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

TL;DR

PaPILO is a new C++ library that enhances presolving in MIP and LP solvers by enabling parallel execution, multiprecision support, and solver independence, thereby improving computational efficiency and robustness.

Contribution

It introduces a parallel, solver-independent presolving library with multiprecision support, addressing limitations of traditional presolving approaches in large-scale problems.

Findings

Reduces computational overhead through parallel presolving.

Supports multiprecision arithmetic for numerical robustness.

Efficiently exploits recursive parallelism in presolving routines.

Abstract

Presolving has become an essential component of modern 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 LP 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 TBB library aids PaPILO to efficiently exploit 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.