Genetic algorithms for root multiselection in constructive geometric constraint solving

Computers and Graphics (Pergamon)

Volumn 27, Issue 1, 2003, Pages 51-60

  Joan Arinyo, R ^a   Luzon M V ^b   Soto, A ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF VIGO   (Spain)

Author keywords

Constructive geometric constraint solving; Genetic algorithms; Root identification problem; Solution selection

Indexed keywords

COMPUTER SIMULATION; GENETIC ALGORITHMS; GRAPH THEORY; NONLINEAR EQUATIONS; SEARCH ENGINES;

ROOT IDENTIFICATION PROBLEM; SEQUENTIAL NICHE METHOD;

COMPUTER GRAPHICS;

EID: 20244369538     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0097-8493(02)00243-1     Document Type: Conference Paper

References (28)

1. Bouma W., Fudos I., Hoffmann C., Cai J., Paige R. Geometric constraint solver. Computer Aided Design. 27(6):1995;487-501.
2. Essert-Villard C., Schreck P., Dufourd J.-.F. Sketch-based pruning of a solution space within a formal geometric constraint solver. Artificial Intelligence. 124:2000;139-159.
3. Luzón M-V. Resolución de Restricciones Geométricas. Selección de la Solución Deseada. Ph.D. thesis, Dept. Informática, Universidad de Vigo, December 2001 (in Spanish).
4. Mata N. Solving incidence and tangency constraints in 2D. Technical Report LSI-97-3R, Department LiSI, Universitat Politècnica de Catalunya, 1997.
5. Durand C. Symbolic and numerical techniques for constraint solving. Ph.D. thesis, Computer Science, Purdue University, December 1998.
6. Joan-Arinyo R., Soto-Riera A. Combining constructive and equational geometric constraint solving techniques. ACM Transactions on Graphics. 18(1):1999;35-55.
7. Fudos I., Hoffmann G.M. A graph-constructive approach to solving systems of geometric constraints. ACM Transactions on Graphics. 16(2):1997;179-216.
8. Joan-Arinyo R., Soto A. A correct rule-based geometric constraint solver. Computer and Graphics. 21(5):1997;599-609.
9. Laman G. On graphs and rigidity of plane skeletal structures. Journal of Engineering Mathematics. 4(4):1970;331-340.
10. Joan-Arinyo R, Mata N. A data structure for solving geometric constraint problems with interval parameters. Technical Report LSI-00-24-R, Department LiSI, Universitat Politècnica de Catalunya, 2000.
11. Mata N. Constructible geometric problems with interval parameters. Ph.D. thesis, Dept. LiSI, Universitat Politècnica de Catalunya, 2000.
12. Bremermann H.-.J., Roghson J., Salaff S. Global properties of evolution processes. Pattee H.H., Edelsack E.A., Fein L., Callahan A.B. Natural automata and useful simulations. 1966;3-42 Macmillan, New York.
13. Mühlenbein H. Genetic algorithms. In: Aarts E, Lenstra JK, editors. Local search in combinatorial optimization, discrete mathematics and optimization. Chichester: Wiley Interscience, 1997. p. 137-71 [Chapter 6].
14. Bäck T., Schwefel H.P. An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation. 1:1993;1-24.
15. Mühlenbein H., Georges-Schleuter M., Krämer O. Evolution algorithm in combinatorial optimization. Parallel Computing. 7:1988;65-85.
16. Holland J.H. Adaptation in natural and artificial systems. 1975;The University of Michigan Press, Ann Arbor.
17. Forrest S, editor. Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, CA, 1993. Los Altos, CA: Morgan Kaufmann.
18. Goldberg D.E. Genetic algorithms in search, optimization machine learning. 1989;Addison-Wesley, Reading, MA.
19. Grefenstette J. Rank-based selection. In: Bäck T, Fogel DB, Michalewicz Z, editors. Handbook of evolutionary computation. Oxford: Institute of Physics Publishing Ltd and Oxford University Press, 1997. p. C2.4:1-6 [Chapter C2.4].
20. Baker JE. Reducing bias and inefficiency in the selection algorithm. Proceedings of the Second International Conference on Genetic Algorithms (ICGA'87), Hillsdale, NJ, USA, 1987. p. 14-21.
21. Michalewicz Z. Genetic. algorithms+data structures=evolution programs: 1996;Springer, Berlin.
22. Booker LB, Fogel DB, Whitley D, Angeline PJ. Recombination. In: Bäck T, Fogel DB, Michalewicz Z, editors. Handbook of evolutionary computation. Oxford: Institute of Physics Publishing Ltd and Oxford University Press, 1997. p. C3.3:1-10 [Chapter C3.3].
23. Bäck T, Fogel DB, Michalewicz Z, editors. Handbook of evolutionary computation. Oxford: Institute of Physics Publishing and Oxford University Press, 1997.
24. Beasly D., Bull D.R., Martin R.R. A sequential niche technique for multimodal function optimization. Evolutionary Computation. 1(2):1993;101-125.
25. Mahfoud SW. Niching methods for genetic algorithms. Ph.D. thesis, University of Illinois at Urbana-Champain, Illinois Genetic Algorithms Laboratory, 1995.
26. Hamming R.W. Error detecting and error correcting codes. Bell Systems Technical Journal. 29:1950;147-160.
27. Pétrowski A. A cleaning procedure as a niching method for generic algorithms. In: First IEEE International Conference on Evolutionary Computation, Nagoya, Japan. IEEE Service Center, 1996. p. 798-803.
28. Grefenstette J.J. Optimization of control parameters for genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics. SMC-16(1):1986;122-128.