参数搜索空间规模对遗传算法稳定性的影响

对基于基因池重组遗传算法的无限种群动力系统进行了分析,讨论了参数搜索空间规模对系统稳定性的影响.特别地,针对处理“大海捞针”函数时参数搜索空间规模与系统不动点的解析关系进行了刻画,证明当参数搜索空间规模较小时,系统只有一个接近最优的稳定不动点;随着参数搜索空间规模的扩大,当超过临界值时,会出现一个不稳定的随机不动点和另外一个稳定不动点;当参数搜索空间规模进一步扩大时,所有的不动点将最终消失.实验和分析进一步证明该理论结果在通常情况下也适用.

Influence of solution space scale on stability of GA

This paper quantitatively analyzes the infinite population dynamics system of the gene pool GA and discusses the influence of the solution space scale on the stability of the gene pool GA.Specially we characterize the analytic relation between the solution space scale and the fixed points of the system in the case of the needle-in-a-haystack fitness function.It shows that only one approximate optimal stable fixed point exists in the infinite population dynamics system when the solution space scale is relatively small.With the increase of the solution space scale,one unstable fixed point and another stable fixed point will appear.When the solution space scale goes beyond some thresholds,all the fixed points will disappear.Further analysis and experiments illustrate that the theoretic result is also applicable to common cases.