Solving the shortest path based on the traveling salesman problem with a genetic algorithm in a Fermatean neutrosophic environment

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. 

DOI: 10.5281/zenodo.14296815