Robust optimization provides a mathematical framework for modeling and
solving decision-making problems under worst-case uncertainty. This work
addresses two-stage robust optimization (2RO) problems (also called adjustable
robust optimization), wherein first-stage and second-stage decisions are made
before and after uncertainty is realized, respectively. This results in a
nested min-max-min optimization problem which is extremely challenging
computationally, especially when the decisions are discrete. We propose
Neur2RO, an efficient machine learning-driven instantiation of
column-and-constraint generation (CCG), a classical iterative algorithm for
2RO. Specifically, we learn to estimate the value function of the second-stage
problem via a novel neural network architecture that is easy to optimize over
by design. Embedding our neural network into CCG yields high-quality solutions
quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital
budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2\%$
of the best-known values in a few seconds compared to the three hours of the
state-of-the-art exact branch-and-price algorithm; for larger and more complex
instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO
outperforms three variants of the $k$-adaptability algorithm, particularly on
the largest instances, with a 5 to 10-fold reduction in solution time. Our code
and data are available at this https URL

该论文研究了两阶段鲁棒优化问题，并提出了一种基于机器学习的方法 Neur2RO 来解决该问题。通过将神经网络嵌入到迭代算法中，Neur2RO 可以高效地找到高质量解决方案。实验证明，与现有算法相比，该方法在几秒内就能找到接近最优解的解决方案。

神经二阶段鲁棒优化

Neur2RO: Neural Two-Stage Robust Optimization

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 & 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 & bound procedure outperforms the
column-and-constraint generation algorithm.

本文研究具有目标不确定性的二阶段鲁棒优化问题，提出了一种算法，通过交替求解基础确定性问题和对抗性问题来高效计算二阶段鲁棒问题的下界。该算法适用于线性和非线性目标函数，研究发现其在非线性目标函数下，具有更高的性能表现。同时作者还测试了基于列生成和约束生成算法的另一种求解方法，发现分支定界算法的表现更胜一筹。