# Oracle-Based Algorithms for Binary Two-Stage Robust Optimization

arXiv: https://arxiv.org/abs/1905.05257 · HTML: https://mlsanity.com/paper/1905.05257/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2019.

## Built on by (most cited first, 3 of 3)

- [Data-driven Prediction of Relevant Scenarios for Robust Combinatorial Optimization](https://mlsanity.com/paper/2203.16642/) (2022)
- [Implicit Bilevel Optimization: Differentiating through Bilevel Optimization Programming](https://mlsanity.com/paper/2302.14473/) (2023)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)

## Abstract (arXiv)

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.