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

Xiaoge Zhang (), Qing Wang, Andrew Adamatzky, Felix T. S. Chan, Sankaran Mahadevan and Yong Deng ()
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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

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 18, 1049-1056

Abstract: 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.

Keywords: Shortest path; Fuzzy numbers; Bio-inspired; Optimization; 65K05; 65K10; 78M50 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-014-0542-6

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