International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1364 2020 2020 School of Computer Science and Engineering (SCOPE), VIT-AP University , Amravati, India Arindam Dey Department of Mathematics, VIT-AP University , Amravati, India Ranjan Kumar Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, MOROCCO Said Broumi 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. 2022 2022 40 46 10.54216/IJNS.190304 https://www.americaspg.com/articleinfo/21/show/1364