A Multilevel Reduction Algorithm to TSP

The TSP (traveling salesman problem) is one of the typical NP-hard problems in combinatorial optimization problem. The fast and effective approximate algorithms are needed to solve the large-scale problem in reasonable computing time. The known approximate algorithm can not give a good enough tour for the larger instance in reasonable time. So an algorithm called multilevel reduction algorithm is proposed, which is based on the analysis of the relation of local optimal tour and global optimal tour of the TSP. The partial tour of the global optimal tour is obtained by a very high probability through simply intersecting the local optimal tours. Using these partial tours it could contract the searching space of the original problem, at the same time it did not cut the searching capability down, this is the so-called reduction theory. And then the scale of the instance could be reduced small enough by multi-reduction. Finally it could solve the small-scaled instance using the known best algorithm and get a good enough tour by putting the partial tours together. The experimental results on TSPLIB (traveling salesman problem library) show that the algorithm could almost get optimal tour every time for instance in reasonable time and thus outperformed the known best ones in the quality of solutions and the running time.