Branch-and-Bound Based on Decision Diagrams

Abstract

This chapter proposes an alternative branch-and-bound method in which decision diagrams take over the functions of the traditional relaxations and heuristics used in general-purpose optimization techniques. In particular, we show an enumeration scheme that branches on the nodes of a relaxed decision diagram, as opposed to variable-value assignments as in traditional branch-and-bound. We provide a computational study of our method on three classical combinatorial optimization problems, and compare our solution technology with mixed-integer linear programming. Finally, we conclude by showing how the diagram-based branch-and-bound procedure is suitable for parallelization, and provide empirical evidence of almost linear speedups on the maximum independent set problem.