Anytime Algorithms for Adaptive Robust Optimization with OWA and WOWA

Abstract

We consider optimization problems in graphs where the utilities of solutions depend on different scenarios. In this context, we study incremental approaches for the determination of robust solutions, i.e. solutions yielding good outcomes in all scenarios. Our approach consists in interleaving adaptive preference elicitation methods aiming to assess the attitude of the Decision Maker towards robustness or risk with combinatorial optimization algorithms aiming to determine a robust solution. Our work focuses on the use of ordered weighted average (OWA) and weighted ordered weighted average (WOWA) to respectively model preferences under uncertainty and risk while accounting for the idea of robustness. These models are parameterized by weighting coefficients or weighting functions that must be fitted to the value system of the Decision Maker. We introduce and justify anytime algorithms for the adaptive elicitation of these parameters until a robust solution can be determined. We also test these algorithms on the robust assignment problem.