International Journal of Neutrosophic Science
IJNS
2690-6805
2692-6148
10.54216/IJNS
https://www.americaspg.com/journals/show/1364
2020
2020
The Neutrosophic Traveling Salesman problem with Neutrosophic EdgeWeight: Formulation and A Genetic Algorithm
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 Mâ€™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