BDDs in a Branch and Cut Framework

Branch & Cut is today's state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1-IPs and thus allow for early pruning of parts of the search tree. In this paper we present a novel approach to generate valid inequalities for 0/1-IPs which is based on Binary Decision Diagrams (BDDs). BDDs are a datastructure which represents 0/1-vectors as paths of a certain acyclic graph. They have been successfully applied in computational logic, hardware verification and synthesis. We implemented our BDD cutting plane generator in a branch-and-cut framework and tested it on several instances of the MAX-ONES problem and randomly generated 0/1-IPs. Our computational results show that we have developed competitive code for these problems, on which state-of-the-art MIP-solvers fall short.

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