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Finding the Optimal Path in 3D Spaces Using EDAs – The Wireless Sensor Networks Scenario

  • Bo Yuan
  • Maria Orlowska
  • Shazia Sadiq
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4431)

Abstract

In wireless sensor networks where sensors are geographically deployed in 3D spaces, a mobile robot is required to travel to each sensor in order to download the data. The effective communication ranges of sensors are represented by spheres with varying diameters. The task of finding the shortest travelling path in this scenario can be regarded as an instance of a class of problems called Travelling Salesman Problem with Neighbourhoods (TSPN), which is known to be NP-hard. In this paper, we propose a novel approach to this problem using Estimation of Distribution Algorithms (EDAs), which can produce significantly improved results compared to an approximation algorithm.

Keywords

Wireless Sensor Network Approximation Algorithm Mobile Robot Optimal Path Distribution Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Arkin, E.M., Hassin, R.: Approximation algorithms for the geometric covering salesman problem. Discrete Applied Mathematics 55(3), 197–218 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation. Oxford University Press, Oxford (1997)zbMATHGoogle 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. Journal of Algorithms 57(1), 22–36 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Dumitrescu, A., Mitchell, J.S.B.: Approximation algorithms for TSP with neighborhoods in the plane. Journal of Algorithms 48(1), 135–159 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Elbassioni, K.M., Fishkin, A.V., Mustafa, N.H., Sitters, R.A.: Approximation Algorithms for Euclidean Group TSP. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1115–1126. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Gudmundsson, J., Levcopoulos, C.: A fast approximation algorithm for TSP with neighborhoods. Nordic Journal of Computing 6(4), 469–488 (1999)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Helsgaun, K.: An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. European Journal of Operational Research 126(1), 106–130 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Larrañaga, P., Lozano, J.A. (eds.): Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  9. 9.
    Mata, C.S., Mitchell, J.S.B.: Approximation algorithms for geometric tour and network design problems (extended abstract). In: The eleventh annual symposium on computational geometry, pp. 360–369 (1995)Google Scholar
  10. 10.
    Papadimitriou, C.H.: The Euclidean travelling salesman problem is NP-complete. Theoretical Computer Science 4(3), 237–244 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Safra, S., Schwartz, O.: On the complexity of approximating tsp with neighborhoods and related problems. Computational Complexity 14(4), 281–307 (2006)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Yuan, B., Gallagher, M.: On the Importance of Diversity Maintenance in Estimation of Distribution Algorithms. In: The 2005 Genetic and Evolutionary Computation Conference, pp. 719–726 (2005)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Bo Yuan
    • 1
  • Maria Orlowska
    • 1
  • Shazia Sadiq
    • 1
  1. 1.School of Information Technology and Electrical Engineering, The University of Queensland, QLD 4072Australia

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