Parallel radial basis function methods for the global optimization of expensive functions

European Journal of Operational Research

Volumn 182, Issue 2, 2007, Pages 514-535

  Regis, Rommel G ^a   Shoemaker, Christine A ^a  

^a Cornell University   (United States)

Author keywords

Expensive function; Function approximation; Global optimization; Parallel optimization; Radial basis function; Response surface model; Surrogate model

Indexed keywords

BIOREMEDIATION; COMPUTATIONAL METHODS; GLOBAL OPTIMIZATION; MATHEMATICAL MODELS; PARALLEL ALGORITHMS; PROBLEM SOLVING;

FUNCTION APPROXIMATION; PARALLEL OPTIMIZATION; RADIAL BASIS FUNCTIONS; RESPONSE SURFACE MODEL; SURROGATE MODEL;

FUNCTION EVALUATION;

EID: 34247494213     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2006.08.040     Document Type: Article

References (51)

1. Barr R.S., and Hickman B.L. Reporting computational experiments with parallel algorithms: Issues, measures, and experts' opinions. ORSA Journal on Computing 5 1 (1993) 2-18
2. Björkman M., and Holmström K. Global optimization of costly nonconvex functions using radial basis functions. Optimization and Engineering 1 4 (2000) 373-397
3. Booker A.J., Dennis J.E., Frank P.D., Serafini D.B., Torczon V., and Trosset M.W. A rigorous framework for optimization of expensive functions by surrogates. Structural Optimization 17 1 (1999) 1-13
4. Box G.E.P., and Draper N.R. Empirical Model-Building and Response Surfaces (1987), John Wiley & Sons, Inc., New York
5. Branin F.H. Widely convergent methods for finding multiple solutions of simultaneous nonlinear equations. IBM Journal of Research Developments 16 (1972) 504-522
6. Brekelmans R., Driessen L., Hamers H., and den Hertog D. Constrained optimization involving expensive function evaluations: A sequential approach. European Journal of Operational Research 160 (2005) 121-138
7. Buhmann M.D. Radial Basis Functions (2003), Cambridge University Press, U.K
8. Byrd R.H., Dert C.L., Rinnooy Kan A.H.G., and Schnabel R.B. Concurrent stochastic methods for global optimization. Mathematical Programming 46 (1990) 1-29
9. Cantu-Paz E. Efficient and Accurate Parallel Genetic Algorithms (2000), Kluwer, Boston
10. Conn A.R., Scheinberg K., and Toint Ph.L. Recent progress in unconstrained nonlinear optimization without derivatives. Mathematical Programming 79 3 (1997) 397-414
11. Cressie N. Statistics for Spatial Data (1993), John Wiley, New York
12. Dixon L.C.W., and Jha M. Parallel algorithms for global optimization. Journal of Optimization Theory and Applications 79 2 (1993) 385-395
13. Dixon L.C.W., and Szegö G. The global optimization problem: An introduction. In: Dixon L.C.W., and Szegö G. (Eds). Towards Global Optimization 2 (1978), North-Holland, Amsterdam 1-15
14. El-Beltagy M.A., Nair P.B., and Keane A.J. Metamodelling techniques for evolutionary optimization of computationally expensive problems: Promises and limitations. In: Banshaf W., Daida J., Eiben A.E., Garzon M.H., Honavar V., Jakiela M., and Smith R.E. (Eds). Proceedings of the Genetic and Evolutionary Computation Conference (GECCO99) (1999), Morgan Kaufman 196-203
15. Friedman J. Multivariate adaptive regression splines. Annals of Statistics 19 1 (1991) 1-141
16. Gilmore P., and Kelley C.T. An implicit filtering algorithm for optimization of functions with many local minima. SIAM Journal on Optimization 5 (1995) 269-285
17. Giunta A.A., Balabanov V., Haim D., Grossman B., Mason W.H., Watson L.T., and Haftka R.T. Aircraft multidisciplinary design optimisation using design of experiments theory and response surface modelling. Aeronautical Journal 101 1008 (1997) 347-356
18. Gutmann H.M. A radial basis function method for global optimization. Journal of Global Optimization 19 3 (2001) 201-227
19. Gutmann, H.M., 2001b. Radial basis function methods for global optimization. Ph.D. Thesis, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.
20. Horst R., Pardalos P.M., and Thoai N.V. Introduction to Global Optimization. second ed. (2000), Kluwer, Dordrecht
21. Jones, D.R., 1996. Global optimization with response surfaces. Presented at the Fifth SIAM Conference on Optimization, Victoria, Canada.
22. Jones D.R., Schonlau M., and Welch W.J. Efficient global optimization of expensive black-box functions. Journal of Global Optimization 13 4 (1998) 455-492
23. Kaufman M., Balabanov V., Burgee S.L., Giunta A.A., Grossman B., Haftka R.T., Mason W.H., and Watson L.T. Variable-complexity response surface approximations for wing structural weight in HSCT design. Computational Mechanics 18 2 (1996) 112-126
24. Kelley C.T. Iterative Methods for Optimization (1999), SIAM, Philadelphia
25. Koehler, J.R., Owen, A.B., 1996. Computer experiments. In: Ghosh, S., Rao, C.R. (Eds.), Handbook of Statistics, vol. 13: Design and Analysis of Computer Experiments, North-Holland, Amsterdam, pp. 261-308.
26. Lai T.H., and Sahni S. Anomalies in parallel branch-and-bound algorithms. Communications of the Association for Computing Machinery 27 (1984) 594-602
27. Locatelli M. Bayesian algorithms for one-dimensional global optimization. Journal of Global Optimization 10 (1997) 57-76
28. Marazzi M., and Nocedal J. Wedge trust region methods for derivative free optimization. Mathematical Programming, Series A 91 (2002) 289-305
29. Minsker B.S., and Shoemaker C.A. Dynamic optimal control of in-situ bioremediation of groundwater. Journal of Water Resources Planning and Management 124 3 (1998) 149-161
30. Myers R.H., and Montgomery D.C. Response Surface Methodology: Process and Product Optimization Using Designed Experiments (1995), John Wiley & Sons Inc., New York
31. Nocedal J., and Wright S.J. Numerical Optimization (1999), Springer, New York
32. Powell, M.J.D., 1992. The theory of radial basis function approximation in 1990. In: Light, W. (Ed.), Advances in Numerical Analysis, vol. 2: Wavelets, Subdivision Algorithms and Radial Basis Functions, Oxford University Press, pp. 105-210.
33. Powell M.J.D. Recent research at Cambridge on radial basis functions. In: Müller M., Buhmann M., Mache D., and Felten M. (Eds). New Developments in Approximation Theory, International Series of Numerical Mathematics vol. 132 (1999), Birkhauser Verlag, Basel 215-232
34. Powell M.J.D. UOBYQA: Unconstrained optimization by quadratic approximation. Mathematical Programming 92 (2002) 555-582
35. Powell M.J.D. On trust region methods for unconstrained minimization without derivatives. Mathematical Programming 97 (2003) 605-623
36. Regis R.G., and Shoemaker C.A. Constrained global optimization of expensive black box functions using radial basis functions. Journal of Global Optimization 31 (2005) 153-171
37. Regis, R.G., Shoemaker, C.A., 2006. Improved strategies for radial basis function methods for global optimization. Journal of Global Optimization. doi:10.1007/s10898-006-9040-1.
38. Sacks J., Welch W.J., Mitchell T.J., and Wynn H.P. Design and analysis of computer experiments. Statistical Science 4 4 (1989) 409-435
39. Schnabel R.B. A view of the limitations, opportunities, and challenges in parallel nonlinear optimization. Parallel Computing 21 (1995) 875-905
40. Schoen F. A wide class of test functions for global optimization. Journal of Global Optimization 3 (1993) 133-137
41. Shoemaker C.A., Willis M., Zhang W., and Gossett J. Model analysis of reductive dechlorination with data from Cape Canaveral field site. In: Magar V., Vogel T., Aelion C., and Leeson A. (Eds). Innovative Methods in Support of Bioremediation (2001), Battelle Press, Columbus, OH 125-131
42. Sóbester A., Leary S., and Keane A.J. A parallel updating scheme for approximating and optimizing high fidelity computer simulations. Structural and Multidisciplinary Optimization 27 (2004) 371-383
43. Storn R., and Price K. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11 (1997) 341-359
44. Taylor S. Modeling enhanced in-situ biodegradation in groundwater: model response to biological parameter uncertainty. Proceedings of the 1993 Groundwater Modeling Conference, International Groundwater Modeling Center 51 (1993), Golden, Colorado 4-51-4-60
45. The Mathworks, Inc., 2004. Optimization Toolbox for Use with MATLAB: User's Guide, Version 3, Natick, MA.
46. Torczon V. On the convergence of pattern search algorithms. SIAM Journal on Optimization 7 1 (1997) 1-25
47. Törn A., and Žilinskas A. Global Optimization. Lecture Notes in Computer Science vol. 350 (1989), Springer Verlag, Berlin
48. Vanden Berghen F., and Bersini H. CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. Journal of Computational and Applied Mathematics 181 (2005) 157-175
49. Ye K.Q., Li W., and Sudjianto A. Algorithmic construction of optimal symmetric latin hypercube designs. Journal of Statistical Planning and Inference 90 (2000) 145-159
50. Yoon, J.-H., 1997. Optimal design of groundwater in situ bioremediation using evolutionary algorithms. Ph.D. Thesis, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY.
51. Yoon J.-H., and Shoemaker C.A. Comparison of optimization methods for ground-water bioremediation. Journal of Water Resources Planning and Management 125 (1999) 54-63