基于Hénon混沌与动态非线性方程的改进粒子群优化算法

Improved particle swarm optimization based on Hénon chaos and dynamic nonlinear equations

为解决粒子群优化算法易于陷入局部最优问题,提出了两种新方法并行改进粒子群优化算法惯性权重:对适应度值比平均值差的粒子,用所设计的动态Hénon混沌映射公式调整惯性权重,在复杂多变的环境中逐步摆脱局部最优值,动态寻找全局最优值;对适应度值好于或等于平均值的粒子,用提出的动态非线性方程调整惯性权重,在保存相对有利环境的基础上逐步向全局最优处收敛。两种方法前后相辅相成、动态协调,使两个动态种群相互协作、协同进化。采用不同复杂程度的标准测试函数进行实验,结果发现,该算法在不同情况下都超越了同类著名改进粒子群优化算法。

To solve the premature problem of particle swarm optimization, introduced＇two new methods to improve particle swarm optimization ： when the fitness values of some particles were worse than the average, devised the dynamic Hénon chaotic map formula to modify the inertia weight, which could make particles break away from the local optima and search the global optima dynamically. On the contrary, when the fitness values of some particles were better than or equal to the average, employed the new introduced dynamic nonlinear equations to modify the inertia weight, which could retain favorable conditions and converge to the global optima continually. Two methods coordinated with each other dynamically, and made two dynamic swarms cooperate to evolve. Some well-known benchmark functions with different complexities were employed to test the performance of the new introduced algorithm. Experimental results demonstrate that the new introduced methods outperformed several other famous improved particle swarm optimization algorithms in different situations.