ACO-iRBA: A Hybrid Approach to TSPN with Overlapping Neighborhoods

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)

Abstract

The traveling salesman problem with neighborhoods (TSPN) is a generalization of TSP and can be regarded as a combination of TSP and TPP (Touring Polygons Problem). In this paper, we propose a hybrid TSPN solution named ACO-iRBA in which the TSP and TPP tasks are tackled simultaneously by ACO (Ant Colony Optimization) and iRBA, an improved version of RBA (Rubber Band Algorithm), respectively. A major feature of ACO-iRBA is that it can properly handle situations where the neighborhoods are heavily overlapped. Experiment results on benchmark problems composed of random ellipses show that ACO-iRBA can solve TSPN instances with up to 70 regions effectively and generally produce higher quality solutions than a recent heuristic method CIH.

Keywords

TSP TPP TSPN Hybrid iRBA 

References

  1. 1.
    Arkin, E.M., Hassin, R.: Approximation algorithms for the geometric covering salesman problem. Discrete Appl. Math. 55(3), 197–218 (1994)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Dumitrescu, A., Mitchell, J. S.: Approximation algorithms for TSP with neighborhoods in the plane. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 38–46. Society for Industrial and Applied Mathematics (2001)Google Scholar
  3. 3.
    de Berg, M., Gudmundsson, J., Katz, M.J., Levcopoulos, C., Overmars, M.H., van der Stappen, A.F.: TSP with neighborhoods of varying size. J. Algorithms 57(1), 22–36 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Jang, D.S., Chae, H.J., Choi, H.L.: Optimal control-based UAV path planning with dynamically-constrained TSP with neighborhoods. arXiv preprint arXiv:1612.06008 (2016)
  5. 5.
    Isaacs, J.T., Klein, D.J., Hespanha, J.P.: Algorithms for the traveling salesman problem with neighborhoods involving a Dubins vehicle. In: American Control Conference, pp. 1704–1709 (2011)Google Scholar
  6. 6.
    Wang, W., Shi, H.S., Wu, D.J., Huang, P.Y., Gao, B.J., Wu, F.P., Xu, D., Chen, X.J.: VD-PSO: an efficient mobile sink routing algorithm in wireless sensor networks. Peer-to-Peer Netw. Appl. 10, 1–10 (2016)Google Scholar
  7. 7.
    Yuan, B., Orlowska, M., Sadiq, S.: On the optimal robot routing problem in wireless sensor networks. IEEE Trans. Knowl. Data Eng. 19(9), 1252–1261 (2007)CrossRefGoogle Scholar
  8. 8.
    Gentilini, I., Margot, F., Shimada, K.: The travelling salesman problem with neighbourhoods: MINLP solution. Optim. Methods Softw. 28(2), 364–378 (2013)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Alatartsev, S., Augustine, M., Ortmeier, F.: Constricting insertion heuristic for traveling salesman problem with neighborhoods. In: ICAPS (2013)Google Scholar
  10. 10.
    Klette, R., Bülow, T.: Critical edges in simple cube-curves. In: 9th International Conference on Discrete Geometry for Computer Imagery, pp. 467–478 (2000)Google Scholar
  11. 11.
    Dror, M., Efrat, A., Lubiw, A., Mitchell, J.S.: Touring a sequence of polygons. In: Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 473–482 (2003)Google Scholar
  12. 12.
    Pan, X., Li, F., Klette, R.: Approximate shortest path algorithms for sequences of pairwise disjoint simple polygons. Department of Computer Science, University of Auckland, pp. 175–178 (2010)Google Scholar
  13. 13.
    Li, F., Klette, R.: Rubberband algorithms for solving various 2D or 3D shortest path problems. In: Computing: Theory and Applications, pp. 9–19. IEEE Press (2007)Google Scholar
  14. 14.
    Ahadi, A., Mozafari, A., Zarei, A.: Touring a sequence of disjoint polygons: complexity and extension. Theoret. Comput. Sci. 556, 45–54 (2014)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Grefenstette, J., Gopal, R., Rosmaita, B., Van Gucht, D.: Genetic algorithms for the traveling salesman problem. In: Proceedings of the First International Conference on Genetic Algorithms and Their Applications, pp. 160–165 (1986)Google Scholar
  16. 16.
    Dorigo, M., Gambardella, L.M.: Ant colonies for the travelling salesman problem. Biosystems 43(2), 73–81 (1997)CrossRefGoogle Scholar
  17. 17.
    Wang, K.P., Huang, L., Zhou, C.G., Pang, W.: Particle swarm optimization for traveling salesman problem. In: 2003 International Conference on Machine Learning and Cybernetics, pp. 1583–1585 (2003)Google Scholar
  18. 18.
    Wong, L.P., Low, M.Y. H., Chong, C.S.: A bee colony optimization algorithm for traveling salesman problem. In: AICMS 2008 Second Asia International Conference on Modeling and Simulation, pp. 818–823 (2008)Google Scholar
  19. 19.
    Alatartsev, S., Mersheeva, V., Augustine, M., Ortmeier, F.: On optimizing a sequence of robotic tasks. In: 2013 IEEE/RSJ International Conference Intelligent Robots and Systems (IROS), pp. 217–223 (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Intelligent Computing Lab, Division of Informatics, Graduate School at ShenzhenTsinghua UniversityShenzhenPeople’s Republic of China

Personalised recommendations