Solving the Illumination Problem with Heuristics

  • Manuel Abellanas
  • Enrique Alba
  • Santiago Canales
  • Gregorio Hernández
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)

Abstract

In this article we propose optimal and quasi optimal solutions to the problem of searching for the maximum lighting point inside a polygon P of n vertices. This problem is solved by using three different techniques: random search, simulated annealing and gradient. Our comparative study shows that simulated annealing is very competitive in this application. To accomplish the study, a new polygon generator has been implemented, which greatly helps in the general validation of our claims on the illumination problem as a new class of optimization task.

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References

  1. 1.
    Auer, T., Held, M.: Heuristics for the Generation of Random Polygons. In: Proc. 8th Canad. Conf. Comput. Geom., Ottawa, Canada, Aug., pp. 38–44 (1996)Google Scholar
  2. 2.
    Back, T.: Evolutionary Algorithms in Theory and Practice. Oxford Press, Oxford (1996)Google Scholar
  3. 3.
    Canales, S.: Métodos Heurísticos en Problemas Geométricos. Visibilidad, Iluminación y Vigilancia. Ph. D. Thesis, UPM, Spain (2004)Google Scholar
  4. 4.
    Dowsland, K.A.: Simulated Annealing. In: Reeves, C.R. (ed.) Modern Heuristic Techniques for Combinatorial Problems, Blackwell Scientific Pub., Oxford (1993)Google Scholar
  5. 5.
    Eidenbenz, S. (In)-Approximability of Visibility Problems on Polygons and Terrains. Ph. D. Thesis, Swiss Federal Institute of Tecnology Zurich (2000)Google Scholar
  6. 6.
    Fogel, D.: Evolutionay Computation. IEEE Computer Society Press, Los Alamitos (1995)Google Scholar
  7. 7.
    Gelatt, C.D., Kirkpatrick, S., Vecchi, M.P.: Optimazation by simulated annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Ghosh, S.K.: Approximation algorithms for Art Gallery Problems. In: Proceedings of the Canadian Information Processing Society Congress (1987)Google Scholar
  9. 9.
    Ingber, L.: Very fast simulated re-annealing. Math. Comput. Modelling 12(8), 967–973 (1989)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lee, D.T., Lin, A.K.: Computational complexity of art gallery problem. IEEE Trans. Info. Th. IT-32, 415–421 (1979)MathSciNetGoogle Scholar
  11. 11.
    Szu, H.H., Hartley, R.L.: Fast simulated annealig. Physic Letters A 122, 157–162 (1987)CrossRefGoogle Scholar
  12. 12.
    Urrutia, J.: Art Gallery and Illumination Problems. In: Sack, J.R., Urrutia, J. (eds.) Handbook on Computational Geometry, Elsevier, Amsterdam (1999)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Manuel Abellanas
    • 1
  • Enrique Alba
    • 2
  • Santiago Canales
    • 3
  • Gregorio Hernández
    • 1
  1. 1.Universidad Politécnica de Madrid. Facultad de Informática, Departamento de Matemática Aplicada.Spain
  2. 2.Universidad de Málaga, Departamento de Lenguajes y CC. CC.Spain
  3. 3.Universidad Pontificia Comillas de Madrid, Departamento de Matemática Aplicada y Computación.Spain

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