from functools import partial
import warnings
import numpy as np
from smt_optim.benchmarks.base import BenchmarkProblem
[docs]
class MFBorehole(BenchmarkProblem):
"""
Reference:
(with 2 fidelity levels)
Xiong, S., Qian, P. Z., & Wu, C. J. (2013). Sequential design and analysis of high-accuracy and low-accuracy
computer codes. Technometrics, 55(1), 37-46.
(with 3 fidelity levels)
Tran, A., Wildey, T., & McCann, S. (2020). sMF-BO-2CoGP: A sequential multi-fidelity constrained Bayesian
optimization framework for design applications. Journal of Computing and Information Science in Engineering,
20(3), 031007.
"""
def __init__(self):
super().__init__()
self.num_dim = 8
self.num_cstr = 0
self.num_fidelity = 2
self.num_obj = 1
self.bounds = np.array(
[
[0.05, 0.15],
[100, 50_000],
[63_070, 115_600],
[990, 1_110],
[63.1, 116],
[700, 820],
[1_120, 1680],
[9_855, 12_045],
]
)
self.objective = [
partial(self.func, A=1.5),
partial(self.func, A=1.0),
]
[docs]
def set_num_fid(self, num_fidelity):
if num_fidelity not in [2, 3]:
warnings.warn(
"MF Borehole can have 2 or 3 fidelity levels. Defaulting to 2."
)
num_fidelity = 2
if num_fidelity == 2:
self.objective = [
partial(self.func, A=5, B=1.5),
partial(self.func, A=2 * np.pi, B=1.0),
]
else:
self.objective = [
partial(self.func, A=7, B=0.5),
partial(self.func, A=5, B=1.5),
partial(self.func, A=2 * np.pi, B=1.0),
]
self.num_fidelity = len(self.objective)
[docs]
def func(self, x, A=2 * np.pi, B=1.0):
term1 = A * x[2] * (x[3] - x[5])
term2 = np.log10(x[1] / x[0])
term3 = (
B
+ (2 * x[6] * x[2]) / (np.log(x[1] / x[0]) * x[0] ** 2 * x[7])
+ x[2] / x[4]
)
return term1 / (term2 * term3)
if __name__ == "__main__":
import scipy.optimize as so
prob = MFBorehole()
x0 = np.array([7.0e-02, 2.0e02, 7.0e04, 1.0e03, 1.0e02, 7.5e02, 1.4e03, 1.0e04])
x_ref = np.array(
[
5.00000000e-02,
2.00184597e02,
6.99999998e04,
9.90000000e02,
9.69866639e01,
8.20000000e02,
1.68000000e03,
9.96047429e03,
]
)
res = so.minimize(prob.objective[-1], x0, bounds=prob.bounds, method="SLSQP")
# print(res.fun)
# print(res.x)
print(np.linalg.norm(res.x - x_ref))
prob.set_num_fid(2)
print(len(prob.objective))
prob.set_num_fid(3)
print(len(prob.objective))
