Effective Implementation of GPU-based Revised Simplex algorithm applying new memory management and cycle avoidance strategies

TL;DR

This paper presents a GPU-based implementation of the revised simplex algorithm that incorporates new memory management and cycle avoidance strategies, achieving significant speedups over traditional methods.

Contribution

It introduces novel memory management techniques and a tabu rule for cycle prevention in GPU-accelerated linear programming, enhancing performance and robustness.

Findings

Achieved maximum speedup factors of 165.2 and 65.46 over sequential and Matlab Linprog solutions.

Demonstrated high effectiveness of the proposed GPU implementation on benchmark problems.

Validated the approach's scalability and efficiency for large-scale linear programming.

Abstract

Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex algorithm. To implement this algorithm, we propose some new memory management strategies. In addition, to avoid cycling because of degeneracy conditions, we use a tabu rule for entering variable selection in the revised simplex algorithm. To evaluate this algorithm, we consider two sets of benchmark problems and compare the speedup factors for these problems. The comparisons demonstrate that the proposed method is highly effective and solve the problems with the maximum speedup factors 165.2 and 65.46 with respect to the sequential version and Matlab Linprog solver respectively.