A Hybrid Multi-GPU Implementation of Simplex Algorithm with CPU Collaboration

TL;DR

This paper presents a novel hybrid CPU-GPU implementation of the simplex algorithm that efficiently utilizes multicore CPUs and multiple GPUs, demonstrating superior performance over GPU-only and CPU-only approaches on a high-end hybrid platform.

Contribution

The paper introduces a new hybrid collaboration scheme combining multithreaded CPU and GPU computations for the simplex algorithm, achieving enhanced performance on multi-GPU systems.

Findings

Hybrid scheme outperforms GPU-only implementations in most conditions.

Concurrently using all resources yields significant performance gains.

Implementation is comparable or superior to existing methods and CPU-only solutions.

Abstract

The simplex algorithm has been successfully used for many years in solving linear programming (LP) problems. Due to the intensive computations required (especially for the solution of large LP problems), parallel approaches have also extensively been studied. The computational power provided by the modern GPUs as well as the rapid development of multicore CPU systems have led OpenMP and CUDA programming models to the top preferences during the last years. However, the desired efficient collaboration between CPU and GPU through the combined use of the above programming models is still considered a hard research problem. In the above context, we demonstrate here an excessively efficient implementation of standard simplex, targeting to the best possible exploitation of the concurrent use of all the computing resources, on a multicore platform with multiple CUDA-enabled GPUs. More concretely, we present a novel hybrid collaboration scheme which is based on the concurrent execution of suitably spread CPU-assigned (via multithreading) and GPU-offloaded computations. The experimental results extracted through the cooperative use of OpenMP and CUDA over a notably powerful modern hybrid platform (consisting of 32 cores and two high-spec GPUs, Titan Rtx and Rtx 2080Ti) highlight that the performance of the presented here hybrid GPU/CPU collaboration scheme is clearly superior to the GPU-only implementation under almost all conditions. The corresponding measurements validate the value of using all resources concurrently, even in the case of a multi-GPU configuration platform. Furthermore, the given implementations are completely comparable (and slightly superior in most cases) to other related attempts in the bibliography, and clearly superior to the native CPU-implementation with 32 cores.