Novel Heuristic for Intuitionistic Triangular Fuzzy Travelling Salesman Problem

Abstract

The travelling salesman problem (TSP) is a well-known combinatorial problem frequently used in real-world industries to find the minimum cost cycle between all cities. In this paper, the authors consider the distance matrix between all cities in a vagueness environment, where each element in the distance matrix is presented as an intuitionistic triangular fuzzy set. To solve this problem, the novel heuristic Dhouib-Matrix-TSP1 (DM-TSP1) is enhanced with the centroid ranking function for defuzzification and the range statistical metric for cities selection. In fact, this paper presents the first adaptation of DM-TSP1 to solve TSP under intuitionistic environment. DM-TSP1 can easily generate a good initial basic feasible solution just after just n iterations (where n represents the number of cities). The performance of DM-TSP1 is demonstrated by suitable numerical examples.