Incorporating bounds from decision diagrams into integer programming

  • Decision diagrams have been successfully used to help solve several classes of discrete optimization problems. We explore an approach to incorporate them into integer programming solvers, motivated by the wide adoption of integer programming technology in practice. The main challenge is to map generic integer programming models to a recursive structure that is suitable for decision diagram compilation. We propose a framework that opportunistically constructs decision diagrams for suitable substructures, if present. In particular, we explore the use of a prevalent substructure in integer programming solvers known as the conflict graph, which we show to be amenable to decision diagrams. We use Lagrangian relaxation and constraint propagation to consider constraints that are not represented directly by the substructure. We use the decision diagrams to generate dual and primal bounds to improve the pruning process of the branch-and-bound tree of the solver. Computational results on the independent set problem with side constraints indicate that our approach can provide substantial speedups when conflict graphs are present.

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Metadaten
Author:Christian Tjandraatmadja, Willem-Jan van Hoeve
DOI:https://doi.org/10.1007/s12532-020-00191-6
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2020
Tag:Software; Theoretical Computer Science
Volume:13
Issue:2
Page Number:32
First Page:225
Last Page:256
Mathematical Programming Computation :MPC 2021 - Issue 2
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