A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions

References

• Björkman M., Holmström K. Global optimization of costly nonconvex functions using radial basis functions. Optim. Engrg. (2000) 1:373–397Crossref, Google Scholar
• Booker A. J., Dennis J. E., Frank P. D., Serafini D. B., Torczon V., Trosset M. W. A rigorous framework for optimization of expensive functions by surrogates. Structural Optim. (1999) 17:1–13Crossref, Google Scholar
• Box G. E. P., Draper N. R.Empirical Model-Building and Response Surfaces (1987) (John Wiley and Sons, New York) Google Scholar
• Buhmann M. D.Radial Basis Functions (2003) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Conn A. R., Scheinberg K., Toint Ph. L. Recent progress in unconstrained nonlinear optimization without derivatives. Math. Programming (1997) 79:397–414Crossref, Google Scholar
• Cressie N.Statistics for Spatial Data (1993) (John Wiley and Sons, New York) Crossref, Google Scholar
• Dennis J. E., Torczon V. Direct search methods on parallel machines. SIAM J. Optim. (1991) 1:448–474Crossref, Google Scholar
• Dixon L. C. W., Szegö G., Dixon L. C. W., Szegö G. The global optimization problem: An introduction. Towards Global Optimization 2 (1978) (North-Holland, Amsterdam, The Netherlands) 1–15Google Scholar
• Friedman J. Multivariate adaptive regression splines (with discussion). Ann. Statist. (1991) 19:1–141Crossref, Google Scholar
• Gilmore P., Kelley C. T. An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Optim. (1995) 5:269–285Crossref, Google Scholar
• Glover F., Hao J.-K., Lutton E., Ronald E., Schoenauer M., Snyers D. A template for scatter search and path relinking. Artificial Evolution, Lecture Notes in Computer Science (1998) 1363(Springer Verlag, Berlin, Germany) 13–54Crossref, Google Scholar
• Griewank A. O. Generalized descent for global optimization. J. Optim. Theory Appl. (1981) 34:11–39Crossref, Google Scholar
• Gutmann H.-M. A radial basis function method for global optimization. J. Global Optim. (2001) 19:201–227Crossref, Google Scholar
• Horst R., Pardalos P. M., Thoai N. V.Introduction to Global Optimization (1995) (Kluwer, Dordrecht, The Netherlands) Google Scholar
• Ishikawa T., Tsukui Y., Matsunami M. A combined method for the global optimization using radial basis function and deterministic approach. IEEE Trans. Magnetics (1999) 35:1730–1733Crossref, Google Scholar
• Jones D. R. A taxonomy of global optimization methods based on response surfaces. J. Global Optim. (2001) 21:345–383Crossref, Google Scholar
• Jones D. R., Schonlau M., Welch W. J. Efficient global optimization of expensive black-box functions. J. Global Optim. (1998) 13:455–492Crossref, Google Scholar
• Kelley C. T.Iterative Methods for Optimization (1999) (SIAM, Philadelphia, PA) Crossref, Google Scholar
• Koehler J. R., Owen A. B., Ghosh S., Rao C. R. Computer experiments. Handbook of Statistics, 13: Design and Analysis of Computer Experiments (1996) (North-Holland, Amsterdam, The Netherlands) 261–308Crossref, Google Scholar
• Laguna M., Marti R., Voss S., Woodruff D. The OptQuest callable library. Optimization Software Class Libraries (2002) (Kluwer Academic Publishers, Boston, MA) 193–218Google Scholar
• Laguna M., Marti R.Scatter Search: Methodology and Implementations in C (2003) (Kluwer Academic Publishers, Boston, MA) Crossref, Google Scholar
• Moore A., Schneider J. Memory-based stochastic optimization. Neural Inform. Processing Systems (1996) 8:1066–1072Google Scholar
• Moore A., Schneider J., Boyan J., Lee M. S., Shavlik J. Q2: Memory-based active learning for optimizing noisy continuous functions. Proc. Fifteenth Internat. Conf. Machine Learn. (1998) (Morgan Kaufmann, San Francisco, CA) 386–394Google Scholar
• Morris M. D., Mitchell T. J. Exploratory designs for computational experiments. J. Statist. Planning Inference (1995) 43:381–402Crossref, Google Scholar
• Myers R. H., Montgomery D. C.Response Surface Methodology: Process and Product Optimization Using Designed Experiments (1995) (John Wiley and Sons, New York) Google Scholar
• Nelder J. A., Mead R. A simplex method for function minimization. Comput. J. (1965) 7:308–313Crossref, Google Scholar
• Nocedal J., Wright S. J.Numerical Optimization (1999) (Springer, New York) Crossref, Google Scholar
• Powell M. J. D., Light W.Advances in Numerical Analysis, Volume 2: Wavelets, Subdivision Algorithms and Radial Basis Functions (1992) (Oxford University Press, Oxford, UK) 105–210Crossref, Google Scholar
• Powell M. J. D., Müller M., Buhmann M., Mache D., Felten M. Recent research at Cambridge on radial basis functions. New Developments in Approximation Theory, International Series of Numerical Mathematics (1999) 132(Birkhäuser Verlag, Basel, Switzerland) 215–232Crossref, Google Scholar
• Powell M. J. D. UOBYQA: Unconstrained optimization by quadratic approximation. Math. Programming (2002) 92:555–582Crossref, Google Scholar
• Powell M. J. D. On trust region methods for unconstrained minimization without derivatives. Math. Programming (2003) 97:605–623Crossref, Google Scholar
• Rinnooy Kan A. H. G., Timmer G. T. Stochastic global optimization methods, Part II: Multi level methods. Math. Programming (1987) 39:57–78Crossref, Google Scholar
• Sacks J., Welch W. J., Mitchell T. J., Wynn H. P. Design and analysis of computer experiments. Statist. Sci. (1989) 4:409–435Crossref, Google Scholar
• Schoen F. A wide class of test functions for global optimization. J. Global Optim. (1993) 3:133–137Crossref, Google Scholar
• Simpson T. W., Mauery T. M., Korte J. J., Mistree F. Comparison of response surface and kriging models for multidisciplinary design optimization. Proc. 7th AIAA/USAF/NASA/ISSMO Sympos. Multidisciplinary Anal. Optim. (1998) 1St. Louis, MO:381–391Crossref, Google Scholar
• Spall J. C.Introduction to Stochastic Search and Optimization (2003) (John Wiley and Sons, Hoboken, NJ) Crossref, Google Scholar
• The MathWorksGenetic Algorithm and Direct Search Toolbox for Use with MATLAB: User's Guide, Version 1 (2004a) (The MathWorks, Natick, MA) Google Scholar
• The MathWorksOptimization Toolbox for Use with MATLAB: User's Guide, Version 3 (2004b) (The MathWorks, Natick, MA) Google Scholar
• Torczon V. On the convergence of pattern search algorithms. SIAM J. Optim. (1997) 7:1–25Crossref, Google Scholar
• Torn A., Zilinskas A.Global Optimization, Lecture Notes in Computer Science (1989) 350(Springer-Verlag, Berlin, Germany) Google Scholar
• Ugray Z., Lasdon L., Plummer J., Glover F., Kelley J., Marti R. Scatter search and local NLP solvers: A multistart framework for global optimization. INFORMS J. Comput. (2006) . ForthcomingGoogle Scholar
• Vanden Berghen F., Bersini H. CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. J. Comput. Appl. Math. (2005) 181:157–175Crossref, Google Scholar
• Vavasis S. A.Nonlinear Optimization: Complexity Issues (1991) (Oxford University Press, New York) Google Scholar
• Wolpert D. H., Macready W. G. No free lunch theorems for optimization. IEEE Trans. Evolutionary Comput. (1997) 1:67–82Crossref, Google Scholar
• Ye K. Q., Li W., Sudjianto A. Algorithmic construction of optimal symmetric latin hypercube designs. J. Statist. Planning Inference (2000) 90:145–159Crossref, Google Scholar
• Yoon J.-H., Shoemaker C. A. Comparison of optimization methods for ground-water bioremediation. J. Water Resources Planning Management (1999) 125:54–63Crossref, Google Scholar