Nested queue-jumping algorithm for solving a traveling salesman problem

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