Simultaneous Solving of Batched Linear Programs on a GPU

TL;DR

This paper introduces a GPU-based batched LP solver that significantly accelerates solving large numbers of small to medium-sized LPs, achieving up to 95x speed-up over traditional CPU solvers.

Contribution

It presents a novel CUDA implementation for batched LP solving, optimizing memory access and load balancing, and demonstrates substantial performance improvements over existing solvers.

Findings

Maximum speed-up of 95x over CPLEX

Achieves 5x speed-up over GLPK

Effective for large batch sizes of LPs

Abstract

Linear Programs (LPs) appear in a large number of applications and offloading them to a GPU is viable to gain performance. Existing work on offloading and solving an LP on a GPU suggests that there is performance gain generally on large sized LPs (typically 500 constraints, 500 variables and above). In order to gain performance from a GPU, for applications involving small to medium sized LPs, we propose batched solving of a large number of LPs in parallel. In this paper, we present the design and implementation of a batched LP solver in CUDA, keeping memory coalescent access, low CPU-GPU memory transfer latency and load balancing as the goals. The performance of the batched LP solver is compared against sequential solving in the CPU using the open source solver GLPK (GNU Linear Programming Kit) and the CPLEX solver from IBM. The evaluation on selected LP benchmarks from the Netlib repository displays a maximum speed-up of 95x and 5x with respect to CPLEX and GLPK solver respectively, for a batch of 1e5 LPs. We demonstrate the application of our batched LP solver to enhance performance in the domain of state-space exploration of mathematical models of control systems design.