具有模糊关系约束的线性规划的解法  

Solution for linear programming with fuzzy relation constraints

作　　者：杨吉会[1,2] 曹炳元[3] 

机构地区：[1]沈阳炮兵学院基础教研室,辽宁沈阳110161 [2]汕头大学医学院伤害预防研究中心,广东汕头515041 [3]广州大学数学与信息科学学院,广东广州510006

出　　处：《系统工程学报》2008年第5期627-631,共5页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(70771030)

摘　　要：研究了具有模糊关系方程约束的线性规划问题.由于此类规划的非空可行集一般是一个非凸集,传统的求解线性规划的方法不适合求解此类规划问题,因此有必要提出一个求解此类规划问题的有效算法,本文首先刻画了该类规划可行集的结构,基于该可行集的结构,应用惩罚函数和遗传算法给出了该类规划问题的一个具体求解方法,得到了近似最优解.为了说明该方法的有效性,最后给出了具体的算例.An optimization model with a linear objective function subject to a system of fuzzy relation equations is presented. Since the non-empty feasible solution set of the fuzzy relation equations is generally a non-convex set, the conventional linear programming method will not be suitable for solving such a problem. Therefore, an efficient solution procedure for such problems is necessary. The structure of the feasible solution set for the problems is characterized first. A penalty function and genetic algorithm are applied to find approximate optimal solution based on the solution set structure of fuzzy relation equations. Finally, a concrete example is given to explain its validity.

关 键 词：模糊关系方程 模糊关系线性规划 遗传算法 近似最优解 

分 类 号：N945.25[自然科学总论—系统科学] C934[经济管理—管理学]