遗传算法收敛性的动力学分析及其应用

DYNAMIC ANALYSIS OF GA'S CONSTRINGENCY AND ITS APPLICATION

遗传算法的收敛性 ,特别是交叉算子的作用 ,一直缺乏深入的理论分析 .当系统动力学的方法被应用于遗传算法的运行机理分析时 ,可以探讨在没有变异算子情况下遗传算法的收敛性问题 .从而 ,明确了局部极值点的含义 ,指出了局部极值点的存在性和存在条件 ,证明了遗传算法在局部极值点附近的收敛性 .并针对遗传算法的各种改进给出了理论上的依据 。

The convergence of genetic algorithm (GA), especially the consequence of crossover operator, is devoid of theoretic analysis. When the system dynamic analysis of running mechanism of GA is applied, the constringency of GA can be discussed when mutation operator is omitted. An explicit definition of local peak is shown, and the existence condition of local peak is given. It is proved that the GA is constringent at the neighbor of its local peak. The theoretical evidences of some improvements on GA are given, which points out the way forward for improving GA's performance.