Branch and Bound Algorithms for Highly Constrained Integer Programs

In this paper we describe a new branch and bound algorithm for solving 0-1 integer linear programs (ILP). The algorithm is specifically targeted at ILP instances that are highly constrained, i.e. instances for which the constraints are hard to satisfy. Our approach is based on recent algorithms for solving instances of Propositional Satisfiability (SAT) which are also highly constrained. In particular we illustrate how the branch and bound algorithm for solving ILPs can be improved with search pruning techniques commonly used in SAT algorithms. The usefulness of the proposed branch and bound algorithm is illustrated on a practical application for which instances are in general highly constrained. Branch and Bound Algorithms for Highly Constrained Integer Programs 1