Abstract: The hybrid Powell-LLPSO algorithm based on the Powell search method and the local constriction approach particle swarm optimization with linear varying inertia weight for unconstrained optimization was proposed. Powel-LLPSO is very easy to implement in practice since does not require gradient computation. The modification of both the Powell search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybrid strategy. In a suit of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid Powell-LLPSO approach outperforms other three relevant search techniques (the original PSO, the guaranteed convergence particle swarm optimization (GCPSO) and hybrid NM-PSO) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the Powell-LLPSO algorithm was compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the Powell-LLPSO algorithm in the performance of accuracy, robustness and function evaluation.

Key words: Powell search method, Particle swarm method, Unconstrained optimization

摘要： 提出一个求解无约束最优化问题的新的混合算法——Powell搜索法和惯性权重线性调整的局部收缩的微粒群算法的混合算法。该算法不需要计算梯度，容易应用于实际问题中。通过对微粒群算法的修正，使混合算法具有更加精确和快速的收敛性。主要目的是通过加入混合策略证明标准微粒群算法是能够被改进的。首先利用20个基准测试函数进行仿真计算并比较，计算结果表明，新混合算法在求解质量和收敛速率上都优于其它的3种算法（PSO，GPSO和NM-PSO算法）。同时将新混合算法和最新的各种协同的PSO算法进行分析比较，比较结果表明，新混合算法在解的搜索质量、效率和关于初始点的鲁棒性都远优于其他的进化算法。仿真结果证明了新算法是求解无约束最优化问题的一个高效的算法。

关键词: Powell搜索法, 微粒群算法, 无约束最优化