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.
Partially supported by TIN 2005-08818-C04-01 and CAM S-0505/DPI/023.
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References
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)
Back, T.: Evolutionary Algorithms in Theory and Practice. Oxford Press, Oxford (1996)
Canales, S.: Métodos Heurísticos en Problemas Geométricos. Visibilidad, Iluminación y Vigilancia. Ph. D. Thesis, UPM, Spain (2004)
Dowsland, K.A.: Simulated Annealing. In: Reeves, C.R. (ed.) Modern Heuristic Techniques for Combinatorial Problems, Blackwell Scientific Pub., Oxford (1993)
Eidenbenz, S. (In)-Approximability of Visibility Problems on Polygons and Terrains. Ph. D. Thesis, Swiss Federal Institute of Tecnology Zurich (2000)
Fogel, D.: Evolutionay Computation. IEEE Computer Society Press, Los Alamitos (1995)
Gelatt, C.D., Kirkpatrick, S., Vecchi, M.P.: Optimazation by simulated annealing. Science 220, 671–680 (1983)
Ghosh, S.K.: Approximation algorithms for Art Gallery Problems. In: Proceedings of the Canadian Information Processing Society Congress (1987)
Ingber, L.: Very fast simulated re-annealing. Math. Comput. Modelling 12(8), 967–973 (1989)
Lee, D.T., Lin, A.K.: Computational complexity of art gallery problem. IEEE Trans. Info. Th. IT-32, 415–421 (1979)
Szu, H.H., Hartley, R.L.: Fast simulated annealig. Physic Letters A 122, 157–162 (1987)
Urrutia, J.: Art Gallery and Illumination Problems. In: Sack, J.R., Urrutia, J. (eds.) Handbook on Computational Geometry, Elsevier, Amsterdam (1999)
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Abellanas, M., Alba, E., Canales, S., Hernández, G. (2007). Solving the Illumination Problem with Heuristics. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_24
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DOI: https://doi.org/10.1007/978-3-540-70942-8_24
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