2021 Volume 15 Issue 2 Pages 70-79
Particle swarm optimization (PSO) is one of the most effective optimization methods for the black-box optimization problem. PSO involves a large number of particles that share information with each other to search for an optimal solution. The method in which a large number of search individuals cooperate to search for an optimal solution is called swarm intelligence optimization. In group intelligence optimization, the balance between exploration and exploitation is important. However, in PSO, it is unclear to what extent each parameter affects exploration and exploitation. Therefore, we proposed a deterministic PSO without probabilistic elements and analyzed the dynamics of PSO using the dynamical systems theory. Each particle in deterministic PSO has its motion determined by its eigenvalue. To make this motion clearer, a canonical deterministic PSO on a regularized phase space was proposed. The results of these analyses clarified what is attributed to the parameters for exploration and exploitation, i.e., global and local search capabilities. On the basis of this fact, we proposed a nonlinear map optimization (NMO) with improved local search capability. In this paper, we present the background of our proposal and consider the solution-search capability of NMO.
