Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

Journal of Global Optimization

Volumn 60, Issue 2, 2014, Pages 123-144

  Müller, Juliane ^a   Shoemaker, Christine A ^a  

^a School of Operations Research and Industrial Engineering   (United States)

Author keywords

Computationally expensive; Derivative free; Global optimization; Kriging; Matlab toolbox; Model combination; Radial basis function; Response surface; Surrogate model

Indexed keywords

BIOREMEDIATION; FUNCTIONS; GLOBAL OPTIMIZATION; GROUNDWATER; INTERPOLATION; POLYNOMIAL REGRESSION; SAMPLING; SURFACE PROPERTIES;

COMPUTATIONALLY EXPENSIVE; DERIVATIVE-FREE; KRIGING; MATLAB TOOLBOXES; MODEL COMBINATION; RADIAL BASIS FUNCTIONS; RESPONSE SURFACE; SURROGATE MODEL;

ITERATIVE METHODS;

EID: 84920706520     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-014-0184-0     Document Type: Article

References (52)

1. Ackley, D.H.: A connectionist machine for genetic hillclimbing. Kluwer, Boston (1987)
2. Argatov, I., Rautakorpi, P., Silvennoinen, R.: Estimation of the mechanical energy output of the kite wind generator. Renew. Energy 34, 1525–1532 (2009)
3. Audet, C., Béchard, V., Le Digabel, S.: Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search. J. Glob. Optim. 41, 299–318 (2008)
4. Björkman, M., Holmström, K.: Global optimization of costly nonconvex functions using radial basis functions. Optim. Eng. 1, 373–397 (2001)
5. Booker, A.J., Dennis Jr, J.E., Frank, P.D., Serafini, D.B., Torczon, V., Trosset, M.W.: A rigorous framework for optimization of expensive functions by surrogates. Struct. Multidiscip. Optim. 17, 1–13 (1999)
6. Breukels, J.: An engineering methodology for kite design. Ph.D. thesis, Delft University of Technology (2011)
7. Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. SIAM, Philadelphia (2009)
8. De Jong, K.A.: An Analysis of the Behavior of a Class of Genetic Adaptive Systems. Ph.D. thesis, University of Michigan (1975)
9. Dixon, L.C.W., Szegö, G. P. (eds.): The global optimization problem: an introduction. In: Towards Global Optimization, vol. 2. North-Holland, Amsterdam (1978)
10. Espinet, A.J., Shoemaker, C.A.: Estimation of plume distribution for carbon sequestration using parameter estimation, optimization and monitoring data. Water Resour. Res. 49, 4442–4464 (2013)
11. Fagiano, L.: Control of tethered airfoils for high-altitude wind energy generation. Ph.D. thesis, Politecnico di Torino (2009)
12. Forrester, A., Sóbester, A., Keane, A.: Engineering Design Via Surrogate Modelling—a Practical Guide. Wiley, New York (2008)
13. Friedman, J.H.: Multivariate adaptive regression splines. Ann. Stat. 19, 1–67 (1991)
14. Glaz, B., Friedmann, P.P., Liu, L.: Surrogate based optimization of helicopter rotor blades for vibration reduction in forward flight. Struct. Multidiscip. Optim. 35, 341–363 (2008)
15. Goel, T., Haftka, R.T., Shyy, W., Queipo, N.V.: Ensemble of surrogates. Struct. Multidiscip. Optim. 33, 199–216 (2007)
16. Gutmann, H.-M.: A radial basis function method for global optimization. J. Glob. Optim. 19, 201–227 (2001)
17. Holmström, K., Quttineh, N.-H., Edvall, M.M.: An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization. J. Glob. Optim. 41, 447–464 (2008)
18. Houska, B.: Robustness and stability optimization of open-loop controlled power generating kites. Master’s thesis, Ruprecht-Karls-Universität Heidelberg, Fakultät für Mathematik und Informatik (2007)
19. Jekabsons, G.: ARESLab: adaptive regression splines toolbox for Matlab. Available at http://www.cs.rtu.lv/jekabsons/ (2010)
20. Jones, D.R.: A taxonomy of global optimization methods based on response surfaces. J. Glob. Optim. 21, 345–383 (2001)
21. Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Glob. Optim. 13, 455–492 (1998)
22. Jouhaud, J.-C., Sagaut, P., Montagnac, M., Laurenceau, J.: A surrogate-model based multidisciplinary shape optimization method with application to a 2D subsonic airfoil. Comput. Fluids 36, 520–529 (2007)
23. Lam, X.B., Kim, Y.S., Hoang, A.D., Park, C.W.: Coupled aerostructural design optimization using the kriging model and integrated multiobjective optimization algorithm. J. Optim. Theory Appl. (2009). doi:10.1007/s10957-009-9520-9
24. Le Digabel, S.: Algorithm 909: nomad: nonlinear optimization with the MADS algorithm. ACM Trans. Math. Softw. 37:44:1–44:15 (2011)
25. Levy, A., Montalvo, A., Gomez, S., Galderon, A.: Topics in Global Optimization. Springer, New York (1981)
26. Li, C., Wang, F.-L., Chang, Y.-Q., Liu, Y.: A modified global optimization method based on surrogate model and its application in packing profile optimization of injection molding process. Int. J. Adv. Manuf. Technol. 48, 505–511 (2010)
27. Liao, X., Li, Q., Yang, X., Zhang, W., Li, W.: Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct. Multidiscip. Optim. 35, 561–569 (2008)
28. Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE a Matlab kriging toolbox. Technical report, IMM-TR-2002-12 (2002)
29. Martin, J.D., Simpson, T.W.: Use of kriging models to approximate deterministic computer models. AIAA J. 43, 853–863 (2005)
30. Matheron, G.: Principles of geostatistics. Econ. Geol. 58, 1246–1266 (1963)
31. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1992)
32. Moré, J.J., Wild, S.M.: Benchmarking derivative-free optimization algorithms. SIAM J. Optim. 20, 172–191 (2009)
33. Mühlenbein, H., Schomisch, D., Born, J.: The parallel genetic algorithm as function optimizer. Parallel Comput. 17, 619–632 (1991)
34. Müller, J., Piché, R.: Mixture surrogate models based on Dempster–Shafer theory for global optimization problems. J. Glob. Optim. 51, 79–104 (2011)
35. Myers, R.H., Montgomery, D.C.: Response Surface Methodology, Process and Product Optimization Using Designed Experiments. Wiley-Interscience Publication, New York (1995)
36. Powell, M.J.D.: An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 7, 155–162 (1964)
37. Powell, M.J.D.: The theory of radial basis function approximation in 1990. In: Light, W.A. (ed.) Advances in Numerical Analysis, vol. 2: Wavelets, Subdivision Algorithms and Radial Basis Functions. pp. 105–210, Oxford University Press, Oxford (1992)
38. Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Tucker, P.K.: Surrogate-based analysis and optimization. Prog. Aerosp. Sci. 41, 1–28 (2005)
39. Regis, R.G., Shoemaker, C.A.: Constrained global optimization of expensive black-box functions using radial basis functions. J. Glob. Optim. 31, 153–171 (2005)
40. Regis, R.G., Shoemaker, C.A.: A stochastic radial basis function method for the global optimization of expensive functions. INFORMS J. Comput. 19, 497–509 (2007)
41. Regis, R.G., Shoemaker, C.A.: Improved strategies for radial basis function methods for global optimization. J. Glob. Optim. 37, 113–135 (2007)
42. Regis, R.G., Shoemaker, C.A.: Parallel radial basis function methods for the global optimization of expensive functions. Eur. J. Oper. Res. 182, 514–535 (2007)
43. Regis, R.G., Shoemaker, C.A.: Parallel stochastic global optimization using radial basis functions. INFORMS J. Comput. 21, 411–426 (2009)
44. Regis, R.G., Shoemaker, C.A.: A quasi-multistart framework for global optimization of expensive functions using response surface models. J. Glob. Optim. (2012). doi:10.1007/s10898-012-9940-1
45. Regis, R.G., Shoemaker, C.A.: Combining radial basis function surrogates and dynamic coordinate search in high-dimensional expensive black-box optimization. Eng. Optim. 45, 529–555 (2013)
46. Schoen, F.: A wide class of test functions for global optimization. J. Glob. Optim. 3, 133–137 (1993)
47. Tolson, B.A., Shoemaker, C.A.: Dynamically dimensioned search algorithm for computationally efficient watershed model calibration. Water Res. Res. 43, W01413 (2007)
48. Törn, A., Zilinskas, A.: Global Optimization. In: Lecture Notes in Computer Science, vol. 350. Springer, Berlin (1989)
49. Vaz, A.I.F., Vicente, L.N.: A particle swarm pattern search method for bound constrained global optimization. J. Glob. Optim. 39, 197–219 (2007)
50. Viana, F.A.C., Haftka, R.T., Watson, L.T.: Efficient global optimization algorithm assisted by multiple surrogate techniques. J. Glob. Optim. 56, 669–689 (2013)
51. Yang, R.J., Wang, N., Tho, C.H., Bobineau, J.P., Wang, B.P.: Metamodeling development for vehicle frontal impact simulation. J. Mech. Des. 127, 1014–1021 (2005)
52. Yoon, J.-H., Shoemaker, C.A.: Comparison of optimization methods for groundwater bioremediation. J. Water Resour. Plan. Manag. 125, 54–63 (1999)