Waltraud Huyer
Skip Abstract Section
Abstract
The software package SNOBFIT for bound-constrained (and soft-constrained) noisy optimization of an expensive objective function is described. It combines global and local search by branching and local fits. The program is made robust and flexible for practical use by allowing for hidden constraints, batch function evaluations, change of search regions, etc.
- Anderson, E. J. and Ferris, M. C. 2001. A direct search algorithm for optimization of expensive functions by surrogates. SIAM J. Optim. 11, 837--857. Google Scholar
Digital Library
- Booker, A. J., Dennis, Jr., J. E., Frank, P. D., Serafini, D. B., Torczon, V., and Trosset, M. W. 1999. A rigorous framework for optimization of expensive functions by surrogates. Structural Optim. 17, 1--13.Google ScholarCross Ref
- Carter, R. G., Gablonsky, J. M., Patrick, A., Kelley, C. T., and Eslinger, O. J. 2001. Algorithms for noisy problems in gas transmission pipeline optimization. Optim. Eng. 2, 139--157.Google ScholarCross Ref
- Choi, T. D. and Kelley, C. T. 2000. Superlinear convergence and implicit filtering. SIAM J. Optim. 10, 1149--1162. Google ScholarDigital Library
- Conn, A. R., Scheinberg, K., and Toint, P. L. 1997. Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. 79B, 397--414. Google ScholarDigital Library
- Dallwig, S., Neumaier, A., and Schichl, H. 1997. GLOPT -- A program for constrained global optimization. In Developments in Global Optimization, I. M. Bomze et al., eds. Nonconvex Optimization and its Applications, vol. 18. Kluwer, Dordrecht, 19--36.Google Scholar
- Deuflhard, P. and Heindl, G. 1979. Affine invariant convergence theorems for Newton's method and extensions to related methods. SIAM J. Numer. Anal. 16, 1--10.Google ScholarDigital Library
- Elster, C. and Neumaier, A. 1995. A grid algorithm for bound constrained optimization of noisy functions. IMA J. Numer. Anal. 15, 585--608.Google ScholarCross Ref
- Fiacco, A. and McCormick, G. P. 1990. Sequential Unconstrained Minimization Techniques. Classics in Applied Mathematics, vol. 4. SIAM, Philadelphia, PA.Google Scholar
- Guratzsch, R. F. 2007. Sensor placement optimization under uncertainty for structural health monitoring systems of hot aerospace structures. Ph.D. thesis, Department of Civil Engineering, Vanderbilt University, Nashville, TN.Google Scholar
- Hirsch, M. J., Meneses, C. N., Pardalos, P. M., and Resende, M. G. C. 2007. Global optimization by continuous grasp. Optim. Lett. 1, 201--212.Google ScholarCross Ref
- Hock, W. and Schittkowski, K. 1981. Test Examples for Nonlinear Programming. Lecture Notes in Economics and Mathematical Systems, vol. 187. Springer. Google ScholarDigital Library
- Huyer, W. and Neumaier, A. 1999. Global optimization by multilevel coordinate search. J. Global Optim. 14, 331--355. Google ScholarDigital Library
- Jones, D. R. 2001. A taxonomy of global optimization methods based on response surfaces. J. Global Optim. 21, 345--383. Google ScholarDigital Library
- Jones, D. R., Perttunen, C. D., and Stuckman, B. E. 1993. Lipschitzian optimization without the Lipschitz constant. J. Optim. Theory Appl. 79, 157--181. Google ScholarDigital Library
- Jones, D. R., Schonlau, M., and Welch, W. J. 1998. Efficient global optimization of expensive black-box functions. J. Global Optim. 13, 455--492. Google ScholarDigital Library
- McKay, M. D., Beckman, R. J., and Conover, W. J. 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239--245. Google ScholarDigital Library
- Nocedal, J. and Wright, S. J. 1999. Numerical Optimization. Springer Series in Operations Research. Springer.Google Scholar
- Owen, A. B. 1992. Orthogonal arrays for computer experiments, integration and visualization. Statistica Sinica 2, 439--452.Google Scholar
- Owen, A. B. 1994. Lattice sampling revisited: Monte Carlo variance of means over randomized orthogonal arrays. Ann. Stat. 22, 930--945.Google ScholarCross Ref
- Powell, M. J. D. 1998. Direct search algorithms for optimization calculations. Acta Numerica 7, 287--336.Google ScholarCross Ref
- Powell, M. J. D. 2002. UOBYQA: Unconstrained optimization by quadratic approximation. Math. Program. 92B, 555--582.Google ScholarCross Ref
- Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. 1989. Design and analysis of computer experiments. With comments and a rejoinder by the authors. Statist. Sci. 4, 409--435.Google ScholarCross Ref
- Scheinberg, K. 2003. Manual for Fortran software package DFO v2.0. https://projects.coin-or.org/Dfo/browser/trunk/manual2_0.ps.Google Scholar
- Schonlau, M. 1997. Computer experiments and global optimization. Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada. Google ScholarDigital Library
- Schonlau, M. 1997--2001. SPACE Stochastic Process Analysis of Computer Experiments. http://www.schonlau.net.Google Scholar
- Schonlau, M., Welch, W. J., and Jones, D. R. 1998. Global versus local search in constrained optimization of computer models. In New Developments and Applications in Experimental Design, N. Flournoy et al., eds. Institute of Mathematical Statistics Lecture Notes -- Monograph Series 34. Institute of Mathematical Statistics, Hayward, CA, 11--25.Google Scholar
- Tang, B. 1993. Orthogonal array-based Latin hypercubes. J. Amer. Statist. Assoc. 88, 1392--1397.Google ScholarCross Ref
- Trosset, M. W. and Torczon, V. 1997. Numerical optimization using computer experiments. Tech. Rep. 97-38, ICASE. Google ScholarDigital Library
- Vanden Berghen, F. and Bersini, H. 2005. CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. J. Comput. Appl. Math. 181, 157--175. Google ScholarDigital Library
- Welch, W. J., Buck, R. J., Sacks, J., Wynn, H. P., Mitchell, T., and Morris, M. D. 1992. Screening, predicting, and computer experiments. Technometrics 34, 15--25. Google ScholarDigital Library
Index Terms
- SNOBFIT -- Stable Noisy Optimization by Branch and Fit
Recommendations
An adaptive radial basis algorithm (ARBF) for expensive black-box global optimization
Powerful response surface methods based on kriging and radial basis function (RBF) interpolation have been developed for expensive, i.e. computationally costly, global nonconvex optimization. We have implemented some of these methods in the solvers ...
Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions
This paper presents a new algorithm for derivative-free optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. The proposed algorithm, called ConstrLMSRBF, uses radial basis function (RBF) ...
Approximating robust Pareto fronts by the MEOF-based multiobjective evolutionary algorithm with two-level surrogate models
AbstractThe multiobjective optimization problems (MOPs) under uncertain environments are very challenging to be solved due to the sensitivities of some robust decision variables. To find the robust Pareto fronts (PFs) of these MOPs, the mean effective ...
Comments