八皇后问题所有解的模拟DNA算法  

Simulation DNA algorithm of all solutions of Eight Queens Problem

作　　者：周康[1] 魏传佳[1] 刘朔[1] 卢军[1] 

机构地区：[1]武汉工业学院数理科学系,湖北武汉430023

出　　处：《华中科技大学学报（自然科学版）》2009年第6期24-27,39,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60574041);湖北省自然科学基金资助项目(2007ABA407;2005ABA233);湖北省优秀中青年科技创新团队计划资助项目;湖北省教育厅A类项目(D20091805)

摘　　要：建立了求解八皇后问题所有解的数学模型.根据八皇后问题解的性质提出了7个相关的算子:主转置算子、行翻转算子、列翻转算子、倒置算子、顺旋算子、逆旋算子和倒转算子.给出了等价可行解的概念,并以这7个相关算子为工具研究了等价可行解的性质和八皇后问题解空间的性质.由此给出了求解八皇后问题所有解的模拟DNA算法,并用Mathematica软件进行了实现,并得到了所有的可行解,进而验证了算法的正确性和可行性.Mathematics model of Eight Queens Problem is set up in this paper. According to characteristic of Eight Queens Problem, seven operators of Eight Queens Problem are brought forward, which are dominant transposed operator, row-flip operator, list-flip operator, inversion operator, ordinalturn operator, contrary-turn operator, reverse operator. Equipollence feasible solution of Eight Queens Problem is brought forward, and characteristic of quipollence feasible solution and characteristic of solution space of Eight Queens Problem are studied using these seven operators. Thereby, simulation DNA algorithm of all solutions of Eight Queens Problem is found, which is realized on Mathematica software, then all feasible solutions of Eight Queens Problem are obtained.

关 键 词：八皇后问题 数学模型 等价可行解 算子 模拟DNA算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]