Abstract. We investigate the application of multivalued decision diagrams (MDDs) to multidimensional bin packing problems. In these problems, each bin has a multidimensional capacity and each item has an associated multidimensional size. We develop several MDD representations for this problem, and explore different MDD construction methods including a new heuristic-driven depth-first compilation scheme. We also derive MDD restrictions and relaxations, using a novel application of a clustering algorithm to identify approximate equivalence classes among MDD nodes. Our experimental results show that these techniques can significantly outperform current CP and MIP solvers.
Abstract. Nogood learning is a critical component of Boolean satisfiability (SAT) solvers, and increasingly popular in the context of integer programming and constraint programming. We present a generic method to learn valid clauses from exact or approximate binary decision diagrams (BDDs) and resolution in the context of SAT solving. We show that any clause learned from SAT conflict analysis can also be generated using our method, while, in addition, we can generate stronger clauses that cannot be derived from one application of conflict analysis. Importantly, since SAT instances are often too large for an exact BDD representation, we focus on BDD relaxations of polynomial size and show how they can still be used to generated useful clauses. Our experimental results show that when this method is used as a preprocessing step and the generated clauses are appended to the original instance, the size of the search tree for a SAT solver can be significantly reduced.
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