  Multi-stage problems with uncertain parameters and integer decisions
variables are among the most difficult applications of robust optimization
(RO). The challenge in these problems is to find optimal here-and-now
decisions, taking into account that the wait-and-see decisions have to adapt to
the revealed values of the uncertain parameters. Postek and den Hertog (2016)
and Bertsimas and Dunning (2016) propose to solve these problems by
constructing piecewise constant decision rules by adaptively partitioning the
uncertainty set. The partitions of this set are iteratively updated by
separating so-called critical scenarios of the uncertain parameters. Both
references present methods for identifying these critical scenarios. However,
these methods are most suitable for problems with continuous decision variables
and many uncertain constraints. In particular, they are not able to identify
informative sets of critical scenarios for integer problems with uncertainty in
the objective function only. In this note, we address this shortcoming of
existing methods by introducing a general critical scenario detection method
for mixed-integer adjustable robust optimization problems that is based on the
branch-and-bound tree used to solve the corresponding static problem. Numerical
experiments on a route planning problem show that our general-purpose method
outperforms the problem-specific approach of Postek and den Hertog (2016).
