Abstract
The DIRECT (DIviding RECTangles) algorithm of Jones, Perttunen, and Stuckman (Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 157–181, 1993), a variant of Lipschitzian methods for bound constrained global optimization, has proved effective even in higher dimensions. However, the performance of a DIRECT implementation in real applications depends on the characteristics of the objective function, the problem dimension, and the desired solution accuracy. Implementations with static data structures often fail in practice, since it is difficult to predict memory resource requirements in advance. This is especially critical in multidisciplinary engineering design applications, where the DIRECT optimization is just one small component of a much larger computation, and any component failure aborts the entire design process. To make the DIRECT global optimization algorithm efficient and robust on large-scale, multidisciplinary engineering problems, a set of dynamic data structures is proposed here to balance the memory requirements with execution time, while simultaneously adapting to arbitrary problem size. The focus of this paper is on design issues of the dynamic data structures, and related memory management strategies. Numerical computing techniques and modifications of Jones' original DIRECT algorithm in terms of stopping rules and box selection rules are also explored. Performance studies are done for synthetic test problems with multiple local optima. Results for application to a site-specific system simulator for wireless communications systems (S 4 W) are also presented to demonstrate the effectiveness of the proposed dynamic data structures for an implementation of DIRECT.
Similar content being viewed by others
References
C.A. Baker, L.T. Watson, B. Grossman, R.T. Haftka, and W.H. Mason, “Parallel global aircraft configuration design space exploration,” in Proc. High Performance Computing Symposium 2000. A. Tentner (Ed.), Soc. for Computer Simulation Internat: San Diego, CA, 2000, pp. 101–106.
C.A. Baker, “Parallel global aircraft configuration design space exploration,” Technical Report MAD 2000-06-28, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2000.
S.E. Cox, R.T. Haftka, C. Baker, B. Grossman, W.H. Mason, and L.T. Watson, “Global multidisciplinary optimization of a high speed civil transport,” in Proc. Aerospace Numerical Simulation Symposium'99, Tokyo, Japan, June 1999, pp. 23–28.
S. Cox, R.T. Haftka, C. Baker, B. Grossman, W. Mason, and L.T. Watson, “A comparison of optimization methods for the design of a high speed civil transport,” Journal of Global Optimization, vol. 21, pp. 415–433, 2001.
S.J. Fortune, D.M. Gay, B.W. Kernighan, O. Landron, R.A. Valenzuela, and M.H. Wright (AT&T Bell Laboratories), “WISE design of indoor wireless systems: Practical computation and optimization,” IEEE Computational Science & Engineering, vol. 2, no. 1, pp. 58–68, 1995.
J.M. Gablonsky, “An implementation of the DIRECT algorithm,” Technical Report CRSC-TR98-29, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 1998.
J.M. Gablonsky and C.T. Kelley, “A locally-biased form of the DIRECT algorithm,” Technical Report CRSCTR00-31, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, 2001.
D.R. Jones, “The DIRECT global optimization algorithm,” in Encyclopedia of Optimization, vol. 1, Kluwer Academic: Boston, 2001, pp. 431–440.
D.R. Jones, C.D. Perttunen, and B.E. Stuckman, “Lipschitzian optimization without the Lipschitz constant,” Journal of Optimization Theory and Applications, vol. 79, no. 1, pp. 157–181, 1993.
R.M. Lewis, V. Torczon, and M.W. Trosset, “Direct search methods: Then and now,” Journal of Computational and Applied Mathematics, vol. 124, pp. 191–207, 2000.
J.D. Pinter, Global Optimization In Action, Kluwer Academic: Boston, 1996.
V. Torczon, “On the convergence of the multidirectional search algorithm,” SIAM Journal on Optimization, vol. 1, no. 1, pp. 123–145, 1991.
A. Verstak, M. Vass, N. Ramakrishnan, C. Shaffer, L.T. Watson, K.K. Bae, J. Jiang, W.H. Tranter, and T.S. Rappaport, “Lightweight data management for compositional modeling in problem solving environments,” in Proc. High Performance Computing Symposium 2001. A. Tentner (Ed.), soc. for Modeling and Simulation Internat.: San Diego, CA, 2001, pp. 148–153.
L.T. Watson and C.A. Baker, “Afully-distributed parallel global search algorithm,” Engineering Computations, vol. 18, no. 1/2, pp. 155–169, 2001.
L.T. Watson, M. Sosonkina, R.C. Melville, A.P. Morgan, and H.F. Walker, “Algorithm 777: HOMPACK90: A suite of FORTRAN 90 codes for globally convergent homotopy algorithms,” ACM Transactions on Mathematical Software, vol. 23, pp. 514–549, 1997.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
He, J., Watson, L.T., Ramakrishnan, N. et al. Dynamic Data Structures for a Direct Search Algorithm. Computational Optimization and Applications 23, 5–25 (2002). https://doi.org/10.1023/A:1019992822938
Issue Date:
DOI: https://doi.org/10.1023/A:1019992822938