参数选取对遗传算法动力学形态的影响

Effects of Paramenters Selection on Global Dynamical Shape of Genetic Algorithms

遗传算法中参数的选取决定遗传算法的运行性能 .目前 ,对算法中参数选取都是经验性的 .本文针对一个典型的 2 - bit问题 ,分析了在不同参数选取下 GA的全局动力学形态 .通过对标准遗传算法的各种参数的选取 ,分别建立了数学模型 .分析了这些模型的吸引子 ,揭示了不同参数对动力学形态的影响 .世代重叠模型和无参数模型的动力学形态相似 .当变异概率很小时 ,模型与没有变异算子相类似 ;当变异算子足够大时 ,模型的动力学形态随着变异概率的增加发生了突变 .原有的吸引不动点消失 ,原来的排斥不动点变成吸引不动点 .这些论证为遗传算法中参数选取提供了一些理论上的证据 .

The parameters of GA have effects on its performance. Now, the values of these parameters are selected by hand. The GA's global dynamic shapes of different parameters are analyzed in accordance with a simple 2-bit problem. A series of mathematic models are established based on different parameters selection of standard genetic algorithm. The attractors of these models are solved. It is proved that the overlapped generations model is same as the no-parameter model. When the mutation probability is small enough, this model is same as that of no-parameter; when the mutation probability is large, the dynamical shape has changed. Old attraction fixed points have disappeared, the old ejection point became attractor. These conclusions provide some theoretical evidences of parameter selection.