PaPILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support

Abstract

Presolving has become an essential component of modern mixed integer program (MIP) solvers, both in terms of computational performance and numerical robustness. In this paper, we present PaPILO, a new C++ header-only library that provides a large set of presolving routines for MIP and linear programming problems from the literature. The creation of PaPILO was motivated by the current lack of (a) solver-independent implementations that (b) exploit parallel hardware and (c) support multiprecision arithmetic. Traditionally, presolving is designed to be fast. Whenever necessary, its low computational overhead is usually achieved by strict working limits. PaPILO’s parallelization framework aims at reducing the computational overhead also when presolving is executed more aggressively or is applied to large-scale problems. To rule out conflicts between parallel presolve reductions, PaPILO uses a transaction-based design. This helps to avoid both the memory-intensive allocation of multiple copies of the problem and special synchronization between presolvers. Additionally, the use of Intel’s Threading Building Blocks library aids PaPILO in efficiently exploiting recursive parallelism within expensive presolving routines, such as probing, dominated columns, or constraint sparsification. We provide an overview of PaPILO’s capabilities and insights into important design choices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: This work has been financially supported by Research Campus MODAL, funded by the German Federal Ministry of Education and Research [Grants 05M14ZAM, 05M20ZBM], and the European Union’s Horizon 2020 research and innovation programme under grant agreement No 773897 (plan4res). The content of this paper only reflects the author’s views. The European Commission / Innovation and Networks Executive Agency is not responsible for any use that may be made of the information it contains. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0171 ), as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0171 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .