Solving traveling salesman problem with Nested Queue-Jumping Algorithm

This paper presents a new approximate algorithm Nested Queue-Jumping Algorithm (NQJA) to solve traveling salesman problem. The proposed algorithm incorporates the thoughts of heuristic algorithm, randomized algorithm and local optimization. Numerical results show that to the small-scale instances, using Queue-Jumping Algorithm (QJA) directly can obtain the known optimal solution with a large probability. In the case of large-scale instances, NQJA generates high-quality solution compared to well know heuristic methods. Moreover, the shortest tour to China 144 TSP found by NQJA is shorter than the known optimal tour. It can be a very promising alternative for finding a solution to the TSP. NQJA is specially devised for TSP, But its thought can give elicitation for other NP-hard combinatorial optimization problems.