|National Travelling Salesman Problems
The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem which is easy to be stated, but hard to be solved. By literature, many hybridization approaches have been launched but none of them can provide the exact optimal solution and prober hybridization must be used to get solutions closer to the optimal. So we propose the new Discrete Velocity Propelled Averaged Crossover (DVPAC) introduced a hybrid model of Particle Swarm Optimization (PSO), Simulated Annealing ( SA), and Genetic Algorithm (GA) used in solving practical TSP in different countries. The practical experiment shows that our DVPAC can provide very satisfactory solutions and outperforms other algorithms.
We list below 14 TSP instances taken from the National Travelling Salesman Problems website. For these instances, the cost of travel between cities is specified by the Euclidean distance (EUC_2D-norm).
We will be most happy to report any improved tours or improved lower bounds that you may find.