International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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International Journal of Neutrosophic Science

Volume 19 , Issue 3 , PP: 40-46, 2022 | Cite this article as | XML | Html | PDF

The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm

Arindam Dey 1 * , Ranjan Kumar 2 , Said Broumi 3

  • 1 School of Computer Science and Engineering (SCOPE), VIT-AP University , Amravati, India - (arindam84nit@gmail.com)
  • 2 Department of Mathematics, VIT-AP University , Amravati, India - (ranjank.nit52@gmail.com)
  • 3 Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, MOROCCO - (broumisaid78@gmail.com)
  • Doi: https://doi.org/10.54216/IJNS.190304

    Received: June 06, 2022 Accepted: November 12, 2022
    Abstract

    The traveling salesman problem (TSP) is an important and well known classical combinatorial network optimization

    problem in operation research, where the TSP finds a shortest possible route through a set of n nodes

    such that each and every node are visited exactly one time except for the starting node. In this problem, the

    arc lengths are generally considered to represent the traveling time or travelling cost rather than geographical

    distance. It is not possible to predict the exact arc length because the traveling time or traveling cost fluctuated

    with payload, weather, traffic conditions and so on. neutrosophic set theory provides a new tool to handle the

    uncertainties in TSP. In this paper, we concentrate on TSP on a network in which neutrosophic set, Instead of

    real number is assigned to edge as edge weight. We propose a mathematical model for a TSP with neutrosophic

    arc lengths. We present the utility of neutrosophic sets as arc length for TSP. An algorithmic method based

    on Genetic Algorithm (GA) is proposed for solving this problem. We have designed a new heuristic crossover

    and heuristic mutation our proposed GA. We have used a numerical example to illustrate the effectiveness of

    our proposed algorithm.

    Keywords :

    Neutrosophic Edge Weight , Formulation , Genetic Algorithm , Traveling Salesman problem

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    Cite This Article As :
    Arindam Dey, Ranjan Kumar, Said Broumi. "The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm." Full Length Article, Vol. 19, No. 3, 2022 ,PP. 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)
    Arindam Dey, Ranjan Kumar, Said Broumi. (2022). The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm. Journal of , 19 ( 3 ), 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)
    Arindam Dey, Ranjan Kumar, Said Broumi. "The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm." Journal of , 19 no. 3 (2022): 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)
    Arindam Dey, Ranjan Kumar, Said Broumi. (2022). The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm. Journal of , 19 ( 3 ), 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)
    Arindam Dey, Ranjan Kumar, Said Broumi. The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm. Journal of , (2022); 19 ( 3 ): 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)
    Arindam Dey, Ranjan Kumar, Said Broumi, The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm, Journal of , Vol. 19 , No. 3 , (2022) : 40-46 (Doi   :  https://doi.org/10.54216/IJNS.190304)