  While research in robust optimization has attracted considerable interest
over the last decades, its algorithmic development has been hindered by several
factors. One of them is a missing set of benchmark instances that make
algorithm performance better comparable, and makes reproducing instances
unnecessary. Such a benchmark set should contain hard instances in particular,
but so far, the standard approach to produce instances has been to sample
values randomly from a uniform distribution.
  In this paper we introduce a new method to produce hard instances for min-max
combinatorial optimization problems, which is based on an optimization model
itself. Our approach does not make any assumptions on the problem structure and
can thus be applied to any combinatorial problem. Using the Selection and
Traveling Salesman problems as examples, we show that it is possible to produce
instances which are up to 500 times harder to solve for a mixed-integer
programming solver than the current state-of-the-art instances.
