基于自适应排斥因子的改进粒子群算法

基本粒子群算法在求解复杂的多峰问题时，由于存在较多的局部最优解，算法极易出现早熟现象。为克服这一缺陷，采用蒙特卡洛(Monte Carlo)方法模拟了种群飞行轨迹，得出种群极易陷入局部最优解的原因;在此基础上，通过定义粒子间距离、粒子间最大距离和粒子间平均距离，提出一种自适应控制粒子自身最优位置和种群最优位置间距离的排斥因子(ARF)，来提升种群跳出局部最优的能力。为测试提出策略的有效性，在60次独立运行时，基于ARF的改进PSO算法(ARFPSO)在Rosenbrock，Ackley和Griewank函数上所获得的最好值分别为53.82，2.1203和5.32E-004，都优于其他两种对比算法，这表明ARFPSO能有效地跳出局部最优解；算法的复杂度分析表明引入的策略没有增加计算复杂度。

Improved particle swarm optimization based on adaptive rejection factor

As the multimodal complex problem has many local optima, it is difficult for the basic Particle Swarm Optimization (PSO) to effectively solve this kind of problem. To conquer this defect, firstly, Monte Carlo method was used to simulate the fly trajectory of particle, and the reason for falling into local optima was concluded. Then, by defining distance, average distance and maximal distance between particles, an adaptive control factor named Adaptive Rejection Factor (ARF) for controlling local optimum position and global optimum position was proposed to increase the ability for escaping from local optima. In order to test the proposed strategy, three test benchmarks including Rosenbrock, Ackley and Griewank were selected to conduct the analysis of convergence property and statistical property. The 60 times independent runs show that the improved PSO based on ARF (ARFPSO) has the best value of 53.82, 2.1203 and 5.32E-004, which is better than the both contrast algorithms. The results show that ARFPSO can effectively avoid premature phenomenon, and the complexity analysis of the algorithm also shows that the introduced strategy does not increase computational complexity.