区间型极小极大遗憾优化问题的双预言机方法
A double oracle approach for minmax regret optimization problems with interval data
摘要：
在本文中，我们提供了一个通用的任何时候下边界程序的极小极大遗憾优化问题。我们证明，所获得的下界总是至少与Chassein和Goerigk（2015）最近提出的下界一样准确。该下限可以被视为极小极大遗憾优化的混合整数规划公式的线性规划松弛的最优值，但该论文的贡献是通过双预言算法计算该下限（McMahan等人，2003年，我指定。双预言机算法的设计依赖于鲁棒优化的博弈论观点，类似于Mastin et al.（2015）开发的算法，它可以有效地实现任何标准版本为“简单”的极小极大遗憾优化问题。我们描述了如何有效地嵌入这个下界在一个分支定界过程。最后，我们将我们的方法应用于鲁棒最短路径问题。我们的数值结果表明，在计算时间的显着增益相比，以前的方法在文献中。
英文摘要：
In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk (2015). This lower bound can be viewed as the optimal value of a linear programming relaxation of a mixed integer programming formulation of minmax regret optimization, but the contribution of the paper is to compute this lower bound via a double oracle algorithm (McMahan et al., 2003) that we specify. The double oracle algorithm is designed by relying on a game theoretic view of robust optimization, similar to the one developed by Mastin et al. (2015), and it can be efficiently implemented for any minmax regret optimization problem whose standard version is "easy". We describe how to efficiently embed this lower bound in a branch and bound procedure. Finally, we apply our approach to the robust shortest path problem. Our numerical results show a significant gain in the computation times compared to previous approaches in the literature.
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