Network Flow Models for Robust Binary Optimization with Selective Adaptability

Abstract: Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for adaptive robust binary optimization (ARBO) problems with objective uncertainty. Without loss of generality, we focus on ARBO problems with "selective adaptability", a term we coin to describe a common class of linking constraints between first-stage and second-stage solutions. Our main contribution revolves around a collection of exact and approximate network flow reformulations for the ARBO problem, which we develop by building upon ideas from the decision diagram literature. Our proposed models can generate feasible solutions, primal bounds and dual bounds, while their size and approximation quality can be precisely controlled through user-specified parameters. Furthermore, and in contrast with existing solution methods, these models are easy to implement and can be solved directly with standard off-the-shelf solvers. Through an extensive set of computational experiments, we show that our models can generate high-quality solutions and dual bounds in significantly less time than popular benchmark methods, often by orders of magnitude.