In the context of a larger optimization problem I realized that I am missing the skill to implement/exploit the following observation:
In the problem I was faced with two related sets of indicator variables which contributed to the objective function through two separate terms. I obtained very weak root relaxation bounds (only considered one part of the objective function) and correspondingly long solution times (Gurobi). While this slow approach eventually worked out I kept wondering how to do it better the next time:
When I manually relaxed the set of binary variables related to the part that was properly captured and retained the formulation the problem very quickly solved yielding a very strong LB - but of course just including the LB value does not help. So here comes the question: How to "suggest" such a partial relaxation scheme to the solver? Is there a modeling technique that achieves this or am I missing a feature/parameter? I first thought about lazy handling of integrality but could not figure out how to do this.