Parallel Stochastic Global Optimization Using Radial Basis Functions

Published Online:https://doi.org/10.1287/ijoc.1090.0325

References

  • Barr R. S., Hickman B. L. Reporting computational experiments with parallel algorithms: Issues, measures, and experts' opinions. ORSA J. Comput. (1993) 5(1):2–18LinkGoogle Scholar
  • Benson S. J., Moré J. A limited-memory variable-metric algorithm for bound-constrained minimization. (2001) . Technical Report ANL/MCS-P909-0901, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, ILGoogle 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):1–13CrossrefGoogle Scholar
  • Box G. E. P., Draper N. R.Empirical Model-Building and Response Surfaces (1987) (John Wiley & Sons, New York) Google Scholar
  • Buhmann M. D.Radial Basis Functions (2003) (Cambridge University Press, Cambridge, UK) CrossrefGoogle Scholar
  • Conn A. R., Scheinberg K., Toint P. L. Recent progress in unconstrained nonlinear optimization without derivatives. Math. Programming (1997) 79(3):397–414CrossrefGoogle Scholar
  • Cressie N.Statistics for Spatial Data (1993) (John Wiley & Sons, New York) CrossrefGoogle Scholar
  • Dixon L. C. W., Szegö G., Dixon L. C. W., Szegö G. The global optimization problem: An introduction. Towards Global Optimization (1978) 2(North-Holland, Amsterdam) 1–15Google Scholar
  • Giunta A. A., Balabanov V., Haim D., Grossman B., Mason W. H., Watson L. T., Haftka R. T. Aircraft multidisciplinary design optimisation using design of experiments theory and response surface modelling. Aeronautical J. (1997) 101(1008):347–356CrossrefGoogle 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) 13–54CrossrefGoogle Scholar
  • Gutmann H.-M. A radial basis function method for global optimization. J. Global Optim. (2001) 19(3):201–227CrossrefGoogle Scholar
  • Hough P., Kolda T. G., Torczon V. J. Asynchronous parallel pattern search for nonlinear optimization. SIAM J. Sci. Comput. (2001) 23(1):134–156CrossrefGoogle Scholar
  • Jones D. R., Schonlau M., Welch W. J. Efficient global optimization of expensive black-box functions. J. Global Optim. (1998) 13(4):455–492CrossrefGoogle 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) 261–308CrossrefGoogle Scholar
  • Kolda T. G., Torczon V. On the convergence of asynchronous parallel pattern search. SIAM J. Optim. (2004) 14(4):939–964CrossrefGoogle Scholar
  • Kolda T. G., Lewis R. M., Torczon V. Optimization by direct search: New perspectives on some classical and modern methods. SIAM Rev. (2003) 45(3):385–482CrossrefGoogle Scholar
  • Laguna M., Marti R.Scatter Search: Methodology and Implementations in C (2003) (Kluwer Academic Publishers, Boston) CrossrefGoogle Scholar
  • MathWorksMatlab Compiler: User's Guide, Version 4 (2008) (The MathWorks, Inc., Natick, MA) Google Scholar
  • Moré J. J., Garbow B. S., Hillstrom K. E. Testing unconstrained optimization software. ACM Trans. Math. Software (1981) 7(1):17–41CrossrefGoogle Scholar
  • Mugunthan P., Shoemaker C. A., Regis R. G. Comparison of function approximation, heuristic and derivative-based methods for automatic calibration of computationally expensive groundwater bioremediation models. Water Resources Res. (2005) 41:W11427doi:10.1029/2005WR004134CrossrefGoogle Scholar
  • Myers R. H., Montgomery D. C.Response Surface Methodology: Process and Product Optimization Using Designed Experiments (1995) (John Wiley & Sons, New York) Google Scholar
  • Numerical Algorithms GroupNAG C Library Manual, Mark 8 (2005) (The Numerical Algorithms Group Ltd., Oxford, UK) Google Scholar
  • Powell M. J. D., Light W. The theory of radial basis function approximation in 1990. Advances in Numerical Analysis, Volume 2: Wavelets, Subdivision Algorithms and Radial Basis Functions (1992) (Oxford University Press, Oxford, UK) 105–210CrossrefGoogle Scholar
  • Powell M. J. D. UOBYQA: Unconstrained optimization by quadratic approximation. Math. Programming (2002) 92(3):555–582CrossrefGoogle Scholar
  • Powell M. J. D. On trust region methods for unconstrained minimization without derivatives. Math. Programming (2003) 97(3):605–623CrossrefGoogle Scholar
  • Raphael B., Smith I. F. C. A direct stochastic algorithm for global search. Appl. Math. Comput. (2003) 146(2–3):729–758CrossrefGoogle Scholar
  • Regis R. G., Shoemaker C. A. Constrained global optimization of expensive black box fuctions using radial basis functions. J. Global Optim. (2005) 31(1):153–171CrossrefGoogle Scholar
  • Regis R. G., Shoemaker C. A. A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput. (2007a) 19(4):497–509LinkGoogle Scholar
  • Regis R. G., Shoemaker C. A. Improved strategies for radial basis function methods for global optimization. J. Global Optim. (2007b) 37(1):113–135CrossrefGoogle Scholar
  • Regis R. G., Shoemaker C. A. Parallel radial basis function methods for the global optimization of expensive functions. Eur. J. Oper. Res. (2007c) 182(2):514–535CrossrefGoogle Scholar
  • Sacks J., Welch W. J., Mitchell T. J., Wynn H. P. Design and analysis of computer experiments. Statist. Sci. (1989) 4(4):409–435CrossrefGoogle Scholar
  • Schoen F. A wide class of test functions for global optimization. J. Global Optim. (1993) 3(2):133–137CrossrefGoogle Scholar
  • Simpson T. W., Mauery T. M., Korte J. J., Mistree F. Kriging metamodels for global approximation in simulation-based multidisciplinary design optimization. AIAA J. (2001) 39(12):2233–2241CrossrefGoogle Scholar
  • Sóbester A., Leary S. J., Keane A. J. A parallel updating scheme for approximating and optimizing high fidelity computer simulations. Structural Multidisciplinary Optim. (2004) 27(5):371–383CrossrefGoogle Scholar
  • Torczon V. On the convergence of pattern search algorithms. SIAM J. Optim. (1997) 7(1):1–25CrossrefGoogle 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. (2007) 19(3):328–340LinkGoogle Scholar
  • Wild S., Regis R. G., Shoemaker C. A. ORBIT: Optimization by radial basis function interpolation in trust-regions. SIAM J. Sci. Comput. (2008) 30(6):3197–3219CrossrefGoogle Scholar
  • Ye K. Q., Li W., Sudjianto A. Algorithmic construction of optimal symmetric Latin hypercube designs. J. Statist. Planning Inference (2000) 90(1):145–159CrossrefGoogle Scholar
  • Yoon J.-H., Shoemaker C. A. Comparison of optimization methods for ground-water bioremediation. J. Water Resources Planning Management (1999) 125(1):54–63CrossrefGoogle Scholar
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