A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

A genetic algorithm for solving fuzzy shortest path problems with mixed fuzzy arc lengths

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Article ID: iaor20125743
Volume: 57
Issue: 1-2
Start Page Number: 84
End Page Number: 99
Publication Date: Jan 2013
Journal: Mathematical and Computer Modelling
Authors: , , ,
Keywords: heuristics, fuzzy sets, networks
Abstract:

We are concerned with the design of a model and an algorithm for computing the shortest path in a network having various types of fuzzy arc lengths. First, a new technique is devised for the addition of various fuzzy numbers in a path using a equ1‐cuts by proposing a least squares model to obtain membership functions for the considered additions. Due to the complexity of the addition of various fuzzy numbers for larger problems, a genetic algorithm is presented for finding the shortest path in the network. For this, we apply a recently proposed distance function for comparison of fuzzy numbers. Examples are worked out to illustrate the applicability of the proposed approach.

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