演化算法的最优轨道分析

Optimal Trajectory Analysis for the Evolutionary Algorithm

基于最优控制理论,提出了演化算法的一种最优轨道分析方法.将演化算法描述成一个动力系统,定义了它的时间最优控制模型.运用著名的Pontryagain极大值原理,分析了演化算法的最优轨道,并利用矩阵范数理论对最优轨道进行了一些理论估计.同时将理论分析结果应用于演化算法的设计之中,导出了一种新的选择策略和终止条件.

Based on optimal control theory, an optimal trajectory method is proposed for analyzing the evolutionary algorithm in this paper. The evolutionary algorithm is described as a dynamical system. And its optimal control model over time is then defined. Using the well known Pontryagain maximum principle (PMP), the optimal trajectory of the evolutionary algorithm is analyzed. The optimal trajectory is estimated by applying the theory of matrix norms. The results are used in the design of evolutionary algorithms. A new selection strategy and new stopping criteria are derived.