Neutrosophic Approach in Route-Optimization of Traveling Salesman Problems

Udit Sharma¹, Tarun Kumar¹, Jahnvi¹, Kailash Dhanuk², M. K. Sharma^1,*

¹Department of Mathematics, Chaudhary Charan Singh University, Meerut, U.P., 250004, India

²Department of Mathematics, Dyal Singh College (University of Delhi), New Delhi, 110003, India

Email: kumarsharmau9@gmail.com; tkvats3@gmail.com; rathijhanvi@gmail.com; kailash.dhanuk@dsc.du.ac.in; drmukeshsharma@gmail.com

Abstract

The Travelling Salesman Problem (TSP) possesses a significant challenge in optimization, complicated by real-world uncertainties such as fluctuating traffic conditions, weather variability and inconsistent travel durations. Traditional mathematical formulation fails to adequately incorporate these uncertainties, thus limiting their effectiveness. This paper introduces a modified approach to solving the TSP by employing Single-Valued Triangular Neutrosophic Sets (SVTNS), which effectively manages the indeterminate and ambiguous data. The proposed methodology to transform the neutrosophic fuzzy data into crisp numbers using a specifically modified score function. A stepwise procedure is introduced, encompassing crisp conversion, range evaluation and iterative optimization processes to attain an optimal and practically viable solution. The proposed methodology is validated through numerical computation to demonstrate its efficiency in determining the minimal crisp travelling costs and optimizing travelling schedules under the various weighting scenarios. This research advances the applicability of neutrosophic sets in decision-making to provide a reliable framework to address the uncertainties inherent in practical travelling Salesman issues.

Keywords: Fuzzy Set; Single-Valued Neutrosohic Fuzzy Set; Traveling Salesman Problem; Optimization; Score Function