Robust Min-Max (Regret) Optimization using Ordered Weighted Averaging

TL;DR

This paper introduces a new variant of ordered weighted averaging (OWA) for optimization under uncertainty, unifying and extending robust min-max and min-max regret approaches, with improved complexity results and practical evaluation.

Contribution

It generalizes the classic OWA approach, providing a unified framework that includes robust min-max and regret optimization, along with new complexity and approximation results.

Findings

Stronger approximation bounds for the new OWA variant.

Computational experiments show improved solution quality.

The new approach outperforms classic OWA and min-max regret methods.

Abstract

In decision-making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios. This paper introduces a novel variant of ordered weighted averaging (OWA) for optimization problems. It generalizes the classic OWA approach, which includes robust min-max optimization as a special case, as well as min-max regret optimization. We derive new complexity results for this setting, including insights into the inapproximability and approximability of this problem. In particular, we provide stronger positive approximation results that asymptotically improve the previously best-known bounds for the classic OWA approach. In computational experiments, we evaluate the quality of the proposed methods and compare the proposed setting with classic OWA and min-max regret approaches.