Theoretical analysis of canonical deterministic PSO and the development of itsapplications

粒子群优化（PSO）系统是求解全局优化问题的有力系统之一。与已有的元启发式算法相比，粒子群算法可以快速搜索给定评价函数的最优值。由于常规粒子群系统中存在一些随机因素，因此系统的动力学可以看作是随机动力学系统。为了严格地分析动力学，一些论文关注不包含任何随机因素的确定性粒子群系统。根据这些结果，系统的特征值对粒子的动力学有影响。随着参数的变化，确定性粒子群的搜索能力降低。为了克服这一问题，我们提出了一种典型确定性粒子群算法，它可以很容易地控制其特征值，从而提高了搜索能力。通过数值实验证实了特征值与最优值搜索能力之间的关系。

A particle swarm optimization (PSO) system is one of the powerful systems for solving global optimization problems. The PSO algorithm can search an optimal value of a given evaluation function quickly compared with other proposed meta-heuristics algorithms. The conventional PSO system contains some random factors, therefore, the dynamics of the system can be regarded as stochastic dynamical systems. In order to analyze the dynamics rigorously, some papers pay attention to deterministic PSO systems which does not contain any stochastic factors. According to these results, the eigenvalues of the system impinge on the dynamics of the particles. Depending on the parameter, the searching ability of the deterministic PSO is decreased. In order to overcome this, we propose a canonical deterministic PSO which can control its eigenvalues easily, and can improve the searching ability. We confirmed relation between the eigenvalues and the searching ability of the optimal value from some numerical experiments.