统计遗传算法

本文讨论了遗传算法中框架定理的不足之处，并对之进行了改进，然后分析了遗传算法与Ａ算法的相似性，以及遗传算法的概率性质．由此联想到它与ＳＡ算法的相似性，在此基础上，作者将原先发展的一套ＳＡ算法的理论移植到遗传算法中来，建立一个新的算法，称之为统计遗传算法（简记为ＳＧＡ算法）．为适合于优化计算，作者引入最大值统计量及其对应的ＳＡ算法（简称为ＳＭＡ算法），并将ＳＭＡ算法与ＧＡ算法相结合（记为ＳＧＡ（ＭＡＸ）算法）．新的算法不仅提高了算法的精度和降低了计算的复杂性，而且能克服ＧＡ算法中出现“早熟”的现象以及提供进行并行计算的可能性．更主要的是新的方法为ＧＡ算法的精度、可信度和计算复杂性的定量分析提供了理论和方法上的有力工具.

THE STATISTICAL GENETIC ALGORITHMS

The deficiency of the schema theory in GA(genetic algorithms) and its improvement are discussed in this paper. The similarity between GA and heuristic search algorithm (a algorithm) and the probabilistic properties of GA are analyzed as well. Form the discussion, the similarity between GA and SA (statistical heuristic search) proposed by the authors is discovered. Therefore, when transferring the theory and results of SA to GA, a new statistical genetic algorithm can be established. In order to adapt to optimization computation, the maximal statistic and its corresponding SA called SMA are introduced. By combining the SMA and GA, a new algorithm SMA(MAX) is obtained. Using the new algorithm, the prematurity in general GAs can be overcome. The new algorithm also provides the possibility for parallel computing and a powerful tool for quantitative analysis of accuracy, confidence and computational complexity of GA.