TY - CHAP A1 - Devriendt, Jo A1 - Gleixner, Ambros A1 - Nordström, Jakob T1 - Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search T2 - Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2020 N2 - 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. Y1 - 2020 VL - 12296 SP - xxiv EP - xxvi PB - Springer ER - TY - JOUR A1 - Devriendt, Jo A1 - Gleixner, Ambros A1 - Nordström, Jakob T1 - Learn to Relax: Integrating 0-1 Integer Linear Programming with Pseudo-Boolean Conflict-Driven Search JF - Constraints N2 - Conflict-driven pseudo-Boolean solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though pseudo-Boolean 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 programming (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 pseudo-Boolean search. This hybrid approach, which for the first time combines MIP techniques with full-blown conflict analysis operating directly on linear inequalities using the cutting planes method, significantly improves performance on a wide range of benchmarks, approaching a "best-of-both-worlds" scenario between SAT-style conflict-driven search and MIP-style branch-and-cut. Y1 - 2021 U6 - https://doi.org/10.1007/s10601-020-09318-x VL - 26 SP - 26 EP - 55 ER - TY - CHAP A1 - Mexi, Gioni A1 - Berthold, Timo A1 - Gleixner, Ambros A1 - Nordström, Jakob T1 - Improving Conflict Analysis in MIP Solvers by Pseudo-Boolean Reasoning T2 - 29th International Conference on Principles and Practice of Constraint Programming (CP 2023) N2 - Conflict analysis has been successfully generalized from Boolean satisfiability (SAT) solving to mixed integer programming (MIP) solvers, but although MIP solvers operate with general linear inequalities, the conflict analysis in MIP has been limited to reasoning with the more restricted class of clausal constraint. This is in contrast to how conflict analysis is performed in so-called pseudo-Boolean solving, where solvers can reason directly with 0-1 integer linear inequalities rather than with clausal constraints extracted from such inequalities. In this work, we investigate how pseudo-Boolean conflict analysis can be integrated in MIP solving, focusing on 0-1 integer linear programs (0-1 ILPs). Phrased in MIP terminology, conflict analysis can be understood as a sequence of linear combinations and cuts. We leverage this perspective to design a new conflict analysis algorithm based on mixed integer rounding (MIR) cuts, which theoretically dominates the state-of-the-art division-based method in pseudo-Boolean solving. We also report results from a first proof-of-concept implementation of different pseudo-Boolean conflict analysis methods in the open-source MIP solver SCIP. When evaluated on a large and diverse set of 0-1 ILP instances from MIPLIB2017, our new MIR-based conflict analysis outperforms both previous pseudo-Boolean methods and the clause-based method used in MIP. Our conclusion is that pseudo-Boolean conflict analysis in MIP is a promising research direction that merits further study, and that it might also make sense to investigate the use of such conflict analysis to generate stronger no-goods in constraint programming. Y1 - 2023 U6 - https://doi.org/10.4230/LIPIcs.CP.2023.27 VL - 280 SP - 27:1 EP - 27:19 PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik ER - TY - CHAP A1 - Hoen, Alexander A1 - Oertel, Andy A1 - Gleixner, Ambros A1 - Nordström, Jakob T1 - Certifying MIP-based presolve reductions for 0-1 integer linear programs T2 - Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2024 N2 - It is well known that reformulating the original problem can be crucial for the performance of mixed-integer programming (MIP) solvers. To ensure correctness, all transformations must preserve the feasibility status and optimal value of the problem, but there is currently no established methodology to express and verify the equivalence of two mixed-integer programs. In this work, we take a first step in this direction by showing how the correctness of MIP presolve reductions on – integer linear programs can be certified by using (and suitably extending) the VeriPB tool for pseudo-Boolean proof logging. Our experimental evaluation on both decision and optimization instances demonstrates the computational viability of the approach and leads to suggestions for future revisions of the proof format that will help to reduce the verbosity of the certificates and to accelerate the certification and verification process further. Y1 - 2024 U6 - https://doi.org/10.1007/978-3-031-60597-0_20 VL - 14742 ER -