  Robust optimization typically follows a worst-case perspective, where a
single scenario may determine the objective value of a given solution.
Accordingly, it is a challenging task to reduce the size of an uncertainty set
without changing the resulting objective value too much. On the other hand,
robust optimization problems with many scenarios tend to be hard to solve, in
particular for two-stage problems. Hence, a reduced uncertainty set may be
central to find solutions in reasonable time. We propose scenario reduction
methods that give guarantees on the performance of the resulting robust
solution. Scenario reduction problems for one- and two-stage robust
optimization are framed as optimization problems that only depend on the
uncertainty set and not on the underlying decision making problem. Experimental
results indicate that objective values for the reduced uncertainty sets are
closely correlated to original objective values, resulting in better solutions
than when using general-purpose clustering methods such as K-means.
