An Adaptive Three-Stage Algorithm For Solving Adjustable Min-Max-Regret Problems

TL;DR

This paper introduces an adaptive three-stage algorithm that combines affine decision rules with min-max-regret robustness, effectively solving complex bilevel optimization problems with improved scalability for uncertain systems.

Contribution

It presents a novel three-stage algorithm that adaptively discretizes uncertainty sets, blending affine decision rules with min-max-regret robustness, and proves its convergence.

Findings

Algorithm effectively scales to larger problem instances.

Demonstrates applicability to robust water supply system planning.

Shows improved solution quality over traditional methods.

Abstract

This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not over-conservative. This combination results in a bilevel optimization problem. For solving this problem, a three-stage algorithm which uses adaptive discretization of the uncertainty set via two criteria is presented and its convergence is proven. The algorithm is applicable for an example of optimizing a robust pump operation plan for a drinking water supply system facing uncertain demand. The algorithm shows a notable ability to scale, presenting an opportunity to solve larger instances that might challenge existing optimization approaches.