Neutrosophic Sets and Systems
Abstract
The Traveling Salesman Problem (TSP) is one of the most significant and well-known optimization problem that is frequently limited by uncertainty in edge lengths. Existing methods fail to effectively model and solve such problems in uncertain environments. To address this gap, we propose a novel approach that combines a genetic algorithm (GA) with Fermatean neutrosophic numbers to provide a more robust representation of uncertainty. This work presents a comprehensive framework for evaluating the shortest path in a given network by precisely characterizing uncertain edge lengths. The proposed methodology is tested on various TSP scenarios of varying complexities, demonstrating its ability to generate near-optimal solutions with higher efficiency and accuracy than traditional techniques. Our findings highlight the method's potential for advancing uncertain route optimization and have significant practical implications for real-world logistics.
Recommended Citation
Raut, Prasanta Kumar; Surapati Pramanik; Deepak Kumar Mohapatra; and Srikanta Kumar Sahoo. "Solving the shortest path based on the traveling salesman problem with a genetic algorithm in a Fermatean neutrosophic environment." Neutrosophic Sets and Systems 78, 1 (2025). https://digitalrepository.unm.edu/nss_journal/vol78/iss1/21
