基于不动点算法和K_2(m)剖分的遗传算法的改进  

Improved genetic algorithm based on fixed point algorithm and K_2(m) triangulation

作　　者：陈焕[1] 范志红[1] 高瑞贞[1] 张京军[1] 

机构地区：[1]河北工程大学信息与电气工程学院,河北邯郸056038

出　　处：《河北工程大学学报（自然科学版）》2011年第2期56-59,67,共5页Journal of Hebei University of Engineering:Natural Science Edition

基　　金：国家自然科学基金项目(60875037);河北省自然科学基金项目(E2008000731)

摘　　要：针对n维闭包腔函数优化问题,把单纯形自映射不动点算法与遗传算法结合进行求解。首先将解空间利用同胚映射转化为n维标准单纯形,然后对n维标准单纯形进行K2(m)剖分和相应的整数标号得到个体的承载单纯形顶点的标号信息,依据顶点信息和函数设计编码和遗传算子,当个体的承载单纯形是全标单纯形时,算法终止,得到优化问题的近似解。算例结果表明,改进后的算法在6代之内完成收敛,显示了极高的全局优化形态与计算效率。The genetic algorithm was combined with the simplex self-mapping fixed point algorithm to solve the n-dimensional closure cavity function optimization problems.Solution space of the optimization problem would be transformed as ndimensional standard simplex by homeomorphism mapping,then the vertex label information of the individual loading simplex of n-dimensional standard simplex could be calculated with K2（m） triangulation and integer label,and the coding and genetic operators were designed by vertex label information and function.When the loading simplexes of individuals were transformed into the completely labeled simplexes,the algorithm would be terminated and the approximate solution of the optimization problem would be obtained.The results of a computing example showed that the improved algorithm converged in the 6th generation, which had high global optimization form and computing efficiency.

关 键 词：遗传算法 同胚映射 不动点 K2(m)剖分 整数标号 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]