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

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%.