Piecewise Constant Decision Rules via Branch-and-Bound Based Scenario Detection for Integer Adjustable Robust Optimization

Multistage problems with uncertain parameters and integer decisions variables are among the most difficult applications of robust optimization (RO). The challenge in these is to find optimal here-and-now decisions, taking into account that wait-and-see have adapt revealed values parameters. An existing approach solve construct piecewise constant decision rules by adaptively partitioning uncertainty set. partitions this set iteratively updated separating so-called criticial scenarios, methods for identifying critical scenarios available. However, suitable continuous many constraints, providing no mathematically rigorous methodology case decisions. In particular, they not able identify sets objective function only. paper, we address shortcoming introducing a general scenario detection method. new method leverages information embedded dual vectors LP relaxations at nodes branch-and-bound tree used corresponding static problem. Numerical experiments on route planning problem show our general-purpose outperforms problem-specific from literature.