多目标线性规划的Projective geometry和外逼近算法
Projective geometry and the outer approximation algorithm for multiobjective linear programming
摘要：
多目标线性规划的一个关键问题是求目标空间中所有有效极值点的集合。在本文中，我们引入定向射影几何作为一个高效和有效的框架来解决这个问题。定向射影几何的主要优点是我们可以处理一个“最优简单”但无界的效率等价多面体，但可以将传统上限制在有界多面体上的熟悉理论和算法应用于它。我们将这些技术应用于本森的外近似算法，使用面向投影几何删除的算法的指数大的复杂性，从而消除了显着的负担，从运行时间。
英文摘要：
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this problem. The key advantage of oriented projective geometry is that we can work with an "optimally simple" but unbounded efficiency-equivalent polyhedron, yet apply to it the familiar theory and algorithms that are traditionally restricted to bounded polytopes. We apply these techniques to Benson's outer approximation algorithm, using oriented projective geometry to remove an exponentially large complexity from the algorithm and thereby remove a significant burden from the running time.
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