文化算法的收敛性分析  

Analysis on the convergence of cultural algorithm

作　　者：郭一楠[1] 陈美蓉[1,2] 王春[1] 刘海媛[1,2] 

机构地区：[1]中国矿业大学信息与电气工程学院,江苏徐州221116 [2]中国矿业大学理学院,江苏徐州221116

出　　处：《控制与决策》2013年第9期1361-1364,1371,共5页Control and Decision

基　　金：国家自然科学基金项目(60805025);江苏省自然科学基金项目(BK2010183);江苏省中青年骨干教师及校长境外研究项目(2011-2012)

摘　　要：虽然文化算法已被广泛应用于解决各个领域的优化问题,但与其收敛能力相关的理论分析还比较缺乏.为此,针对传统文化算法,应用有限状态Markov链来分析文化算法的搜索过程,进一步使用公理化模型深入研究了种群在决策空间上的概率分布情况,证明了在文化算法信度空间的标准知识、拓扑知识和状况知识引导下,变异算子和最优保留选择策略保证了文化算法依概率弱收敛到全局最优解.Though cultural algorithms have been applied to many optimization problems in various fields,there lakes the theory analysis related to the convergence performance of these algorithms.Therefore,aiming at traditional cultural algorithms,the search process of cultural algorithm is analyzed by means of finite Markov chains.Furthermore,the probability distribution of population in decision spaces is deeply studied by making use of the axiomatic model.It is proved that cultural algorithms quasi-converge to the optimal solution in probability under the guidance of normative knowledge,topographical knowledge and situational knowledge in belief space.

关 键 词：文化算法 MARKOV链 满意集 依概率弱收敛 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]