[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
research-article

GPU-accelerated transportation simplex algorithm

Published: 01 February 2024 Publication History

Abstract

Transportation Problem (TP) is a popular linear program for optimally matching several supply centers to several demand centers at the smallest transportation cost. Recent disruptions in the physical supply chains and the growth of internet marketplaces such as ride-sharing, doorstep delivery, and expedited shipping have engendered a need for efficient algorithms to solve large-scale TPs in near real-time. The Transportation Simplex Algorithm (TSA) is a traditional method to solve TP to optimality. However, TSA is unsuitable for these new applications because of its long run time. The evolution of accelerated computing using Graphics Processing Units (GPUs) has recently attracted some interest in solving optimization problems. In this paper, we develop a GPU-accelerated TSA for large-dimensions. The underlying parallelism in the iterative steps of TSA has been uncovered and exploited. The results show that the accelerated algorithm performs up to 8 times faster on average compared to the known sequential algorithm and up to 4 times faster on average compared to the state-of-the-art commercial Linear Programming solver.

Highlights

Transportation Problem is a fundamental problem in operations research.
Transportation Simplex Algorithm has been accelerated on a GPU.
Creative parallelism in the iterative steps has been uncovered and exploited.
Large problems with 1000 supply and 10,000 demand nodes can be solved.
It is 4x faster than a leading LP solver and 8x faster than sequential counterpart.

References

[1]
Background on transportation simplex algorithm (2023) : https://arxiv.org/search/?query=Mohit+Mahajan&searchtype=author.
[2]
V. Boyer, D. El Baz, Recent advances on gpu computing in operations research, in: 2013 IEEE International Symposium on Parallel Distributed Processing, Workshops and Phd Forum, 2013, pp. 1778–1787,.
[3]
H. Bulut, Multiloop transportation simplex algorithm, Optim. Methods Softw. 32 (6) (2017) 1206–1217,.
[4]
A. Charnes, W.W. Cooper, The stepping stone method of explaining linear programming calculations in transportation problems, Manag. Sci. 1 (1) (1954).
[5]
(2022): CUDA toolkit documentation. https://docs.nvidia.com/cuda/.
[6]
G.B. Dantzig, 14. The Classical Transportation Problem, Princeton University Press, 2016,.
[7]
K. Date, R. Nagi, Gpu-accelerated Hungarian algorithms for the linear assignment problem, Parallel Comput. 57 (2016) 52–72,.
[8]
U. Derigs, The Hitchcock Transportation Problem, Springer, Berlin Heidelberg, Berlin, Heidelberg, 1988,.
[9]
U. Ekanayake, P. C., W. Daundasekera, J. S., An effective alternative new approach in solving transportation problems, Am. J. Electr. Comput. Eng. 5 (2021) 1,.
[10]
F. Hillier, G. Lieberman, Introduction to Operations Research, McGraw-Hill International Editions, McGraw-Hill, 2001, https://books.google.com/books?id=SrfgAAAAMAAJ.
[11]
Z. Juman, M. Hoque, An efficient heuristic to obtain a better initial feasible solution to the transportation problem, Appl. Soft Comput. 34 (2015) 813–826,. https://www.sciencedirect.com/science/article/pii/S1568494615003099.
[12]
G. Kara, C. Özturan, Parallel network simplex algorithm for the minimum cost flow problem, Concurr. Comput., Pract. Exp. 34 (4) (2022),.
[13]
D. Klingman, R. Russell, Solving constrained transportation problems, Oper. Res. 23 (1) (1975) 91–106,.
[14]
S. Korukoğlu, S. Ballı, An improved Vogel's approximation method for the transportation problem, Math. Comput. Appl. 16 (2) (2011) 370–381,. https://www.mdpi.com/2297-8747/16/2/370.
[15]
G.V. Loch, A.C.L. da Silva, A computational study on the number of iterations to solve the transportation problem, Appl. Math. Sci. 8 (2014) 4579–4583,.
[16]
T. Matsui, R. Scheifele, A linear time algorithm for the unbalanced Hitchcock transportation problem, Networks 67 (2) (2016) 170–182,.
[17]
D. Merrill, M. Garland, A. Grimshaw, Scalable gpu graph traversal, in: Proceedings of the 17th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPoPP '12, Association for Computing Machinery, New York, NY, USA, 2012, pp. 117–128,.
[18]
J. Owens, M. Houston, D. Luebke, S. Green, J. Stone, J. Phillips, Gpu computing, Proc. IEEE 96 (2008) 879–899,.
[19]
N. Ploskas, N. Samaras, Gpu accelerated pivoting rules for the simplex algorithm, J. Syst. Softw. 96 (2014) 1–9,.
[20]
N.V. Reinfeld, W.R. Vogel, Mathematical Programming, Prentice-Hall, 1958.
[22]
H.A. Taha, Operations Research: An Introduction, 8th edition, Prentice-Hall, Inc., USA, 2006.

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Journal of Parallel and Distributed Computing
Journal of Parallel and Distributed Computing  Volume 184, Issue C
Feb 2024
141 pages

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 February 2024

Author Tags

  1. GPU accelerated algorithm
  2. Linear programming
  3. Transportation problem

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 0
    Total Downloads
  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 09 Mar 2025

Other Metrics

Citations

View Options

View options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media