# Adaptive Relaxations for Multistage Robust Optimization

arXiv: https://arxiv.org/abs/2106.12858 · HTML: https://mlsanity.com/paper/2106.12858/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2021.

## Built on by (most cited first, 1 of 1)

- [An Expansion-Based Approach for Quantified Integer Programming](https://mlsanity.com/paper/2506.04452/) (2025)

## Abstract (arXiv)

Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In this algorithmic environment relaxations are repeatedly called to asses the quality of a branching variable and for the generation of bounds. A useful relaxation, however, must be well balanced with regard to its quality and its computing time. We present two relaxations that incorporate scenarios from the uncertainty set, whereby the considered set of scenarios is continuously adapted according to the latest information gathered during the search process. Using selection, assignment, and runway scheduling problems as a testbed, we show the impact of our findings.