The traveling salesman problem is analyzed with genetic algorithms. The best route map and tendency of optimal grade of 500 cities before the first mutation, best route map after 15 times of mutation and tendency of optimal grade of the final mutation are displayed with algorithm animation. The optimal grade is about 0.0455266 for the best route map before the first mutation, but is raised to about 0.058241 for the 15 times of mutation. It shows that through the improvements of algorithms and coding methods, the efficiency to solve ...