Relaxed Decision Diagrams

Abstract

Bounds on the optimal value are often indispensable for the practical solution of discrete optimization problems, as for example in branch-and-bound procedures. This chapter explores an alternative strategy of obtaining bounds through relaxed decision diagrams, which overapproximate both the feasible set and the objective function of the problem. We first show how to modify the top-down compilation from the previous chapter to generate relaxed decision diagrams. Next, we present three modeling examples for classical combinatorial optimization problems, and provide a thorough computational analysis of relaxed diagrams for the maximum independent set problem. The chapter concludes by describing an alternative method to generate relaxed diagrams, the incremental refinement procedure, and exemplify its application to a single-machine makespan problem.