an:06762523
Zbl 1369.90160
Ji, Ying; Qu, Shaojian; Yu, Zhensheng
A new method for solving multiobjective bilevel programs
EN
Discrete Dyn. Nat. Soc. 2017, Article ID 2870420, 10 p. (2017).
1026-0226 1607-887X
2017
j
90C29 90C30
Summary: We study a class of multiobjective bilevel programs with the weights of objectives being uncertain and assumed to belong to convex and compact set. To the best of our knowledge, there is no study about this class of problems. We use a worst-case weighted approach to solve this class of problems. Our ``worst-case weighted multiobjective bilevel programs'' model supposes that each player (leader or follower) has a set of weights to their objectives and wishes to minimize their maximum weighted sum objective where the maximization is with respect to the set of weights. This new model gives rise to a new Pareto optimum concept, which we call ``robust-weighted Pareto optimum''; for the worst-case weighted multiobjective optimization with the weight set of each player given as a polytope, we show that a robust-weighted Pareto optimum can be obtained by solving mathematical programing with equilibrium constraints (MPEC). For an application, we illustrate the usefulness of the worst-case weighted
multiobjective optimization to a supply chain risk management under demand uncertainty. By the comparison with the existing weighted approach, we show that our method is more robust and can be more efficiently applied to real-world problems.