# Exploiting solution property in MIP

I am having to solve integer programming problem that has the following property:

For feasible solution $x$ maps to a large set $S(x)$ or other admissible solutions and I can find the best solution of $S(x)$ is polynomial time.

What is the best way exploit this property?

The only thing that comes to my mind is: every time an admissible integer solution $x$ is found, compute the best solution in $S(x)$ and update the current bound.

• Gurobi allows for callbacks which should allow you to do this. – combo Aug 25 '17 at 16:56