采用重复交叉操作及最优保留策略的遗传算法

基于有限次重复交叉操作和将父代的最好个体代替子代的最差个体的思想，提出了一种新的遗传算法（REGA）。该方法克服了基本遗传算法容易出现的早熟现象，并利用马尔可夫极限定理获得全局收敛性，求得基于有限次重复交叉操作的基本遗传算法（记为RSGA）的渐近性质，以及提供关于这两种算法吸收时间的数学期望的计算方法，仿真事例表明，它不仅克服了局部最优的缺点，而且适用于有多个最优解问题，同时群体的平均适应度增加较快，运行效率更高，因而，该方法对于优化问题具有一定的应用价值。

A Genetic Algorithm Based on Repeating Crossover and Optimum Maintaining Strategy

A novel genetic algorithm,simply written as REGA, is proposed with the idea to limit the number of repeating crossover and replacing the worst individuals of the current generation by the best ones of the former generation. The algorithm overcomes the premature phenomenon of the simple genetic algorithm. According to Markov's limitation theorem, we prove its global convergence,explore the properties of the genetic algorithm written as RSGA only based on repeating crossover,and provide a method to calculate the mathematic expectation on the absorption time for the two algorithms. Finally,the simulation shows that the algorithm REGA can solve the optimization problem containing more than one global optimal solutions,on one hand,while eliminating the drawback of local optimum and rapidly enhancing the average fitness. On the other hand, REGA is valuable for function optimization.