Nested queue-jumping algorithm for Traveling Salesman Problem

This paper proposes a new approximate algorithm, the nested queue-jumping algorithm (NQJA), for traveling salesman problem. The proposed algorithm incorporates the ideas of heuristic algorithm, randomized algorithm and local optimization. Numerical results show that, using queue-jumping algorithm directly can obtain the known best solution with a large probability. In the case of large-scale instances, nested queue-jumping algorithm generates high-quality solution compared to well-known heuristic methods. Moreover, the shortest tour to China144 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. Nested queue-jumping algorithm is specially devised for TSP. But its concept can tackle other NP-hard combinatorial optimization problems.