基于实数编码的遗传算法的收敛性研究

用基于实数（浮点）编码的遗传算法（FGA）求解连续参数优化问题是遗传算法的重要应用领域，但一直缺少其完整的收敛性结果。分析了在绝大多数实际应用中使用的FGA的收敛性问题，在采用最优个体保留策略的前提下得到了保证收敛性的一般条件，并以之检验了采用常用的变异与交叉算子时FGA的收敛性。这些结论不仅给出了有用的收敛性结果，而且对进一步认识算子的本质，指导自适应变异算子的设计等都提供了帮助。同时所用的方法和结论也适用于进化规划和进化策略的收敛性问题。

ON THE CONVERGENCE OF REAL-CODED GENETIC ALGORITHMS

Genetic algorithms based on real (floating) coded (FGAs) have received a great deal of attention regarding their potential as optimization techniques for complex functions, but the complete convergent results are still rare. In this paper, the convergence of FGAs used in most applications is analyzed and some general conclusions are obtained under best individual preservation strategy. Then by using them the convergence of FGAs is examined when using ordinary mutation and crossover operators. These results not only give useful convergence conclusions but also provide more insights into operators and give help to design adaptation operators. Besides, the process and results still hold true when discussing the convergence of EP(evdutionary programming) and ESs(evdutionary strategies).