IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0110214.html
   My bibliography  Save this article

The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems

Author

Listed:
  • Carsten Gottschlich
  • Dominic Schuhmacher

Abstract

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

Suggested Citation

  • Carsten Gottschlich & Dominic Schuhmacher, 2014. "The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-10, October.
    • Handle: RePEc:plo:pone00:0110214
    DOI: 10.1371/journal.pone.0110214
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0110214
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0110214&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0110214?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Edward J. Russell, 1969. "Letters to the Editor---Extension of Dantzig's Algorithm to Finding an Initial Near-Optimal Basis for the Transportation Problem," Operations Research, INFORMS, vol. 17(1), pages 187-191, February.
    2. Mikael Vejdemo-Johansson & Susanne Vejdemo & Carl-Henrik Ek, 2014. "Comparing Distributions of Color Words: Pitfalls and Metric Choices," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-8, February.
    3. George B. Dantzig, 1990. "The Diet Problem," Interfaces, INFORMS, vol. 20(4), pages 43-47, August.
    4. H. S. Houthakker, 1955. "On the Numerical Solution of the Transportation Problem," Operations Research, INFORMS, vol. 3(2), pages 210-214, May.
    5. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, April.
    6. E. Bonabeau & M. Dorigo & G. Theraulaz, 2000. "Inspiration for optimization from social insect behaviour," Nature, Nature, vol. 406(6791), pages 39-42, July.
    7. Spieksma, Frits C. R. & Woeginger, Gerhard J., 1996. "Geometric three-dimensional assignment problems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 611-618, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Florian Ziel, 2020. "The energy distance for ensemble and scenario reduction," Papers 2005.14670, arXiv.org, revised Oct 2020.
    2. Espen Bernton & Pierre E. Jacob & Mathieu Gerber & Christian P. Robert, 2019. "Approximate Bayesian computation with the Wasserstein distance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 235-269, April.
    3. Filippo Zanetti & Jacek Gondzio, 2023. "An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1061-1078, September.
    4. Carsten Gottschlich, 2016. "Convolution Comparison Pattern: An Efficient Local Image Descriptor for Fingerprint Liveness Detection," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-12, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. F Dubeau, 2019. "Behavior Related to Taxation System: Example of Bi-Criteria Linear Program for Animal Diet Formulation," Annals of Social Sciences & Management studies, Juniper Publishers Inc., vol. 3(3), pages 60-65, April.
    2. Shahmohammadi, Ali & Sioshansi, Ramteen & Conejo, Antonio J. & Afsharnia, Saeed, 2018. "Market equilibria and interactions between strategic generation, wind, and storage," Applied Energy, Elsevier, vol. 220(C), pages 876-892.
    3. Alp Atakan & Mehmet Ekmekci & Ludovic Renou, 2021. "Cross-verification and Persuasive Cheap Talk," Papers 2102.13562, arXiv.org, revised Apr 2021.
    4. Arthur Medeiros & Thales Ramos & José Tavares de Oliveira & Manoel F. Medeiros Júnior, 2020. "Direct Voltage Control of a Doubly Fed Induction Generator by Means of Optimal Strategy," Energies, MDPI, vol. 13(3), pages 1-28, February.
    5. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.
    6. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    7. Ashrafi, M. & Khanjani, M.J. & Fadaei-Kermani, E. & Barani, G.A., 2015. "Farm drainage channel network optimization by improved modified minimal spanning tree," Agricultural Water Management, Elsevier, vol. 161(C), pages 1-8.
    8. Sergey Badikov & Antoine Jacquier & Daphne Qing Liu & Patrick Roome, 2016. "No-arbitrage bounds for the forward smile given marginals," Papers 1603.06389, arXiv.org, revised Oct 2016.
    9. Szidarovszky, Ferenc & Luo, Yi, 2014. "Incorporating risk seeking attitude into defense strategy," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 104-109.
    10. Torres-Rojo, J. M., 2001. "Risk management in the design of a feeding ration: a portfolio theory approach," Agricultural Systems, Elsevier, vol. 68(1), pages 1-20, April.
    11. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    12. Huang, Edward & Mital, Pratik & Goetschalckx, Marc & Wu, Kan, 2016. "Optimal assignment of airport baggage unloading zones to outgoing flights," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 94(C), pages 110-122.
    13. Csaba I. Fábián, 2021. "Gaining traction: on the convergence of an inner approximation scheme for probability maximization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 491-519, June.
    14. Liying Xu & Jiadi Zhu & Bing Chen & Zhen Yang & Keqin Liu & Bingjie Dang & Teng Zhang & Yuchao Yang & Ru Huang, 2022. "A distributed nanocluster based multi-agent evolutionary network," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    15. Bouslah, B. & Gharbi, A. & Pellerin, R., 2016. "Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint," Omega, Elsevier, vol. 61(C), pages 110-126.
    16. Rafał Wiśniowski & Krzysztof Skrzypaszek & Tomasz Małachowski, 2020. "Selection of a Suitable Rheological Model for Drilling Fluid Using Applied Numerical Methods," Energies, MDPI, vol. 13(12), pages 1-17, June.
    17. François Dubeau & Pierre-Olivier Julien & Candido Pomar, 2011. "Formulating diets for growing pigs: economic and environmental considerations," Annals of Operations Research, Springer, vol. 190(1), pages 239-269, October.
    18. Martins Barros, Rafael & Guimarães Lage, Guilherme & de Andrade Lira Rabêlo, Ricardo, 2022. "Sequencing paths of optimal control adjustments determined by the optimal reactive dispatch via Lagrange multiplier sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 301(1), pages 373-385.
    19. Yuichi Takano & Renata Sotirov, 2012. "A polynomial optimization approach to constant rebalanced portfolio selection," Computational Optimization and Applications, Springer, vol. 52(3), pages 645-666, July.
    20. Xiaoqing Zhao & Qifa Yue & Jianchao Pei & Junwei Pu & Pei Huang & Qian Wang, 2021. "Ecological Security Pattern Construction in Karst Area Based on Ant Algorithm," IJERPH, MDPI, vol. 18(13), pages 1-21, June.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0110214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.