A novel solution to traveling salesman problem using fuzzy sets, gravitational search algorithm, and genetic algorithm

Abstract

Throughout the history, many researchers have come across a problem in their real lives, called the Traveling Salesman Problem (TSP). This problem is to find the shortest route of a traveling salesperson that starts at a home city, visits a prescribed set of other cities and returns to the starting city. The distance travelled in such a tour obviously depends on the order in which the cities are visited and, thus, the problem is to find an optimal ordering of the cities. TSP is a representative of a large class of problems known as the combinatorial optimization problems. TSP is among the most important areas to explore, since it is very easy to describe, but very difficult to solve. There are several real-life applications of the TSP in several areas of knowledge including mathematics, computer science, operations research, genetics, engineering, and electronics. Many of the existing methods by which the TSP solved, suffer from considerable problems, such as lack of accuracy and speed. In this study, a hybrid method of TSP is proposed that can yield accurate results and relatively fast, without being trapped in a local optimum during the searching. In this approach, suitable fuzzy matrices are used to illustrate the details of the problem. A new optimization algorithm, called the Gravitational Search Algorithm (GSA) is applied to solve TSP as precise as possible, and finally the Genetic Algorithm (GA) finds the final answer in an acceptable amount of time. The results have illustrated that the proposed method are convincing compared to other related methods.