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用随机过程中的马尔科夫链模型来分析遗传算法的收敛性是遗传算法理论研究的重要领域。但在用随机过程理论来分析非齐次的一般状态空间下的遗传算法的收敛性,还缺少完整的收敛性结果。运用非时齐转移函数以及它满足K—C方程来分析一般状态空间下遗传算法的收敛性,在保留最优个体的策略下得到了收敛的一般条件。在二进制编码的可数状态空间下转移函数为非齐次时,得到保证收敛性的充分条件。
Analyzing the convergence of genetic algorithm by using Markov chain model in random process is an important area of theoretical research in genetic algorithms. However, using the stochastic process theory to analyze the convergence of genetic algorithms under nonhomogeneous general state space, we still lack a complete convergence result. The non-homogeneous transfer function and its K-C equation are used to analyze the convergence of genetic algorithm in general state space. The general condition of convergence is obtained under the strategy of preserving the optimal individual. When the transfer function in binary state is non-homogeneous, a sufficient condition for ensuring convergence is obtained.