Novel Heuristic for New Pentagonal Neutrosophic Travelling Salesman Problem

Abstract

This paper presents a new variant of Travelling Salesman Problem (TSP) and its first resolution. In literature there is not any research work that has presented the TSP under pentagonal fuzzy neutrosophic environment yet. TSP is a critical issue for manufacturing companies where all cities need to be visited only once except the starting city with a minimal cost. In real life, information provided (cost, time … etc.) are generally uncertain, indeterminate or inconsistent
that’s why in this paper parameters of the TSP are presented as neutrosophic pentagonal fuzzy numbers. To solve this problem, the novel heuristic Dhouib-Matrix-TSP1 (DM-TSP1) is applied using a ranking function in order to transform the fuzzy set to crisp data and range function to select cities. To prove the efficiency of the proposed DM-TSP1 in solving the new variant of TSP, we create novel benchmark instances. Then, a stepwise application of DM-TSP1 is illustrated in details.