Optimization of Travelling Salesman Problem on Single Valued Triangular Neutrosophic Number using Dhouib-Matrix-TSP1 Heuristic

Abstract

The Travelling Salesman Problem is one of the fundamental operational research problems where the objective is to generate the cheapest route for a salesman starting from a given city, visiting all the other cities only once and finally returning to the starting city. In this paper, we study the Travelling Salesman Problem in uncertain environment. Particularly, the single valued triangular neutrosophic environment is considered viewing that it is more realistic and general in real-world industrial problems. Each element in the distance matrix of the Travelling Salesman Problem is presented as a single valued triangular neutrosophic number. To solve this problem, we enhance our novel column-row heuristic Dhouib-Matrix-TSP1 by the means of the center of gravity ranking function and the standard deviation metric. In fact, the center of gravity ranking function is applied for defuzzification in order to convert the single valued triangular neutrosophic number to crisp number.A stepwise application of several numerical Travelling Salesman Problems on the single valued triangular neutrosophic environment shows that the optimal or a near optimal solution can be easily reached thanks to the Dhouib-Matrix-TSP1 heuristic enriched with the center of gravity ranking function and the standard deviation metric.