Theoretical analysis of canonical deterministic PSO and the development of itsapplications

粒子群优化系统是求解全局优化问题的一种强有力的系统。与已有的元分析算法相比，粒子群算法能快速地搜索到给定评价函数的最优值。传统的粒子群优化系统中含有一些随机因素，因此，系统的动力学可以看作是随机动力学系统。为了严格地分析系统的动力学行为，一些文献将注意力集中在不包含任何随机因素的确定性PSO系统上。根据这些结果，系统的本征值影响粒子的动力学。确定性粒子群算法的搜索能力随着参数的变化而降低。为了克服这一点，我们提出了一个规范的确定性粒子群算法，它可以很容易地控制其特征值，并可以提高搜索能力。通过数值实验，我们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.