区间二次双层规划的最好最优解  

The best optimal solution of quadratic bi-level programming with interval coefficients

作　　者：高小妮[1] 孙玉华[1] GAO Xiao-ni SUN Yu-hua(School of Mathematics and Physics ,University of Science and Technology Beijing ,Beijing 100083 ,China)

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《经济数学》2017年第2期58-62,共5页Journal of Quantitative Economics

基　　金：国家自然科学基金项目(11471010)

摘　　要：双层规划问题是一类具有递阶结构的优化问题.在不确定的双层规划优化问题中,目标函数系数或约束条件系数为区间数的双层规划模型在实际问题中有着广泛的应用.在二次-线性双层规划模型的基础上,提出了上、下层目标函数以及约束条件系数均具有区间系数的二次-线性双层规划模型,给出了求解其最好最优解的方法.首先,通过选取约束条件中不同的基矩阵,求得区间二次-线性双层规划的可能最优解.再比较求得的全部可能最优解,便可得到区间二次-线性双层规划模型的最好最优解.最后给出数值算例验证该方法的有效性.Bi level programming problem is a class of optimization problems with hierarchical structure. The uncertain bi level programming optimization problems, in which the coefficients of the objective function or the coefficients of the constraint conditions are interval coefficients, has been widely used in the actual problem.For a kind of quadratic-linear bi-level pro gramming problems with interval coefficients in the objective function and constraint conditions, an algorithm was proposed to solve its best optimal solution on the basis of quadratic-linear bi level programming problems. First, by choosing the different basis matrix of constraint, we can solve the possible optimal solution of quadratic linear bi-level programming problems with interval coefficients. Second, compared with all possible optimal solution, we obtain the best optimal solution of the model. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.

关 键 词：运筹学与控制论 区间二次-线性双层规划 基矩阵 最好最优解 

分 类 号：O221[理学—运筹学与控制论]