A Genetic Algorithm for Solving Shortest Path Problem Under Neutrosophic Environment

The shortest path problem is a widely recognized and fundamental optimization problem in operations research. Nearly all practical implementations of the shortest path issue include uncertainties. A neutrosophic set is an effective tool for managing uncertainties in the shortest path issue, whereas a normal fuzzy set may be inadequate for delivering a suitable solution. In the neutrosophic shortest path problem, we frequently use the neutrosophic set to represent the arc length. A neutrosophic set is an effective way to manage uncertainty. This manuscript presents a genetic algorithm as a solution to this problem. We are looking at a method that could accurately find the shortest path in a neutrosophic graph. Triangular neutrosophic numbers, representing the lengths of the arcs connecting a starting node to a desired node, form a neutrosophic graph. In addition, we illustrate the efficacy of employing a neutrosophic set for this problem. Our analysis of the current literature revealed a lack of evolutionary approaches capable of addressing the neutrosophic shortest path problem with neutrosophic arc lengths. We present an illustrative example using numerical data to demonstrate the functionality of the proposed approach.