Improving the filtering of Branch-And-Bound MDD solver (extended)

TL;DR

This paper introduces and evaluates two new pruning techniques, local-bound and rough upper-bound, to improve the efficiency of branch-and-bound MDD-based constraint optimization solvers, demonstrating significant performance gains.

Contribution

The paper presents two novel pruning methods, local-bound and rough upper-bound, enhancing the efficiency of MDD-based branch-and-bound solvers for combinatorial optimization problems.

Findings

RUB delivers excellent results but requires model effort.

LocB provides automatic, significant improvements.

Combined use of RUB and LocB outperforms individual techniques.

Abstract

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in 2016 to solve dynamic programs to optimality. In particular, our paper presents and evaluates the effectiveness of the local-bound (LocB) and rough upper-bound pruning (RUB). LocB is a new and effective rule that leverages the approximate MDD structure to avoid the exploration of non-interesting nodes. RUB is a rule to reduce the search space during the development of bounded-width-MDDs. The experimental study we conducted on the Maximum Independent Set Problem (MISP), Maximum Cut Problem (MCP), Maximum 2 Satisfiability (MAX2SAT) and the Traveling Salesman Problem with Time Windows (TSPTW) shows evidence indicating that rough-upper-bound and local-bound pruning have a high impact on optimization solvers based on branch-and-bound with MDDs. In particular, it shows that RUB delivers excellent results but requires some effort when defining the model. Also, it shows that LocB provides a significant improvement automatically; without necessitating any user-supplied information. Finally, it also shows that rough-upper-bound and local-bound pruning are not mutually exclusive, and their combined benefit supersedes the individual benefit of using each technique.