P a PILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support

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 P a PILO, 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 P a PILO 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. P a PILO’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, P a PILO 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 P a PILO in efficiently exploiting recursive parallelism within expensive presolving routines, such as probing, dominated columns, or constraint sparsification. We provide an overview of P a PILO’s capabilities and insights into important design choices.