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 uniformly . 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.  Using the Selection problem as an example , we show that it is possible to produce instances which are ten times as hard to solve on average for a state-of-the-art mixed-integer programming solver  .
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 .
R
uniformly
from a uniform distribution
A
Our approach does not make any assumptions on the problem structure and can thus be applied to any combinatorial problem.
R
problem as an example
and Traveling Salesman problems as examples
R
ten times as hard to solve on average for a state-of-the-art
up to 500 times harder to solve for a
A
than the current state-of-the-art instances