Distributed Parallel Structure-Aware Presolving for Arrowhead Linear Programs

TL;DR

This paper introduces a parallel, structure-aware presolve framework for arrowhead linear programs that significantly improves scalability and runtime efficiency in high-performance computing environments, outperforming existing methods.

Contribution

The paper presents a novel distributed presolve technique tailored for AHLPs that preserves structure and reduces communication overhead, enabling scalable parallel processing.

Findings

Outperforms PaPILO by 18x in runtime on a single machine

Outperforms Gurobi's presolve by 6x on a single machine

Outperforms Gurobi's presolve by 13x in distributed environments

Abstract

We present a structure-aware parallel presolve framework specialized to arrowhead linear programs (AHLPs) and designed for high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++. Large-scale LPs arising from automated model generation frequently contain redundancies and numerical pathologies that necessitate effective presolve, yet existing presolve techniques are primarily serial or structure-agnostic and can become time-consuming in parallel solution workflows. Within PIPS-IPM++, AHLPs are stored in distributed memory, and our presolve builds on this to apply a highly parallel, distributed presolve across compute nodes while keeping communication overhead low and preserving the underlying arrowhead structure. We demonstrate the scalability and effectiveness of our approach on a diverse set of AHLPs and compare it against state-of-the-art presolve implementations, including PaPILO and the presolve implemented within Gurobi. Even on a single machine, our presolve significantly outperforms PaPILO by a factor of 18 and Gurobi's presolve by a factor of 6 in terms of shifted geometric mean runtime, while reducing the problems by a similar amount to PaPILO. Using a distributed compute environment, we outperform Gurobi's presolve by a factor of 13.