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

Xavier Gillard; Vianney Coppé; Pierre Schaus; André Augusto Cire

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arXiv · 2104.11951

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

Xavier Gillard·Vianney Coppé·Pierre Schaus·André Augusto Cire

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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.

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Xavier Gillard, Vianney Coppé, Pierre Schaus, André Augusto Cire. 2021-04-24. Improving the filtering of Branch-And-Bound MDD solver (extended). https://arxiv.org/abs/2104.11951

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