Adaptive Relaxations for Multistage Robust Optimization

TL;DR

This paper introduces adaptive relaxation techniques for multistage robust optimization, leveraging game tree search and scenario adaptation to improve solution quality and computational efficiency in complex decision problems.

Contribution

It proposes two novel scenario-based relaxations that adapt during the search, enhancing the solution process for multistage robust optimization problems.

Findings

Adaptive relaxations improve solution quality.

Scenario adaptation reduces computation time.

Effective in scheduling and assignment problems.

Abstract

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.