I am trying to find a way to find a worst-case input for a black-box implementation of an algorithm with worst-case exponential runtime.
The problem that the program solves (integer linear programming) is NP-hard, but since the proof is by reduction from vertex cover, there is no construction of a hard subset or such. Also vertex cover is in NP due to a reduction from 3SAT. Now for 3SAT it is in no way certain that a hard case for a given 3sat solver would translate to a hard problem for one of my black-box ILP implementations.
Is there a systematic way to find a worst-case runtime example for a given problem of size n?