The First Resolution of the Travelling Salesman Problem under Neutrosophic Octagonal Fuzzy Environment

he Travelling Salesman Problem (TSP) is a challenging combinatorial optimization problem classified as NP-hard. Its objective is to identify the shortest cycle that visits every city precisely once before returning to the initial city. To the best of our knowledge there is no one in the literature who solved the TSP under the neutrosophic octagonal fuzzy environment. That’s why, in this paper the novel heuristic namely Dhouib-Matrix-TSP1 (DM-TSP1) is exploited to optimize the TSP under the neutrosophic octagonal fuzzy domain. So, this research work represents the first application of DM-TSP1 on this mentioned environment. A defuzzification function is used to convert neutrosophic octagonal fuzzy numbers to crisp ones then the four simple steps of DM-TSP1 are launched. A numerical example illustrating a step-by-step application of DM-TSP1 on novel created benchmark instances is provided to prove its performance and efficiency in solving the neutrosophic octagonal fuzzy TSP.