A novel globally convergent hybrid evolutionary algorithm for traveling salesman problems

Traveling Salesman Problem (TSP for short) is a class of NP-hard combinatorial optimization problems. It is of great importance in both theory and applications. First, a new and simple encoding scheme is designed. For TSP with (n+1) cities, the encoding scheme is to use an integer in [0,n!-1] to represent a valid tour and each integer is corresponding to unique valid tour, and vice versa. Thus, TSP can be transformed into a problem in which we shall look for an integer in [0,n!-1] such that the length of the corresponding tour is shortest. The most obvious advantage is that it is very easy to design easy-executed and efficient crossover and mutation operators. Second, a novel local search scheme is integrated into the crossover and mutation operators to enhance their ability of exploration. Based on these, a novel and effective evolutionary algorithm for TSP is proposed and its convergence to global optimal solution with probability one is proved. At last, the numerical experiments are made for five standard test problems. The best solutions found by the proposed algorithm are better than or equal to those found by the compared algorithms. These results indicate the proposed algorithm is efficient.