Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique
DOI:
https://doi.org/10.24203/ijcit.v10i3.105Keywords:
Optimization; Fuzzy Numbers; Travelling Salesman Problem; Approximation Method; Ranking Function; α-Cut TechniqueAbstract
This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers.
Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance.
References
S. Dhouib, "A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1", International Journal of Recent Engineering Science, 2021, vol. 8, Issue 1, pp.6-10.
S. Dhouib, "Stochastic Column-Row Method for Travelling Salesman Problem: the Dhouib-Matrix-TSP2", International Journal of Engineering Research & Technology, 2021, vol. 10, Issue 3, pp. 524-527.
Sa. Dhouib and S. Dhouib, "Optimizing the Trapezoidal Fuzzy Travelling Salesman Problem Through Dhouib-Matrix-TSP1 Method Based on Magnitude Technique", International Journal of Scientific Research in Mathematical and Statistical Sciences, 2021, vol. 8, Issue 2 pp. 1-4.
L.A. Zadeh, “Fuzzy sets”, Information and Control, 1965, ,vol.8, pp. 338-353.
L.A. Zadeh, “Fuzzy sets as a basis for a theory of Possibility”, Fuzzy sets and Systems, 1978, vol. 1, pp. 3-28.
A. Aslan, “A Memetic Random Key Algorithm for the Balanced Travelling Salesman Problem”, Metaheuristics for Combinatorial Optimization, 2021, pp.16-22.
Y. Saji and M. Barkatou, “A discrete bat algorithm based on Lévy flights for Euclidean traveling salesman problem”, Expert Systems with Applications, 2021, vol.172, pp.114639.
A. A. Mehmet, C. B. Kalayci, “A Variable Neighborhood Search Algorithm for Cost-Balanced Travelling Salesman Problem”, Metaheuristics for Combinatorial Optimization, 2021, pp. 23-36.
S. Chowdhury, M. Marufuzzaman, H Tunc, L. Bian and W. Bullington “A modified Ant Colony Optimization algorithm to solve a dynamic traveling salesman problem A case study with drones for wildlife surveillance”, Journal of Computational Design and Engineering, 2019, vol. 6, issue 3, pp. 368-386.
P. K. P. Ghadle and P. A. Pathade, “Solving Transportation Problem with Generalized Hexagonal and Generalized Octagonal Fuzzy Numbers by Ranking Method”, Global Journal of Pure and Applied Mathematics, 2017, vol. 13, number 9, pp. 6367-6376.
C. Changdar, G.S.Mahapatra and R. K. Pal, “An efficient genetic algorithm for multi-objective solid travelling salesman problem under fuzziness”, Swarm and Evolutionary Computation, 2014, vol. 15, pp. 27-37.
Y. Liao, D. Yau and C. Chen, "Evolutionary algorithm to traveling salesman problems", Computers & Mathematics with Applications, 2012, vol. 64, issue 5, pp. 788-797.
Z. Wang, J. Guo, M. Zheng and Y. Wang, "Uncertain multiobjective traveling salesman problem", European Journal of Operational Research, 2015, vol. 241, issue 2, pp. 478-489.
A. Gupt and A. Kumar, “A new method for solving linear multi-objective transportation problems with fuzzy parameters”, Applied Mathematical Modelling, 2012, vol 36, issue 4, pp. 1421-1430.
A. Robati, G. A. Barani, H. N. A. Pour and M. J. Fadaee, “Balanced fuzzy particle swarm optimization”, Applied Mathematical Modelling, 2012, vol. 36, issue 5, pp. 2169-2177.
J. Majumdar and A. K. Bhunia, "Genetic algorithm for asymmetric traveling salesman problem with imprecise travel times", Journal of Computational and Applied Mathematics, 2011, vol. 235, issue 9, pp. 3063-3078.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Mariem Miledi, Souhail Dhouib, Taicir Loukil
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The articles published in International Journal of Computer and Information Technology (IJCIT) is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
