I have an application where I am solving millions of ILP instances that differ from each other only on one constraint. The instances, of course, are relatively easy to solve or otherwise this would be hopeless. Their size is less than 1000 variables.
What ILP solvers would be good for this application? What CPLEX settings would be good for this application?
So far I have used the CPLEX C++ API. I use
IloModel::remove() to add and remove the differing constraint every time. With this approach, I am able to solve 100,000 instances in about 40 seconds. However, I'm not sure if this is the best I can do. I have also observed that the model is very unstable: adding a constraint saying
objective <= upper_bound, where
upper_bound is an external upper bound, made the solving more than 10 times slower.