Traveling Salesman Problem has numerous applications in sequencing and scheduling. Branch exchange heuristic is a quick algorithm which can result in a near optimal solution for symmetrical traveling salesman problem. In this paper an new method for selecting the branch is presented which saves the quality of solvings but results in a decrease of one- third in computational time compare with other branch exchange algorithms.

In this paper, we introduce a new approach for solving the traveling salesman problems (TSP) and provide a solution algorithm for a variant of this problem. The concept of the proposed method is based on the Hungarian algorithm, which has been used to solve an assignment problem for reaching an optimal solution. We introduced a new fittest criterion for crossing over such problems, and illustrated it with analytical examples and by computer programming. The proposed method builds on the initial solution of the traveling salesman problem (TSP) which is very simple, easy to understand and apply.

Routing issues have many applications in GIS. The main goal in routing is to find the best route passing a series of determined positions. This process has an effective role in many of spatial decision makings. A lot of studies have been accomplished about the optimization of different kinds of routing problems. Traveling Salesman Problem is one of the very old issues in applied sciences. Emerging of new technologies such as GIS caused a lot of new applications for the TSP. A lot of new approaches have been suggested using these technologies to solve TSP. Evolutionary algorithms are one of the methods have been used to solve various optimization problems. Researches have shown that combining local search methods with the genetic operators can lead to better results in solving TSP. In this paper, a new and innovative method is presented to solve this routing problem. In this method using the concept of mass center for a set of station points a growing convex polygon is assigned to them. During this process a reliable solution, which is a route, is produced. Besides, a local search method based on the genetic algorithm and a nearest neighbor algorithm has been implemented to evaluate the results of the new developed method in solving TSP. Evaluation of the results of the genetic method, local search and nearest neighbors indicate that the new method can provide acceptable solutions during very short time.