二层多目标随机规划逼近有效解集的上半收敛性

The Upper Semi-Convergence of the Sets of Approximation Efficient Solutions for Bi-Level Multi-Objective Stochastic Programming

【目的】为了研究通过逼近方法求解二层多目标随机规划有效解集与精确的有效解集之间的相互关系,针对下层为单目标随机规划,上层为多目标随机规划的一类二层随机规划逼近问题,构建了二层多目标随机规划逼近有效解集上半收敛性的理论框架。【方法】将多目标二层随机规划分解成多个单目标二层随机规划,利用每个单目标二层随机规划逼近最优解集的上半收敛性,借助于多目标二层随机规划有效解集可以表示为所有单目标二层随机规划最优解集的交集的结构特点,对二层多目标随机规划逼近问题的有效解集的收敛性结果进行了推断。【结果】建立了二层多目标随机规划逼近有效解集的上半收敛性。【结论】提供了利用逼近方法求解二层多目标随机规划有效解集可以近似替代精确的有效解集的理论依据。

[Purposes]Our goal is to study the relationship between the effective solution sets and the exact effective solution sets of bi-level multi-objective stochastic programming by the approximate method,and to construct a theoretical framework of the upper semi-convergence of the approximation efficient solution sets for bi-level multi-objective stochastic programming,which is the lower level single objective stochastic programming and the upper level multi-objective stochastic programming.[Methods]The multiobjective bi-level stochastic programming is first decomposed into multiple single objective bi-level stochastic programming,and then the upper semi-convergence of approximate the optimal solution sets of each single objective bi-level stochastic programming is used to solve the bi-level multi-objective stochastic programming.With the help of the structural characteristics,the effective solution sets of multi-objective bi-level stochastic programming can be expressed to the intersection of optimal solution sets for all single objective bi-level stochastic programming,and then the convergence result of the effective solution sets for the approximation problem of bilevel multi-objective stochastic programming is deduced.[Findings]The upper semi-convergence of approximation efficient solution sets of bi-level multi-objective stochastic programming is established.[Conclusions]This conclusion provides the theoretical basis that approximation effective solution sets can approximately replace the exact effective solution sets in bi-level multi-objective stochastic programming.