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Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search

  • Conflict-driven Pseudo-Boolean (PB) solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though PB solvers have the potential to be exponentially more efficient than CDCL solvers in theory, in practice they can sometimes get hopelessly stuck even when the linear program (LP) relaxation is infeasible over the reals. Inspired by mixed integer programming (MIP), we address this problem by interleaving incremental LP solving with cut generation within the conflict-driven PB search. This hybrid approach, which for the first time combines MIP techniques with full-blown conflict analysis over linear inequalities using the cutting planes method, significantly improves performance on a wide range of benchmarks, approaching a "best of two worlds" scenario between SAT-style conflict-driven search and MIP-style branch-and-cut.

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Author:Jo Devriendt, Ambros GleixnerORCiD, Jakob Nordström
Document Type:In Proceedings
Parent Title (English):Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020
First Page:xxiv
Last Page:xxvi
Year of first publication:2020
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