限制速度粒子群优化和自适应速度粒子群优化在无约束优化问题中的应用

限制速度粒子群优化(RVPSO)和自适应速度粒子群优化(SAVPSO)是近年来提出的专门求解约束优化问题(COP)的粒子群优化算法,但目前尚无两算法在无约束优化应用方面的研究。为此,研究上述算法在无约束优化中的有效性和性能特点,并针对算法保守性较强的特点,分别引入混沌因子和随机优化策略对算法进行改进,从而提高算法的全局搜索能力;另外,还研究了不同参数设置对算法性能的影响。在5个典型测试函数上的仿真实验结果表明:RVPSO改进算法的鲁棒性及全局搜索能力优于原算法,但在求解高维多峰函数时仍易于陷入局部最优; SAVPSO改进算法的全局搜索能力比RVPSO改进算法强,且在求解高维多峰函数时具有更快的收敛速度并能取得精度更高的解,表现出较好的全局优化能力,是一种切实有效的求解无约束优化问题的算法。

Application of restricted velocity particle swarm optimization and self-adaptive velocity particle swarm optimization to unconstrained optimization problem

Restricted Velocity Particle Swarm Optimization (RVPSO) and Self-Adaptive Velocity Particle Swarm Optimization (SAVPSO) are two recently proposed Particle Swarm Optimization (PSO) algorithms specially for solving Constrained Optimization Problem (COP), but to our knowledge, no research has been done on the applications of the two algorithms to Unconstrained Optimizations Problem (UOP). To this end, the effectiveness and performance characteristics of the two algorithms in UOP were investigated. Moreover, in view of their relatively strong conservativeness, the algorithms were improved by combining chaos factor and random strategy respectively with the search mechanism to enhance their global exploration ability. Also, the effects of different parameter settings on the performance of all these algorithms were studied. The performance of all these algorithms was evaluated on 5 typical benchmark functions. Experimental and comparison results show that the improved RVPSO is better than RVPSO in terms of robustness and global exploration ability, but it may easily get trapped into local optima when solving high-dimensional multi-modal functions; the improved SAVPSO has stronger exploration ability and faster convergence rate than improved RVPSO, and it can achieve more accurate solutions when applied to high-dimensional multi-modal functions. Therefore, the improved SAVPSO has competitive ability of global optimization, and thus is an effective algorithm for solving unconstrained optimization problems.