Evaluation of the shortest path based on the Traveling Salesman  problem with a genetic algorithm in a neutrosophic environment

Prasanta Kumar Raut; Siva Prasad Behera; Said Broumi; Arindam Dey; Mohamed Talea; Amarendra Baral

Authors

Prasanta Kumar Raut Department of Mathematics, C.V. Raman Global University, Bhubaneswar-752054, Odisha, India
Siva Prasad Behera Department of Mathematics, C.V. Raman Global University, Bhubaneswar-752054, Odisha, India
Said Broumi Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco
Arindam Dey School of Computer Science and Engineering, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
Mohamed Talea Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco
Amarendra Baral Trident Academy of Technology, Bhubaneswar, Odisha, India

Keywords:

Connected network; Neutrosophic number; Shortest path problem; Traveling Salesman problem

Abstract

In The traveling salesman problem (TSP) is an essential and the most popular conventional
combinatorial optimization network problem in operations research, in which the TSP evaluates the
shortest route or path in a network. In TSP, every node has been visited only once, excluding the
starting node. In TSP, edge lengths are usually expressed to indicate journey time and expenses
instead of distance from a location. The exact arc length can't be predicted because journey times
and expenses vary depending on the amount of payload, climate, highway conditions, and so on.
As a result, the Neutrosophic numbers introduce a new tool for dealing with unpredictability in
TSP. The present article addresses TSP on a neutrosophic network where the edge weight is a
neutrosophic number rather than a real number. For solving the Neutrosophic TSP, an algorithmic
technique based on the genetic algorithm (GA) is proposed. We created a new mutation and
crossover for our suggested GA. We used mathematical examples to show the usefulness of the
algorithm that we suggested. The results of experiments suggest that the proposed GA can find the
shortest path in a TSP within a neutrosophic framework. This provides valuable insights for
decision-makers dealing with real-world situations characterized by imprecise and incomplete data.

DOI: 10.5281/zenodo.11479157