Skip to main content
SpringerLink
Log in

A Biologically Inspired Optimization Algorithm for Solving Fuzzy Shortest Path Problems with Mixed Fuzzy Arc Lengths

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The shortest path problem is among fundamental problems of network optimization. Majority of the optimization algorithms assume that weights of data graph’s edges are pre-determined real numbers. However, in real-world situations, the parameters (costs, capacities, demands, time) are not well defined. The fuzzy set has been widely used as it is very flexible and cost less time when compared with the stochastic approaches. We design a bio-inspired algorithm for computing a shortest path in a network with various types of fuzzy arc lengths by defining a distance function for fuzzy edge weights using \(\alpha \) cuts. We illustrate effectiveness and adaptability of the proposed method with numerical examples, and compare our algorithm with existing approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Polimeni, A., Vitetta, A.: Optimising waiting at nodes in time-dependent networks: cost functions and applications. J. Optim. Theory Appl. 156, 805–818 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhang, X., Zhang, Z., Zhang, Y., Wei, D., Deng, Y.: Route selection for emergency logistics management: a bio-inspired algorithm. Saf. Sci. 54, 87–91 (2013)

    Article  Google Scholar 

  3. Zhang, X., Wang, Q., Chan, F.T., Mahadevan, S., Deng, Y.: A physarum polycephalum optimization algorithm for the bi-objective shortest path problem. Int. J. Unconv. Comput. 10, 143–162 (2014)

    Google Scholar 

  4. Yuan, L., Meng, X.Y.: Reliability analysis of a warm standby repairable system with priority in use. Appl. Math. Model. 35, 4295–4403 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, X., Zhang, Y., Hu, Y., Deng, Y., Mahadevan, S.: An adaptive amoeba algorithm for constrained shortest paths. Expert Syst. Appl. 40, 7607–7616 (2013)

    Article  Google Scholar 

  6. Zhang, X., Huang, S., Hu, Y., Zhang, Y., Mahadevan, S., Deng, Y.: Solving 0–1 knapsack problems based on amoeboid organism algorithm. Appl. Math. Comput. 219, 9959–9970 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang, X., Deng, Y., Chan, F.T., Xu, P., Mahadevan, S., Hu, Y.: IFSJSP: a novel methodology for the job-shop scheduling problem based on intuitionistic fuzzy sets. Int. J. Prod. Res. 51, 5100–5119 (2013)

    Article  Google Scholar 

  8. Tseng, M.L., Divinagracia, L., Divinagracia, R.: Evaluating firms sustainable production indicators in uncertainty. Comput. Ind. Eng. 57, 1393–1403 (2009)

    Article  Google Scholar 

  9. Dubois, D.J.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  10. Keshavarz, E., Khorram, E.: A fuzzy shortest path with the highest reliability. J. Comput. Appl. Math. 230, 204–212 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hassanzadeh, R., Mahdavi, I., Mahdavi-Amiri, N., Tajdin, A.: A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths. Math. Comput. Model. 57, 84–99 (2011)

    Article  MathSciNet  Google Scholar 

  12. Zhang, Y., Zhang, Z., Deng, Y., Mahadevan, S.: A biologically inspired solution for fuzzy shortest path problems. Appl. Soft Comput. 13, 2356–2363 (2013)

    Google Scholar 

  13. Hernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A.: The shortest path problem on networks with fuzzy parameters. Fuzzy Sets Syst. 158, 1561–1570 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Stephenson, S.L., Stempen, H., Hall, I.: Myxomycetes: A Handbook of Slime Molds. Timber Press, Oregon (2000)

    Google Scholar 

  15. Nakagaki, T., Yamada, H., Toth, A.: Path finding by tube morphogenesis in an amoeboid organism. Biophys. Chem. 92, 47–52 (2001)

    Article  Google Scholar 

  16. Adamatzky, A.: Slime mold solves maze in one pass, assisted by gradient of chemo-attractants. IEEE Trans. Nanobiosci. 11, 131–134 (2012)

    Article  Google Scholar 

  17. Lin, K.P., Wen, W., Chou, C.C., Jen, C.H., Hung, K.C.: Applying fuzzy GERT with approximate fuzzy arithmetic based on the weakest t-norm operations to evaluate repairable reliability. Appl. Math. Model. 35, 5314–5325 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sadeghpour G.B., Gien D.: La distance-Dp, q et le cofficient de corrélation entre deux variables aléatoires floues. Actes de LFA 97–102 (2001).

  19. Tero, A., Kobayashi, R., Nakagaki, T.: A mathematical model for adaptive transport network in path finding by true slime mold. J. Theor. Biol. 244, 553–564 (2007)

    Article  MathSciNet  Google Scholar 

  20. Nakagaki, T., et al.: Minimum-risk path finding by an adaptive amoebal network. Phys. Rev. Lett. 99, 068104 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

The work is partially supported Chongqing Natural Science Foundation, Grant No. CSCT, 2010BA2003, the National Natural Science Foundation of China, Grant No. 61174022, R&D Program of China (2012BAH07B01), and the National High Technology Research and Development Program of China (863 Program) (No.2013AA013801).

Author information

Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing , 400715, China

    Xiaoge Zhang, Qing Wang & Yong Deng

  2. Unconventional Computing Center, University of the West of England, Bristol , BS16 1QY, UK

    Andrew Adamatzky

  3. Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong

    Felix T. S. Chan

  4. School of Engineering, Vanderbilt University, Nashville, TN , 37235, USA

    Sankaran Mahadevan

Authors
  1. Xiaoge Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrew Adamatzky
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Felix T. S. Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Sankaran Mahadevan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yong Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Deng.

Additional information

Communicated by Bruce A. Conway.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, X., Wang, Q., Adamatzky, A. et al. A Biologically Inspired Optimization Algorithm for Solving Fuzzy Shortest Path Problems with Mixed Fuzzy Arc Lengths. J Optim Theory Appl 163, 1049–1056 (2014). https://doi.org/10.1007/s10957-014-0542-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-014-0542-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation