A Global Optimization Algorithm Based on the Extended Domain Elimination Method

영역 제거법의 확장을 통한 전체 최적화 알고리듬 개선

  • Published : 2000.01.01


An improved global optimization algorithm is developed by extending the domain elimination method. The concept of triangular patch consists of two or more trajectories of local minimizations is introduced to widen the attraction region of the domain elimination method. Using the an-]c between each of three vertices of the patch and a design point, we measure the proximity, between the design point and the patch. With the Gram-Schimidt orthonormalization, this method can be extended to general n-dimensional problems. We code the original domain elimination algorithm and a patch-based algorithm. Then we compare the performance of two algorithms. Through the well-known example problems. the algorithm using patch is shown to be superior to the original domain elimination algorithm in view of computational efficiency.


  1. Elwakeil, O. A. and Arora, J. S., 1996, 'Tow Algorithms for Global Optimization of General NLP Problems,' International Journal for Numerical Methods in Engineering, Vol. 39, pp. 3305-3325<3305::AID-NME1>3.0.CO;2-S
  2. Arora, J. S. , Elwakeil , O. A. and Chahande, A. I., 1995, 'Global Optimization Methods for Engineering Applications: a Review,' Structural Optimization, Vol. 9, pp.137-159
  3. Vanderplaats, 1993, DOT User's Manual, Ver.4, VMA Engineering
  4. Lucidi, S. , 1988, 'New Resultes on a Class of Exact Augmented Lagrangian,' Journal of Optimization Theory and Applications, Vol. 58, pp. 259-277
  5. Goldberg, D. E. and Kou, C. H., 1987, 'Genetic Algorihms in Pipeline Optimization,' Journal of Computing in Civil Engineering, Vol. 1, pp. 128-141
  6. Glover. F., 1977, 'Heuristics for Integer Programming using Surrogate Constraints,' Decision Sience, Vol. 8, pp. 156-166
  7. Myung, H. and Kim J. H.,1996, 'Hybrid Evolutionary Programming for Heavily Constrained Problems,' Biosystems, Vol. 38, pp. 29-43
  8. Lee, J. B., and Lee, B. C., 1996, 'A Global Optimization Algorithm based on the New Filled Function Method and the Genetic Algorithm,' Engineering Optimization, Vol. 27, pp.1-20
  9. Rinnooy, A. H. G. and Timmer, G. T., 1987a, 'Stochastic Global Optimization Methods, Part I: Clustering Methods,' Mathmatical Progress, Vol. 39, pp.27-56
  10. Price, W. L., 1987, 'Global Optimzation Algorithms for a CAD workstation,' Journal of Optimization Theory and Application, Vol. 55, pp.133-146
  11. May, S. A. and Balling, R. J., 1992, 'A Filtered Simulated Annealing Strategy for Discrete Optimization of 3D Frameworks,' Structural Optimization, Vol. 4, pp. 142-148
  12. Evtushenko, Y. G.,1974, 'Methods of Search for the Global Extremum,' Operation Research, Vol. 4, pp. 39-68
  13. Arora, J. S., 1992, 'Global Optimization Methods for Engineering Applications,' Technical Report. Optimal Design Laboratory. Iowa Univ.
  14. Snyman, J. A. and Patti, L. P., 1987, 'A Multistart Global Minimization Algorithm with Dynamic Search Trajectories,' Journal of Optimization Theory and Algorithms, Vol. 54, pp. 121-141
  15. Levy, A.S. and Montalvo, A., 1985, 'The Tunneling Algorithm for Golbal Minimization of Functions,' SIAM Journal of Sciences and Statistical Computation. Vol. 6, pp.15-29