关于“遗传算法的全局收敛性和计算效率分析”一文的商榷

The Discussion about the Paper“The Analysis of Global Convergence and Computational Efficiency for Genetic Algorithm”

文 [1]指出 ,具有比例复制和自适应交叉、变异操作的遗传算法 (简称AGA)满足最优保存GA(简称EGA)的条件 ,则由EGA全局收敛的结论得出AGA也是全局收敛的 ;同时认为 ,AGA构成的Markov链为非时齐的 .本文给出了EGA的严格定义 ,指出了EGA全局收敛的本质 ,说明AGA实际并不属于EGA ,因此也不能沿用EGA全局收敛的结论 .在此基础上证明了AGA不能全局收敛 .最后仔细分析了AGA的遗传操作 ,说明AGA可由时齐Markov链来描述 .

Paper [1]points out that GA with proportional reproduction,adaptive crossover and mutation probability(AGA)meets the condition of elitist preserved GA(EGA)and concludes AGAs global convergence from EGAs global convergence conclusion.At the same time,its considered the Markov chain AGA generates is inhomogeneous. More normative definition of EGA is given and the essence of EGA global convergence is indicated.It illuminates AGA isnt one kind of EGA and its convergence analysis cannt follow the conclusion of EGAs.On the basis of it,AGAs inability to converge globally is proved.Finally,the genetic operation of AGA is analyzed carefully.It shows AGA can be described as a homogeneous Markov chain.