【摘要】 为对树形结构编码的遗传算法进行更深入的研究 ,提出了基于二叉树结构编码的遗传算法的一般形式 ,并以函数模型的波兰表达式为例 ,详细描述了二叉树结构编码的遗传算法的算子。重点分析了二叉树结构编码的遗传算法的收敛性。在实际的研究中 ,对二叉树结构进行空间深度限制后 ,其遗传算法可以用一个有限状态空间的 Markov链来描述。在此基础上 ,证明了二叉树结构编码的遗传算法在对选择算子进行改进后依概率收敛到最优解。更多还原

【Abstract】 A mathematical description of genetic algorithms is proposed based on the bintree structural representation. Taking polish notation of the functional model as an example, the algorithms’ three genetic operators: selection, mutation and crossover, are explained in detail. The convergence of the algorithm is also analyzed. If the space of the bintree structure is limited by the depth of the bintree, the algorithm can be described with Markov chains of finite state space. On the basis of these studies, improved genetic algorithm convergence in probability is proven.更多还原