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Towards Solving TSPN with Arbitrary Neighborhoods: A Hybrid Solution

  • Bo Yuan
  • Tiantian Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10142)

Abstract

As the generalization of TSP (Travelling Salesman Problem), TSPN (TSP with Neighborhoods) is closely related to several important real-world applications. However, TSPN is significantly more challenging than TSP as it is inherently a mixed optimization task containing both combinatorial and continuous components. Different from previous studies where TSPN is either tackled by approximation algorithms or formulated as a mixed integer problem, we present a hybrid framework in which metaheuristics and classical TSP solvers are combined strategically to produce high quality solutions for TSPN with arbitrary neighborhoods. The most distinctive feature of our solution is that it imposes no explicit restriction on the shape and size of neighborhoods, while many existing TSPN solutions require the neighborhoods to be disks or ellipses. Furthermore, various continuous optimization algorithms and TSP solvers can be conveniently adopted as necessary. Experiment results show that, using two off-the-shelf routines and without any specific performance tuning efforts, our method can efficiently solve TSPN instances with up to 25 regions, which are represented by both convex and concave random polygons.

Keywords

TSP TSPN Neighborhood Hybrid Metaheuristic 

Notes

Acknowledgement

This work was supported by Natural Science Foundation of Guangdong Province (No. 2014A030310318) and Research Foundation of Shenzhen (No. JCYJ20160301153317415).

References

  1. 1.
    Applegate, D., Bixby, R., Chvátal, V., Cook, W.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)zbMATHGoogle Scholar
  2. 2.
    Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45, 753–782 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Larrañaga, P., Kuijpers, C., Murga, R., Inza, I., Dizdarevic, S.: Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif. Intell. Rev. 13, 129–170 (1999)CrossRefGoogle Scholar
  4. 4.
    Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126, 106–130 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Alatartsev, S., Stellmacher, S., Ortmeier, F.: Robotic task sequencing problem: a survey. J. Intell. Robot. Syst. 80, 279–298 (2015)CrossRefGoogle Scholar
  6. 6.
    Arkin, E.M., Hassin, R.: Approximation algorithms for the geometric covering salesman problem. Discret. Appl. Math. 55, 197–218 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mitchell, J.: A PTAS for TSP with neighborhoods among fat regions in the plane. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 11–18 (2007)Google Scholar
  8. 8.
    Elbassioni, K., Fishkin, A., Sitters, R.: Approximation algorithms for the Euclidean traveling salesman problem with discrete and continuous neighborhoods. Int. J. Comput. Geom. Appl. 19, 173–193 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chan, T., Elbassioni, K.: A QPTAS for TSP with fat weakly disjoint neighborhoods in doubling metrics. Discret. Comput. Geom. 46, 704–723 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Dumitrescu, A., Tóth, C.: Constant-factor approximation for TSP with disks (2016). arXiv:1506.07903v3 [cs.CG]
  11. 11.
    Gentilini, I., Margot, F., Shimada, K.: The travelling salesman problem with neighborhoods: MINLP solution. Optim. Methods Softw. 28, 364–378 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Yuan, B., Orlowska, M., Sadiq, S.: On the optimal robot routing problem in wireless sensor networks. IEEE Trans. Knowl. Data Eng. 19, 1252–1261 (2007)CrossRefGoogle Scholar
  13. 13.
    Chang, W., Zeng, D., Chen, R., Guo, S.: An artificial bee colony algorithm for data collection path planning in sparse wireless sensor networks. Int. J. Mach. Learn. Cybern. 6, 375–383 (2015)CrossRefGoogle Scholar
  14. 14.
  15. 15.
  16. 16.
    Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evol. Comput. 9, 159–195 (2001)CrossRefGoogle Scholar
  17. 17.
  18. 18.
    Kirk, D., Hwu, W.: Programming Massively Parallel Processors: A Hands-on Approach. Morgan Kaufmann, San Francisco (2012)Google Scholar
  19. 19.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of 6th International Conference on Genetic Algorithms, pp. 184–192 (1995)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Intelligent Computing Lab, Division of InformaticsGraduate School at Shenzhen, Tsinghua UniversityShenzhenPeople’s Republic of China
  2. 2.Shenzhen Engineering Laboratory of Geometry Measurement TechnologyGraduate School at Shenzhen, Tsinghua UniversityShenzhenPeople’s Republic of China

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