Nogood Learning for Mixed Integer Programming

Nogood learning has proven to be an effective CSP technique critical to success in today’s top SAT solvers. We extend the technique for use in combinatorial optimization problems, as opposed to mere constraint satisfaction. In particular, we examine 0-1 integer programming (0-1 IP). Our technique generates globally valid cutting planes for the 01 IP search algorithm from information learned through constraint propagation. Nogoods (cutting planes) are generated not only from infeasibility but also from bounding. All of our techniques are geared toward yielding tighter LP upper bounds, and thus smaller search trees. Experiments suggest that nogood learning does not help in optimization because few cutting planes are generated, and they are weak. We explain why, and identify problem characteristics that affect the effectiveness. We then generalize the technique to mixed-integer programming. Finally, we lay out directions along which the techniques can potentially be made helpful.