Parallel Search Algorithm for Geometric Constraints Solving

  • Hua Yuan
  • Wenhui Li
  • Kong Zhao
  • Rongqin Yi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4563)


We propose a hybrid algorithm – (Parallel Search Algorithm) between PSO and simplex methods to approximate optimal solution for the Geometric Constraint problems. Locally, simplex is extended to reduce the number of infeasible solutions while solution quality is improved with an operation order search. Globally, PSO is employed to gain parallelization while solution diversity is maintained. Performance results on Geometric Constraint problems show that Parallel Search Algorithm outperforms existing techniques.


geometric constraint solving particle swarm optimization simplex method Parallel Search 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Buchanan, S.A., de Pennington, A.: Constraint definition system: a computer algebra based approach to solving geometric problems. Computer Aided Design 25(12), 740–750 (1993)CrossRefGoogle Scholar
  2. 2.
    Lee, J.Y., Kim, K.: Geometric reasoning for knowledge-based parametric design using graph representation. Computer Aided Design 28(10), 831–841 (1996)CrossRefGoogle Scholar
  3. 3.
    Fudos, I., Hoffmann, C.M.: A graph-constructive approach to solving systems of geometric constraints. ACM Transactions on Graphics 16(2), 179–216 (1997)CrossRefGoogle Scholar
  4. 4.
    Lamure, H., Michelucci, D.: Solving geometric constraints by homotopy. IEEE Transactions on Visualization and Computer Graphics 2(1), 28–34 (1996)CrossRefGoogle Scholar
  5. 5.
    Johnson, L.W., Riess, R.D.: Numerical analysis, 2nd edn. Addison-Wesley, Reading (1982)zbMATHGoogle Scholar
  6. 6.
    Liu, S., Tang, M., Dong, J.: Two Spatial Constraint Solving Algorithms. Journal of Computer-Aided Design & Computer Graphics 15(8), 1011–1029 (2003)Google Scholar
  7. 7.
    Kennedy J., Eberhart, R.C.: Particle Swarm Optimization. In: Proc. of the IEEE International Conference on Neural Networks IV, pp. 1942–1948 (1995) Google Scholar
  8. 8.
    Eberhart, R.C., Shi, Y.: Particle swarm optimization: Developments, applications and resources. In: Proc. Congress on Evolutionary Computation, pp. 81–86 (2001)Google Scholar
  9. 9.
    Xie, X., Zhang, W., Yang, Z.: A dissipative particle swarm optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, vol. 2, pp. 1456–1461 (2002)Google Scholar
  10. 10.
    Nelder, J., Mead, R.: A Simplex Method for Function Minimization. Computer J. 7, 308–313 (1965)Google Scholar
  11. 11.
    Liu, S.G., Tang, M., Dong, J.: Two Spatial Constraint Solving Algorithms. Journal of Computer-Aided Design & Computer Graphics 15(8), 1011–1029 (2003)Google Scholar
  12. 12.
    Angeline, P.: Evolutionary Optimization versus Particle Swarm Optimization: Philosophy and Performance Difference, In: The 7th Annual Conference on Evolutionary Programming, San Diego, USA (1998)Google Scholar
  13. 13.
    Parsopoulos, K., Vrahatis, M.: Particle Swarm Optimizer in Noisy and Continuously Changing Environments. In: Hamza, M.H. (ed.) Artificial Intelligence and Soft Computing, pp. 289–294. IASTED/ACTA Press (2001)Google Scholar
  14. 14.
    Branke, J.: Memory Enhanced Evolutionary Algorithms for Changing Optimization Problems. In: Proc. of CEC 1999, pp. 1875–1882. IEEE Press, Los Alamitos (1999)Google Scholar
  15. 15.
    Gartner, B.: The Random-Facet Simplex Algorithm on Combinatorial Cubes. Random Structures & Algorithms 20(3), 353–381 (2002)CrossRefGoogle Scholar
  16. 16.
    Walters, F., Parker, L.R., Morgan, S.L., Deming, S.N.: Sequential Simplex Optimization. CRC Press, Boca Raton, USA (1991)Google Scholar
  17. 17.
    Light, R., Gossard, D.: Modification of geometric models through variational geometry. Geometric Aided Design 14, 208–214 (1982)Google Scholar
  18. 18.
    Elster, K.H. (ed.): Modern mathematical methods of optimization. Berlin, Akademie (1993)zbMATHGoogle Scholar
  19. 19.
    More, J.J., Wright, S.: Optimization software guide, SIAM (1993)Google Scholar
  20. 20.
    Nemhauser, G.L., Rinnooy Kan, A.H.G., Todd, M. (eds.): Optimization. Elsevier, Amsterdam (1989)zbMATHGoogle Scholar
  21. 21.
    Xia, W., Wu, Z.: An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Computers & Industrial Engineering 48(2), 409–425 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hua Yuan
    • 1
    • 2
  • Wenhui Li
    • 1
  • Kong Zhao
    • 3
  • Rongqin Yi
    • 1
  1. 1.Key Laboratory of Symbol Computation and Knowledge Engineering of the Ministry of Education, College of computer science and technology, Jilin University, Changchun 130012China
  2. 2.School of Computer Science & Engineering, Changchun University of Technology, Changchun 130012China
  3. 3.Suzhou Top Institute of Information Technology, Suzhuo 215311China

Personalised recommendations