A Computational Study for Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems

Abstract

Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exploited computationally. Based on the recent results by Goerigk et al. (2025), this paper is the first one that provides an extensive computational study for solving strictly robust optimization problems with decision-dependent uncertainty sets as equivalent bilevel optimization problems. If the uncertainty set can be dualized, the respective bilevel techniques to obtain a single-level reformulation are very similar compared with the classic dualization techniques used in robust optimization but lead to larger single-level problems to be solved. Our numerical study shows that this usually leads to larger computation times. For the more challenging case of decision-dependent uncertainty sets represented by mixed-integer linear models, one cannot apply classic dualization techniques from robust optimization. Thus, we compare the presented bilevel approach with an established method from the literature, which is based on quantified mixed-integer linear programs. Our numerical results indicate that, for the problem class of decision-dependent robust optimization problems with mixed-integer linear uncertainty sets, the bilevel approach performs better in terms of computation times.