Short Paper - A Note on Robust Combinatorial Optimization with Generalized Interval Uncertainty

Abstract

In this paper, we consider a robust combinatorial optimization problem with uncertain weights and propose an uncertainty set that generalizes interval uncertainty by imposing lower and upper bounds on deviations of subsets of items. We prove that if the number of such subsets is fixed and the family of these subsets is laminar, then the robust combinatorial optimization problem can be solved by solving a fixed number of nominal problems. This result generalizes a previous similar result for the case where the family of these subsets is a partition of the set of items.

Keywords

• robust combinatorial optimization
• interval uncertainty
• budgeted uncertainty
• complexity