IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v398y2014icp179-186.html
   My bibliography  Save this article

An amoeboid algorithm for solving linear transportation problem

Author

Listed:
  • Gao, Cai
  • Yan, Chao
  • Zhang, Zili
  • Hu, Yong
  • Mahadevan, Sankaran
  • Deng, Yong

Abstract

Transportation Problem (TP) is one of the basic operational research problems, which plays an important role in many practical applications. In this paper, a bio-inspired mathematical model is proposed to handle the Linear Transportation Problem (LTP) in directed networks by modifying the original amoeba model Physarum Solver. Several examples are used to prove that the provided model can effectively solve Balanced Transportation Problem (BTP), Unbalanced Transportation Problem (UTP), especially the Generalized Transportation Problem (GTP), in a nondiscrete way.

Suggested Citation

  • Gao, Cai & Yan, Chao & Zhang, Zili & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2014. "An amoeboid algorithm for solving linear transportation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 179-186.
    • Handle: RePEc:eee:phsmap:v:398:y:2014:i:c:p:179-186
    DOI: 10.1016/j.physa.2013.12.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113011473
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2013.12.023?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Adlakha, Veena & Kowalski, Krzysztof & Wang, Simi & Lev, Benjamin & Shen, Wenjing, 2014. "On approximation of the fixed charge transportation problem," Omega, Elsevier, vol. 43(C), pages 64-70.
    2. Andrew Adamatzky & Michael Lees & Peter Sloot, 2013. "Bio-Development Of Motorway Network In The Netherlands: A Slime Mould Approach," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 16(02n03), pages 1-28.
    3. Nagatani, Takashi & Tobita, Kazuhiro, 2012. "Effect of periodic inflow on elevator traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4397-4405.
    4. Nagatani, Takashi, 2012. "Delay effect on schedule in shuttle bus transportation controlled by capacity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3266-3276.
    5. Toshiyuki Nakagaki & Hiroyasu Yamada & Ágota Tóth, 2000. "Maze-solving by an amoeboid organism," Nature, Nature, vol. 407(6803), pages 470-470, September.
    6. Cai Gao & Xin Lan & Xiaoge Zhang & Yong Deng, 2013. "A Bio-Inspired Methodology of Identifying Influential Nodes in Complex Networks," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-11, June.
    7. Gao, Lei & Guo, Jin-Li & Fan, Chao & Liu, Xue-Jiao, 2013. "Individual and group dynamics in purchasing activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 343-349.
    8. Maeno, Yoshiharu, 2013. "Transient fluctuation of the prosperity of firms in a network economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3351-3359.
    9. Wei, Daijun & Deng, Xinyang & Zhang, Xiaoge & Deng, Yong & Mahadevan, Sankaran, 2013. "Identifying influential nodes in weighted networks based on evidence theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2564-2575.
    10. Kwon, Okyu & Jung, Woo-Sung, 2012. "Intercity express bus flow in Korea and its network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4261-4265.
    11. Du, Wen-Bo & Wu, Zhi-Xi & Cai, Kai-Quan, 2013. "Effective usage of shortest paths promotes transportation efficiency on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3505-3512.
    12. Luathep, Paramet & Sumalee, Agachai & Lam, William H.K. & Li, Zhi-Chun & Lo, Hong K., 2011. "Global optimization method for mixed transportation network design problem: A mixed-integer linear programming approach," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 808-827, June.
    13. Ghosh, Saptarshi & Banerjee, Avishek & Ganguly, Niloy, 2012. "Some insights on the recent spate of accidents in Indian Railways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2917-2929.
    14. Tero, Atsushi & Kobayashi, Ryo & Nakagaki, Toshiyuki, 2006. "Physarum solver: A biologically inspired method of road-network navigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 115-119.
    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. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Dalbinder Kour & Sathi Mukherjee & Kajla Basu, 2017. "Solving intuitionistic fuzzy transportation problem using linear programming," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1090-1101, November.
    3. Jarosław Ziółkowski & Aleksandra Lęgas & Elżbieta Szymczyk & Jerzy Małachowski & Mateusz Oszczypała & Joanna Szkutnik-Rogoż, 2022. "Optimization of the Delivery Time within the Distribution Network, Taking into Account Fuel Consumption and the Level of Carbon Dioxide Emissions into the Atmosphere," Energies, MDPI, vol. 15(14), pages 1-22, July.

    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. Gao, Cai & Wei, Daijun & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2013. "A modified evidential methodology of identifying influential nodes in weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5490-5500.
    2. Cai Gao & Xin Lan & Xiaoge Zhang & Yong Deng, 2013. "A Bio-Inspired Methodology of Identifying Influential Nodes in Complex Networks," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-11, June.
    3. Wei, Bo & Liu, Jie & Wei, Daijun & Gao, Cai & Deng, Yong, 2015. "Weighted k-shell decomposition for complex networks based on potential edge weights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 277-283.
    4. Zhang, Xiaohong & Li, Zhiying & Qian, Kai & Ren, Jianji & Luo, Junwei, 2020. "Influential node identification in a constrained greedy way," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    5. Liu, Jie & Li, Yunpeng & Ruan, Zichan & Fu, Guangyuan & Chen, Xiaowu & Sadiq, Rehan & Deng, Yong, 2015. "A new method to construct co-author networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 29-39.
    6. Du, Yuxian & Gao, Cai & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2014. "A new method of identifying influential nodes in complex networks based on TOPSIS," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 57-69.
    7. Fei, Liguo & Deng, Yong, 2017. "A new method to identify influential nodes based on relative entropy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 257-267.
    8. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    9. Lu, Xi & Mo, Hongming & Deng, Yong, 2015. "An evidential opinion dynamics model based on heterogeneous social influential power," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 98-107.
    10. Liang, Jinpeng & Wu, Jianjun & Gao, Ziyou & Sun, Huijun & Yang, Xin & Lo, Hong K., 2019. "Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 115-138.
    11. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    12. Chaharborj, Sarkhosh Seddighi & Nabi, Khondoker Nazmoon & Feng, Koo Lee & Chaharborj, Shahriar Seddighi & Phang, Pei See, 2022. "Controlling COVID-19 transmission with isolation of influential nodes," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    13. Ospina, Juan P. & Duque, Juan C. & Botero-Fernández, Verónica & Montoya, Alejandro, 2022. "The maximal covering bicycle network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 159(C), pages 222-236.
    14. Andrew Adamatzky & Olivier Allard & Jeff Jones & Rachel Armstrong, 2017. "Evaluation of French motorway network in relation to slime mould transport networks," Environment and Planning B, , vol. 44(2), pages 364-383, March.
    15. Chen, Jie & Wu, Chao-Yun & Li, Ming & Hu, Mao-Bin, 2019. "Hybrid traffic dynamics on coupled networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 98-104.
    16. Zangui, Mahmood & Aashtiani, Hedayat Z. & Lawphongpanich, Siriphong & Yin, Yafeng, 2015. "Path-differentiated pricing in congestion mitigation," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 202-219.
    17. Tan, Zhijia & Yang, Hai & Tan, Wei & Li, Zhichun, 2016. "Pareto-improving transportation network design and ownership regimes," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 292-309.
    18. Yuchen Pan & Shuai Ding & Wenjuan Fan & Jing Li & Shanlin Yang, 2015. "Trust-Enhanced Cloud Service Selection Model Based on QoS Analysis," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-19, November.
    19. Hao Wu & Rene van den Brink & Arantza Estevez-Fernandez, 2022. "The locally partial permission value for games with a permission structure," Tinbergen Institute Discussion Papers 22-037/II, Tinbergen Institute.
    20. Xiao, Guanping & Zheng, Zheng & Wang, Haoqin, 2017. "Evolution of Linux operating system network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 249-258.

    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:eee:phsmap:v:398:y:2014:i:c:p:179-186. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.