Solving traveling salesman problem by using a fuzzy multi-objective linear programming

Abstract

The traveling salesman problem (TSP) is one of the most intensively studied problems in computational mathematics. Information about real life systems is often available in the form of vague descriptions. Hence, fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters. This study develops a fuzzy multi-objective linear programming (FMOLP) model with piecewise linear membership function for solving a multi-objective TSP in order to simultaneously minimize the cost, distance and time. The proposed model yields a compromise solution and the decision maker’s overall levels of satisfaction with the determined objective values. The primary contribution of this paper is a fuzzy mathematical programming methodology for solving the TSP in uncertain environments. A numerical example is solved to show the effectiveness of the proposed approach. The performance of proposed model with Zimmerman and Hannan’s methods is compared. Computational results show that the proposed FMOLP model achieves higher satisfaction degrees. Key words: Traveling salesman problem, fuzzy multi-objective linear programming, decision maker.