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.
Exploiting solution property in MIP
linear programming;integer programming;branch and bound