In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

中文翻译：

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基于Oracle的二进制两阶段鲁棒优化算法

在这项工作中，我们研究具有目标不确定性的二阶二阶段鲁棒优化问题。我们提出了一种算法，可以通过交替求解基础确定性问题和对抗性问题，有效地计算二进制两阶段鲁棒问题的下界。对于确定性问题，可以使用任何预言机，它为每种可能的情况返回最佳解决方案。我们显示了后者的下界可以在分支定界过程中实现，其中分支仅在第一阶段决策变量上执行。对于不确定参数中凹入的非线性目标函数，所有结果甚至都成立。作为一种替代解决方案方法，我们将列约束生成算法应用于具有目标不确定性的二元二阶段鲁棒问题。我们在无能力的单分配中心位置问题和资本预算问题的基准实例上测试这两种算法。我们的结果表明，分支定界过程的性能优于列约束生成算法。