Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

Abstract

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve stateof-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the use of DDs in discrete optimization, particularly focusing on recent developments. We classify these works into two groups based on the type of diagram (i.e., exact or approximate) and present a thorough description of their use. We discuss the main advantages of DDs, point out major challenges, and provide directions for future work.

New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

“…In the incremental refinement procedure, a relaxed MDD is first built with one node per layer and is then incrementally refined by removing arcs and splitting nodes to eliminate infeasible solutions. We refer to (Castro et al, 2022) for a survey on the use of MDDs in discrete optimization. Maschler and Raidl (2018) presented topdown compilation (TDC) and incremental refinement procedures to build relaxed multivalued decision diagrams (MDDs) used to obtain dual bounds.…”

Generalized Confidence Constraints

“…In the general case, many constraints are represented using polynomial-size MDDs. Such compression power and the many different algorithms defined on top of MDDs make them a useful data-structure for optimization (Bergman et al 2016;Castro, Cire, and Beck 2022).…”