Three-dimensional Euclidian Distance to Neutrosophic Number for  Travelling Salesman Problem

Souhail Dhouib; Saima Dhouib; K. Saritha; R. Rajalakshmi; Mana Donganont; Prasanta Kumar Raut

Authors

Souhail Dhouib Higher Institute of Industrial Management, University of Sfax, Tunisia; souh.dhou@gmail.com 2EPI-Polytechnique, University of Sousse, Sousse, Tunisia
Saima Dhouib EPI-Polytechnique, University of Sousse, Sousse, Tunisia
K. Saritha Department of Mathematics, Panimalar Engineering College, Poonamallee, Chennai-600123, Tamil Nadu, India;
R. Rajalakshmi Department of Mathematics, Panimalar Engineering College, poonamallee, Chennai-600123, Tamil Nadu, India;
Mana Donganont Department of Mathematics, School of Science, University of Phayao, Thailand;
Prasanta Kumar Raut Department of Mathematics, Trident Academy of Technology, Bhubaneswar, Odisha, India.

Keywords:

Neutrosophic Number, Artificial Intelligence, Operations Research, Heuristic, Dhouib-Matrix-TSP1, Euclidian Distance.

Abstract

The main idea in this paper is to study the application of the novel greedy Dhouib
Matrix-TSP1 (DM-TSP1) method to solve the Travel Salesman Problem with simple
neutrosophic numbers. Here, the Euclidian distance is used to convert the neutrosophic
number to crisp values, it is considered that the neutrosophic number as a three
dimensional coordinate. DM-TSP1 is a constructive method and requires just (n-1)
iterations to generate to create a solution (where n is the number of nodes).
Computational results on a case study developed in the literature prove that the proposed DM-TSP1 heuristic can create better solution than the Genetic Algorithm
with a fitness improvement of 92.68%.

DOI 10.5281/zenodo.17334981