矩阵结构遗传算法  

Matrix Structure Genetic Algorithm

作　　者：潘峰[1,2] 龙福海 施启军 魏嘉银 PAN Feng;LONG Fu-hai;SHI Qi-jun;WEI Jia-yin(Provincial Key Laboratory of Pattern Recognition and Intelligent System,Guizhou Minzu University,Guiyang 550025,China;School of Software Engineering,South China University of Technology,Guangzhou 510006,China)

机构地区：[1]贵州民族大学模式识别与智能系统省级重点实验室,贵州贵阳550025 [2]华南理工大学软件学院,广东广州510006

出　　处：《计算机技术与发展》2022年第9期121-125,133,共6页Computer Technology and Development

基　　金：贵州省科技计划项目(黔科合基础[2018]1082);贵州省教育厅教改项目(20161113006,2020047)。

摘　　要：针对传统遗传算法在函数优化问题中的不足,提出构建一种矩阵结构种群的遗传算法MGA(Matrix Structure Genetic Algorithm)。MGA采用矩阵形式的数据结构,借助于矩阵的行、列及主对角线等概念描述种群,并在此结构上对选择、交叉和变异三种算子均进行改进。选择算子是通过逐行寻优构建父代精英种群,具体操作是每行最优个体移动到所在行的主对角线位置;交叉算子采用父代精英种群中任意两个个体A(i,i)和A(j,j)交叉产生两个子代个体A(i,j)和A(j,i),并分别置于关于主对角线对称的位置(i,j)和(j,i);变异算子是对种群全体逐一进行克隆变异,若克隆变异结果优于原个体则选择克隆变异结果,否则不变。经过上述三步的若干次循环迭代,最终以矩阵种群中的最优个体为问题的最优解。通过对若干函数优化问题的实验测试表明,该方法收敛速度很快,全局收敛性能显著提高,可以推广到其他演化算法。Aiming at the shortcomings of traditional genetic algorithm in function optimization,a matrix structure genetic algorithm(MGA)is proposed.MGA adopts a matrix data structure to describe the population with the help of the concepts of row,column and main diagonal of matrix,and improves the three operators of selection,crossover and mutation on this structure.The selection operator constructs the parent elite population through row by row optimization.The specific operation is that the optimal individual in each row moves to the main diagonal of the row.The crossover operator uses any two individuals A(i,i)and A(j,j)in the parent elite population to cross to produce two offspring individuals A(i,j)and A(j,i),which are placed symmetrically about the main diagonal(i,j)and(j,i).Mutation operator is to clone and mutate the whole population one by one.If the clone mutation result is better than the original individual,the clone mutation result is selected,otherwise it will not change.After several cyclic iterations of the above three steps,the optimal individual in the matrix population is finally taken as the optimal solution of the problem.The experimental results on some function optimization problems show that the convergence speed of the proposed method is fast,and the global convergence performance is significantly improved,which can be extended to other evolutionary algorithms.

关 键 词：矩阵结构 遗传算法 精英种群 克隆变异 函数优化问题 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]