Batched First-Order Methods for Parallel LP Solving in MIP

TL;DR

This paper introduces a batched first-order method optimized for GPUs to solve multiple linear programs in parallel, significantly improving efficiency for certain mixed-integer programming tasks.

Contribution

It extends the primal-dual hybrid gradient algorithm to batch processing on GPUs, enabling faster solutions for related LPs in MIP contexts.

Findings

First-order methods outperform simplex in specific problem sizes on GPUs.

Matrix-matrix operations provide computational advantages over matrix-vector operations.

The approach benefits mixed-integer programming techniques like strong branching.

Abstract

We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise in mixed-integer programming techniques such as strong branching and bound tightening. By leveraging matrix-matrix operations instead of repeated matrix-vector operations, we obtain significant computational advantages on GPU architectures. We demonstrate the effectiveness of our approach on various case studies and identify the problem sizes where first-order methods outperform traditional simplex-based solvers depending on the computational environment one can use. This is a significant step for the design and development of integer programming algorithms tightly exploiting GPU capabilities where we argue that some specific operations should be allocated to GPUs and performed in full instead of using light-weight heuristic approaches on CPUs.