Unraveling the Intuitionistic Octagonal Fuzzy Travelling Salesman Problem via Dhouib-Matrix-TSP1 Heuristic

Abstract

The Travelling Salesman Problem (TSP) is an NP-hard problem of optimization that its goal is to obtain the shortest cycle among all cities that should be visited only once by a salesperson. The main goal of a salesperson is to visit each city only once and to obtain the distance traveled as well as the travelling costs as low as possible. In real-life and due to the absence of information, variables coming from experts’ collected data are usually uncertain and imprecise. In such cases, the decision maker cannot exactly expect the TSP cost. That’s why in this paper, the TSP under the intuitionistic octagonal fuzzy environment is considered and solved by adapting the very recent greedy method namely Dhouib-Matrix-TSP1 (DM-TSP1). This heuristic is very simple and it is composed of four steps. DM-TSP1 uses the Sum metric and is enriched with a ranking function. This current research work presents the first resolution of the TSP under the intuitionistic octagonal fuzzy domain. For this reason, new case studies are generated in order to carry out the experimental results. Moreover, a step-by-step execution of DM-TSP1 is detailed in order to prove its effectiveness.