Solving Batched Linear Programs on GPU and Multicore CPU

TL;DR

This paper introduces a GPU-based batched LP solver that significantly accelerates solving large numbers of small to medium LPs, outperforming traditional CPU methods and extending existing solutions to more diverse LP types.

Contribution

The paper presents a novel CUDA implementation of a batched LP solver optimized for small to medium LPs, enabling high parallelism and performance improvements over sequential CPU solving.

Findings

Maximum speedup of 18.3x for 50k LPs of size 100

Up to 63x speedup for nearly 4 million small LPs

Open source GLPK can be extended for parallel LP solving, achieving 9.6x speedup

Abstract

Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs (typically 500 constraints, 500 variables and above). In order to gain performance from 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 CUDA implementation of our batched LP solver library, keeping memory coalescent access, reduced 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 an open source solver GLPK (GNU Linear Programming Kit). The performance is evaluated for three types of LPs. The first type is the initial basic solution as feasible, the second type is the initial basic solution as infeasible and the third type is the feasible region as a Hyperbox. For the first type, we show a maximum speedup of $18.3\times$ when running a batch of $50k$ LPs of size $100$ ($100$ variables, $100$ constraints). For the second type, a maximum speedup of $12\times$ is obtained with a batch of $10k$ LPs of size $200$. For the third type, we show a significant speedup of $63\times$ in solving a batch of nearly $4$ million LPs of size 5 and $34\times$ in solving 6 million LPs of size $28$. In addition, we show that the open source library for solving linear programs-GLPK, can be easily extended to solve many LPs in parallel with multi-threading. The thread parallel GLPK implementation runs $9.6\times$ faster in solving a batch of $1e5$ LPs of size $100$, on a $12$-core Intel Xeon processor. We demonstrate the application of our batched LP solver in the domain of state-space exploration of mathematical models of control systems design.