Probe Machine Based Consecutive Route Filtering Approach to Symmetric Travelling Salesman Problem
The travelling salesman problem (TSP) is one of the NPC combinatorial optimization problems and still now it remains as an interesting and challenging problem in the field of combinatorial optimization. In this paper, we propose a consecutive route filtering approach to solving the symmetric TSP with the help of probe concept such that the worse routes are filtered out step by step by using a rigorous predesigned step proportion. In this way, it is important to set up a reasonable value of the step proportion which is needed in each step during the filtering process. Actually, our proposed algorithm is implemented on the set of symmetric TSP benchmarks with both small and large numbers of cities from the TSPLIB dataset. It is demonstrated by the experimental results that our proposed algorithm can obtain the best results in some cases and generally get the approximation results close to the best known solutions.
KeywordsProbe machine Travelling salesman problem Filtering proportion Discrete optimization
This work is supported by the Natural Science Foundation of China for Grant 61171138.
- 3.Matai, R., Singh, S.P., Mittal, M.L.: Traveling salesman problem: an overview of applications, formulations, and solution approaches. In: Davendra, D. (ed.) Traveling Salesman Problem, Theory and Applications, pp. 1–24. InTech, Croatia (2010)Google Scholar
- 4.MacGregor, J.N., Chu, Y.: Human performance on the traveling salesman and related problems: a review. J. Probl. Solving 3(2), article 2 (2011)Google Scholar
- 18.Guo, D., Chen, H., Wang, B.: An improved genetic algorithm with decision function for solving travelling salesman problem. In: Proceeding of 12th ISKE. IEEE Conferences, Nanjing, China, pp. 1–7 (2017). https://doi.org/10.1109/ISKE.2017.8258774
- 19.Colorni, A., Dorigo, M., Maniezzo, V.: Distributed optimization by ant colonies. In: Varela, F., Bourgine, P. (eds.) Proceedings of European Conference on Artificial Life, Paris, France, pp. 134–142 (1991)Google Scholar
- 21.Xiong, N., Wu, W., Wu, C.: An improved routing optimization algorithm based on travelling salesman problem for social networks. Auton. Sustain. Comput. Prep. Internet Things Environ. 9(6), 985 (2017)Google Scholar
- 22.Ratanavilisagul, C.: Modified ant colony optimization with pheromone mutation for travelling salesman problem. In: Proceeding of 14th ECTI-CON. IEEE Conferences, Phuket, Thailand, pp. 411–414 (2017). https://doi.org/10.1109/ECTICon.2017.8096261
- 28.TSPLIB. http://elib.zib.de/pub/mp-testdata/tsp/tsplib/tsplib.html. Accessed 16 June 2018
- 29.https://people.sc.fsu.edu/~jburkardt/datasets/tsp/tsp.html. Accessed 24 June 2018