椭球不确定集下的鲁棒线性双层规划  

Robust Linear Bilevel Programming under Ellipsoidal Uncertainty

作　　者：李砚[1] 杜纲[1] 

机构地区：[1]天津大学管理与经济学部,天津300072

出　　处：《系统工程》2011年第11期96-100,共5页Systems Engineering

基　　金：国家自然科学基金资助项目(7107110a4)

摘　　要：针对目标函数系数和约束条件系数均在椭球集内扰动的不确定线性双层规划,提出了椭球不确定集下的鲁棒线性双层规划问题。基于上下两层决策者均需获得鲁棒解的前提假设给出了其相应的定义与定理,以此把原问题转化为下层具有二阶锥约束的确定性非线性双层规划问题,并提出了一种混合策略算法(上层采用遗传算法,下层利用具有全局收敛性的非内部连续化算法)进行求解,从而获得不确定双层规划的鲁棒解。用数值算例验证了该算法的可行性及有效性。The robust solution is defined for the linear bilevel programming（BLP） with the coefficients under the ellipsoidal disturbance in objective functions and constrain conditions.Based on the assumption that the decision-makers of the upper and lower levels need to acquire the robust solution,the original uncertain BLP was converted to the deterministic BLP constrained with second-order cone,and then the mixed strategy,which solved the upper programming using genetic algorithm and the lower using the non-interior continuation method,is proposed to obtain the robust solution.A numerical example is shown to demonstrate the effectiveness and feasibility of the algorithm.

关 键 词：线性双层规划 鲁棒优化 椭球扰动 二阶锥规划 混合策略 

分 类 号：O221[理学—运筹学与控制论]