Simulated annealing aplicado a triangulaciones y pseudotriangulaciones de peso M

Muchos problemas de optimización en configuraciones geométricas son NP-duros. En este art́ıculo, consideramos los problemas de Triangulación de Peso Mı́nimo (Minimum Weight Triangulation, MWT ) y PseudoTriangulación de Peso Mı́nimo (Minimum Weight Pseudo-triangulation, MWPT ) para un conjunto dado de puntos en el plano, y mostramos el diseño para la técnica metaheuŕıstica Simulated Annealing(SA) que permite resolverlos de forma aproximada.

[1]  Michael Ian Shamos,et al.  Closest-point problems , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[2]  Francisco Santos,et al.  Pseudo-Triangulations - a Survey , 2006 .

[3]  Edilma Olinda Gagliardi,et al.  Soluciones aproximadas para el problema de Triangulación de Peso Mínimo utilizando ACO , 2009 .

[4]  Michel Pocchiola,et al.  Pseudo-triangulations: theory and applications , 1996, SCG '96.

[5]  Ivana Kolingerová,et al.  Multicriteria-optimized triangulations , 2001, The Visual Computer.

[6]  G. Rote,et al.  Minimum weight triangulation is NP-hard , 2006, SCG '06.

[7]  G. Klincsek.  Minimal Triangulations of Polygonal Domains , 1980 .

[8]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[9]  Edilma Olinda Gagliardi,et al.  Approximations on minimum weight pseudo-triangulations using ant colony optimization metaheuristic , 2009 .

[10]  Yin-Feng Xu,et al.  On Constrained Minimum Pseudotriangulations , 2003, COCOON.

[11]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[12]  J. Mark Keil,et al.  Computing a Subgraph of the Minimum Weight Triangulation , 1994, Comput. Geom..

[13]  Minglun Gong,et al.  A genetic algorithm for the minimum weight triangulation , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[14]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[15]  D. Kirkpatrick,et al.  A Framework for Computational Morphology , 1985 .

[16]  Errol L. Lloyd.  On triangulations of a set of points in the plane , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[17]  S. Dreyfus,et al.  Thermodynamical Approach to the Traveling Salesman Problem : An Efficient Simulation Algorithm , 2004 .

[18]  Bryant A. Julstrom,et al.  A weight-coded genetic algorithm for the minimum weight triangulation problem , 1998, SAC '98.

[19]  Yin-Feng Xu,et al.  Approaching the largest β-skeleton within a minimum weight triangulation , 1996, SCG '96.

[20]  Peter Gilbert.  New Results on Planar Triangulations. , 1979 .