一种改进的自适应遗传算法的收敛性分析

Convergence Analysis of an Improved Adaptive Genetic Algorithm

针对目前遗传算法缺乏有效的分析工具,理论分析困难较大的问题,提出了一种基于压缩映射原理的收敛性分析方法。首先,讨论了遗传算法收敛性的2种定义。然后介绍了一种基于精英保留策略的改进的自适应遗传算法,作为收敛性分析的对象。介绍了压缩映射原理,作为收敛性分析工具。最后,应用该定理对改进的自适应遗传算法进行了收敛性分析,验证了该算法是收敛的,证明压缩映射原理是遗传算法收敛性分析的一种有效工具。

Currendy theoretical analysis for genetic algorithm faces great challenges and few effective analysis tools are available. Here a convergence analysis method based on the compression mapping principle is proposed. First, two definitions of the genetic algorithm convergence are discussed. Then, an improved adaptive genetic algorithm based on the elitism strategy is introduced, which is used as the object of convergence analysis. Next, the principle of compression mapping is introduced as convergence analysis tool. Finally, convergence analysis for the improved adaptive genetic algorithm is performed based on the theory. It concluded that is that it is converged. It proved that the compression mapping principle is an effective tool for genetic algorithm convergence analysis.