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

Author

Listed:
  • Xiaoge Zhang

    (Southwest University)

  • Qing Wang

    (Southwest University)

  • Andrew Adamatzky

    (University of the West of England)

  • Felix T. S. Chan

    (Hong Kong Polytechnic University)

  • Sankaran Mahadevan

    (Vanderbilt University)

  • Yong Deng

    (Southwest University)

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 $$\alpha $$ α cuts. We illustrate effectiveness and adaptability of the proposed method with numerical examples, and compare our algorithm with existing approaches.

Suggested Citation

  • Xiaoge Zhang & Qing Wang & Andrew Adamatzky & Felix T. S. Chan & Sankaran Mahadevan & Yong Deng, 2014. "A Biologically Inspired Optimization Algorithm for Solving Fuzzy Shortest Path Problems with Mixed Fuzzy Arc Lengths," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 1049-1056, December.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:3:d:10.1007_s10957-014-0542-6
    DOI: 10.1007/s10957-014-0542-6
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    References listed on IDEAS

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    1. Antonio Polimeni & Antonino Vitetta, 2013. "Optimising Waiting at Nodes in Time-Dependent Networks: Cost Functions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 805-818, March.
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