Operations Research Transactions ›› 2021, Vol. 25 ›› Issue (2): 1-14.doi: 10.15960/j.cnki.issn.1007-6093.2021.02.001
Fusheng BAI1,*(), Dan FENG1, Ke ZHANG1
Received:
2020-09-17
Online:
2021-06-15
Published:
2021-05-06
Contact:
Fusheng BAI
E-mail:fsbai@cqnu.edu.cn
CLC Number:
Fusheng BAI, Dan FENG, Ke ZHANG. Combined response surface method with adaptive sampling for expensive black-box global optimization[J]. Operations Research Transactions, 2021, 25(2): 1-14.
"
测试问题 | AMGO | 自适应采样组合响应面算法 | |||
均值 | 标准差 | 均值 | 标准差 | ||
Branin | 0.403, 6 | 0.005, 4 | 0.403, 2 | 0.017, 3 | |
Rastrigin2 | -1.617, 0 | 0.490, 5 | -2.000, 0 | 0.000, 0 | |
Schoen3 | 10.551, 8 | 0.408, 4 | 10.224, 0 | 0.015, 7 | |
Schoen4 | 11.235, 6 | 0.813, 5 | 15.938, 5 | 4.996, 6 | |
Schoen4X | 273.679, 2 | 287.659, 0 | -371.900, 9 | 769.190, 0 | |
Schoen4Y | -39.429, 5 | 255.351, 3 | 127.513, 6 | 529.889, 6 | |
Shubert | -134.079, 6 | 54.127, 0 | -135.051, 5 | 45.200, 0 |
"
测试问题 | 最小值 | 最大值 | 维数 | 三次响应面算法 | 自适应采样组合响应面算法 |
Ackley15 | 0 | 2.181 1×10 | 15 | >200 | >200 |
Ackley30 | 0 | 2.174 0×10 | 30 | >200 | >200 |
Ackley8 | 0 | 2.201 2×10 | 8 | 175(1) | >200 |
Branin | 0.397 9 | 3.081 3×102 | 2 | 20.37 (30) | 19.37 (30) |
Easom | -1 | 0 | 2 | >200 | >200 |
Goldstein-Price | 3 | 1.015 7×106 | 2 | 2.43 (30) | 2.37 (30) |
Hartman3 | -3.862 8 | -3.847 9×10-5 | 3 | 58.67 (30) | 58.47 (30) |
Hartman6 | -3.323 4 | -5.715 1×10-7 | 6 | 104.43 (23) | 64.62 (21) |
Levy20 | 0 | 2.915 6×103 | 20 | 45.50 (18) | 45.88 (19) |
Rastrigin2 | -2 | 6.373 0 | 2 | 29.44 (21) | 22.25 (27) |
Rosenbrock10 | 0 | 6.593 1×106 | 10 | 25.07 (30) | 24.77 (30) |
Rosenbrock20 | 0 | 1.248 9×107 | 20 | 45.50 (30) | 46.33 (30) |
Schoen3 | 9.954 2 | 8.980 8×10 | 3 | 81.80 (30) | 40.60 (30) |
Schoen4 | 9.954 2 | 8.980 8×10 | 4 | 130.29 (28) | 58.90 (10) |
Schoen4X | -965.353 3 | 9.892 8×102 | 4 | 155.30 (10) | 118.47 (17) |
Schoen4Y | -967.652 2 | 9.991 4×102 | 4 | >200 | 133 (3) |
Schoen5 | 9.954 2 | 8.980 8×10 | 5 | 158 (9) | 107.88 (25) |
Schoen5X | -965.353 3 | 9.951 6×102 | 5 | >200 | 104.50 (2) |
Schoen5Y | -967.652 2 | 9.984 9×102 | 5 | >200 | 141 (4) |
Shubert | -186.730 9 | 1.656 6×102 | 2 | 96.63 (19) | 105.33 (12) |
Sphere27 | 0 | 7.077 9×102 | 27 | 57(30) | 57.70 (30) |
Zakharov11 | 0 | 2.339 2×107 | 11 | 27.87 (30) | 28.37 (30) |
1 | Myers R H , Montgomery D C . Response Surface Methodology: Process and Product Optimization Using Designed Experiments[M]. New York: Wiley, 1995. |
2 | Khuri A I , Cornell J A . Response Surfaces[M]. New York: Marcel Dekker Inc., 1987. |
3 |
Jones D R , Schonlau M , Welch W J . Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13 (4): 455- 492.
doi: 10.1023/A:1008306431147 |
4 |
Gutmann H M . A radial basis function method for global optimization[J]. Journal of Global Optimization, 2001, 19 (3): 201- 227.
doi: 10.1023/A:1011255519438 |
5 |
Regis R G , Shoemaker C A . Constrained global optimization of expensive black box functions using radial basis functions[J]. Journal of Global Optimization, 2005, 31, 153- 171.
doi: 10.1007/s10898-004-0570-0 |
6 |
Regis R , Shoemaker C . A stochastic radial basis function method for the global optimization of expensive functions[J]. INFORMS Journal on Computing, 2007, 19, 497- 509.
doi: 10.1287/ijoc.1060.0182 |
7 |
Xiang H , Li Y , Liao H , et al. An adaptive surrogate model based on support vector regression and its application to the optimization of railway wind barriers[J]. Structural and Multidisciplinary Optimization, 2017, 55, 701- 713.
doi: 10.1007/s00158-016-1528-9 |
8 |
Crino S , Brown D E . Global optimization with multivariate adaptive regression splines[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2007, 37 (2): 333- 340.
doi: 10.1109/TSMCB.2006.883430 |
9 |
Jie H , Wu Y , Ding J . An adaptive metamodel-based global optimization algorithm for blackbox type problems[J]. Engineering Optimization, 2015, 47 (11): 1459- 1480.
doi: 10.1080/0305215X.2014.979814 |
10 |
Zhou Z , Bai F S . An adaptive framework for costly black-box global optimization based on radial basis function interpolation[J]. Journal of Global Optimization, 2018, 70 (4): 757- 781.
doi: 10.1007/s10898-017-0599-5 |
11 | Powell M J D. The theory of radial basis function approximation in 1990[D]. Oxford: Oxford University, 1992. |
12 | Dixon L C W , Szegö G P . Towards Global Optimisation[M]. Amsterdam: North-Holland Publishing Company, 1978. |
13 |
Schoen F . A wide class of test functions for global optimization[J]. Journal of Global Optimization, 1993, 3 (2): 133- 137.
doi: 10.1007/BF01096734 |
14 | Törn A , Zilinskas A . Global Optimization[M]. Berlin: Springer-Verlag, 1989. |
15 | Surjanovic S, Bingham D. Virtual library of simulation experiments: Test functions and datasets[EB/OL]. (2020-08-25)[2013-03-23]. http://www.sfu.ca/~ssurjano. |
16 | Dolan E D , Moré J J . Benchmarking optimization software with performance profiles[J]. Mathematical Programming, 2001, 91 (2): 201- 213. |
17 | Moré J J , Wild S M . Benchmarking derivative-free optimization algorithms[J]. SIAM Journal on Optimization, 2009, 20 (1): 172- 191. |
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