基于最近区间近似和区间规划方法求解一类模糊双层规划问题  

An approach for Solving a Class of Fuzzy Bilevel Programming Problems Based on Nearest Interval Approximation and Interval Programming

作　　者：任爱红[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721013

出　　处：《模糊系统与数学》2015年第4期139-145,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61272119)

摘　　要：针对一类目标函数和约束函数均具有模糊系数的双层规划问题,提出了一种基于模糊数的最近区间近似和区间规划方法的求解方法。首先,利用模糊数的最近区间近似定义,将模糊双层规划转化为区间双层规划问题。其次,基于满意度的不确定约束转换和基于区间序关系的不确定目标函数的转换,将区间双层规划问题转化为一个确定性的多目标双层规划问题,接着采用线性加权将多目标函数进一步转换为单目标函数。最后,利用分布估计算法来求解确定性的双层规划问题。通过一个数值例子表明了求解方法的可行性。This paper considers the bilevel linear programming problem with fuzzy coefficients in the objective functions as well as in the constraints. Based on the nearest interval approximation operator, the original problem can be transformed into an interval bilevel programming problem. Combining the satisfactory degree of inequality constraints with an order interval relation between interval numbers, an interval bilevel programming problem can be converted into a multi-objective bilevel programming problem which is solved by means of weighted linear combination technique. In addition, an estimation of distribution algorithm is applied to deal with the resulting deterministic bilevel programming problem. Finally, an illustrative example is given to demonstrate the feasibility of the proposed approach.

关 键 词：模糊双层规划 最近区间近似 满意度 分布估计算法 

分 类 号：O221[理学—运筹学与控制论]