPSO, the position of a particle is selected from a multivariate t-distribution. The multivariate t-distribution is used in its hierarchical form as a member of the flexible class of scale mixtures of normal distributions. The t-distribution has heavier tails than those of the normal distribution, which increases the ability of the particles to escape from a local optimum. In addition, the t-distribution includes the normal case when the number of degrees of freedom of the t-distribution is sufficiently large. As a result, the t-distribution can be applied during the optimization process, while maintaining the proper equilibrium between exploration and exploitation. An empirical study has been carried out to evaluate the performance of the proposed approach. The experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness to find good solutions for all benchmark problems tested.