Deterministic Particle Swarm Optimizers with Collision for Discrete Multi-solution Problems

This paper studies a novel particle swarm optimizer with inter-particle collision. The dynamics of particles is governed by a deterministic difference equation on a discrete search space. It is convenient from viewpoints of reproducibility and implementation. The inter-particle collision is controlled by a simple mechanics-like rule. The collision can be effective to enlarge diversity of particles and to avoid trapping into partial/local solutions. The optimizer is applied to an example of a simple discrete multi-solution problem whose solutions corresponds to periodic points of a typical nonlinear dynamical system. This problem can be a first step to a novel application to analysis of nonlinear dynamical systems. The performance of the optimizer is investigated based on three feature quantities: success rate to find all the solutions, the number of iterations to find the solutions and the number of collisions in the search process. The results can provide basic information to develop an efficient algorithm.