On linear bilevel problems with multiple objectives at the lower level
On linear bilevel problems with multiple objectives at the lower level
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DOI：
10.1016/j.omega.2010.02.002
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发表时间：
2011-01-01
影响因子：
6.9
通讯作者：
Gale, Carmen
中科院分区：
文献类型：
--
作者：
Calvete, Herminia I.;Gale, Carmen
双层规划问题提供了一个框架来处理涉及两个具有层次结构的决策者的决策过程。它们的特点是存在两个优化问题，其中上层问题的约束区域隐式地由下层优化问题确定。本文主要研究双层问题，其中下层问题是一个线性多目标规划，两层的约束定义了多面体。这个双层问题被重新表述为一个由所有约束定义的多面体的面的并集给出的非凸区域上的优化问题。在处理低层次问题的有效解和弱有效解时，得到了这种重新表述。假设上层目标函数为拟凹形，则存在一个解决问题的极值点。提出了一种精确算法和一种元启发式算法，并对其性能进行了分析和比较。(C) 2010 Elsevier Ltd.版权所有。
Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared. (C) 2010 Elsevier Ltd. All rights reserved.