An improved genetic algorithm using the convex hull for traveling salesman problem

In this paper, we propose an improved genetic algorithm for the traveling salesman problem(TSP) by using the "visiting order restriction theorem". The visiting order restriction theorem gives a necessary condition for the shortest tour of TSP on the Euclidean plane by using the convex hull. The convex hull for a set of points S on a plane is defined as the smallest convex polygon that encloses S. In our method, the initial tours are produced to satisfy the necessary condition of the theorem for the shortest path without incresing the computation time. The simulation results using 10 well-known benchmark problems show that our algorithm can find better tour with shorter time than Pal's algorithm.