Theoretical insights and algorithmic tools for decision diagram-based optimization

Abstract

The use of decision diagrams has recently emerged as a viable general solution approach for solving discrete optimization problems. The decision diagram data structure is used to explicitly represent, either exactly or approximately, the set of feasible solutions to a given problem. Techniques based on decision diagrams have been successfully used on a diverse set of applications, ranging from scheduling to combinatorial optimization, and have often outperformed commercial state-of-the-art constraint programming and integer programming technology. Lacking, however, is a thorough theoretical investigation into the quality of approximate decision diagrams, as well as the development of structured techniques for tightening relaxation bounds provided by approximate decision diagrams, analogously to how cutting-planes are used in integer programming. This paper provides an analysis of the strength of approximate decision diagrams, as well as the description of several bound-tightening procedures for problems with linear objective functions.