Application of linier fuzzy multi-objective programming model in travelling salesman problem

Abstract

Traveling salesman problem is a problem where a salesman must visit a number of cities, each of which is visited exactly once only, and has to start from and return to the origin city. The objective of this traveling salesman is to determine an optimal travel route by minimizing travel cost or travel distance. If a decision maker wants to determine an optimal route by minimizing travel cost and distance simultaneously, they need more than one destination function, and therefore traveling salesman problem can be formulated as a multi-objective problem. In a traveling salesman problem, salesman make decisions by choosing an optimal route based on an expected measurement. In fact, a number of real problems cannot be expressed as a constraint function and resources in a definite form, so it is necessary to use fuzzy logic which allows us for making decisions based on bias or incorrect data. This paper will discuss a solution to the traveling salesman problem by using a fuzzy multi-objective model, which aims to determine an optimal route of the salesman. Results obtained from data processing of five places to visit by using a Maple 18 software included minimum cost, distance, and time with satisfaction level α = 0.89.