Mutli-fidelity optimization - VF-PI#
import numpy as np
from matplotlib import pyplot as plt
from smt_optim.benchmarks.registry import get_problem
from smt_optim.core import Driver, ObjectiveConfig, ConstraintConfig, DriverConfig, Problem
from smt_optim.surrogate_models.smt import SmtMFCK
from smt_optim.acquisition_strategies import VFPI
Unconstrained 1D optimization#
# high-fidelity function
def sasena2002_hf(x):
return -np.sin(x) - np.exp(x / 100) + 10
# low-fidelity function
def sasena2002_lf(x):
return sasena2002_hf(x) + 0.3 + 0.03 * (x - 3) ** 2
bounds = np.array([[0, 10]])
x_valid = np.linspace(bounds[:, 0], bounds[:, 1], 101)
y_hf = sasena2002_hf(x_valid)
y_lf = sasena2002_lf(x_valid)
obj_config = ObjectiveConfig(
objective=[sasena2002_lf, sasena2002_hf], # multi-fidelity functions must be given in sequential order
type="minimize",
surrogate=SmtMFCK,
)
prob_definition = Problem(
obj_configs=[obj_config],
design_space=bounds,
costs=[0.2, 1], # Set the cost of sampling each level
)
xt_init = [np.array([[0.5], [2.5], [9.5]]) for _ in range(2)]
opt_config = DriverConfig(
max_iter = 10,
max_budget = 10, # stopping criterion
xt_init = xt_init,
verbose = True,
scaling = True,
seed=42,
)
optimizer = Driver(prob_definition, opt_config, VFPI)
state = optimizer.optimize()
iter budget fmin rscv fidelity gp_time acq_time
1 3.800 8.37621e+00 0.000e+00 1 0.681 0.705
2 4.000 8.37621e+00 0.000e+00 1 0.745 0.590
3 4.200 8.37621e+00 0.000e+00 1 0.756 0.446
4 4.400 8.37621e+00 0.000e+00 1 0.779 0.410
5 4.600 8.37621e+00 0.000e+00 1 0.817 0.953
6 4.800 8.37621e+00 0.000e+00 1 0.712 0.420
7 5.000 8.37621e+00 0.000e+00 1 0.725 0.398
8 5.200 8.37621e+00 0.000e+00 1 0.690 0.395
9 6.200 8.04212e+00 0.000e+00 2 0.703 0.404
10 7.200 7.92735e+00 0.000e+00 2 0.738 0.512
data = state.dataset.export_as_dict()
fidelity_masks = [(data["fidelity"] == lvl).ravel() for lvl in range(state.problem.num_fidelity)]
xt = [data["x"][fidelity_masks[lvl], 0] for lvl in range(state.problem.num_fidelity)]
yt = [data["obj"][fidelity_masks[lvl], 0] for lvl in range(state.problem.num_fidelity)]
sample = state.get_best_sample()
fig, ax = plt.subplots(layout="constrained")
ax.plot(x_valid, y_hf, label="HF function")
ax.plot(x_valid, y_lf, label="LF function")
for lvl in reversed(range(2)):
ax.scatter(xt[lvl], yt[lvl], 5, marker="s")
ax.scatter(sample.x, sample.obj, 75, marker="*", color="C3", zorder=20, label=r"MFSEGO $f_{\min}$")
plt.legend()
plt.show()
Constrained 2D optimization#
Importing a test function#
problem = get_problem("Rosenbrock")
VF-PI Configuration#
obj_config = ObjectiveConfig(
problem.objective,
type="minimize",
surrogate=SmtMFCK,
)
# configure the constraint
cstr_config = ConstraintConfig(
problem.constraints[0],
upper=0.0, # g(x) <= 0
surrogate=SmtMFCK, # set which GP to model this constraint
)
prob_definition = Problem(
obj_configs=[obj_config],
design_space=problem.bounds,
costs=[0.2, 1], # Set the cost of sampling each level
cstr_configs=[cstr_config],
)
opt_config = DriverConfig(
max_iter = 30,
max_budget = 20, # stopping criterion
nt_init = 5,
verbose = True,
scaling = True,
seed=42,
)
optimizer = Driver(prob_definition, opt_config, VFPI, strategy_kwargs={"density_penalty": True})
state = optimizer.optimize()
iter budget fmin rscv fidelity gp_time acq_time
1 7.200 2.85223e+02 0.000e+00 1 1.813 1.421
2 7.400 2.85223e+02 0.000e+00 1 2.107 1.314
3 7.600 2.85223e+02 0.000e+00 1 1.958 1.446
4 7.800 2.85223e+02 0.000e+00 1 1.904 1.418
5 8.800 3.20695e+00 0.000e+00 2 1.803 1.374
6 9.000 3.20695e+00 0.000e+00 1 1.777 1.366
7 9.200 3.20695e+00 0.000e+00 1 1.917 1.133
8 10.200 3.20695e+00 0.000e+00 2 1.765 1.245
9 10.400 3.20695e+00 0.000e+00 1 1.739 1.347
10 11.400 2.24581e+00 0.000e+00 2 1.758 1.213
iter budget fmin rscv fidelity gp_time acq_time
11 12.400 2.24581e+00 0.000e+00 2 1.698 1.439
12 12.600 2.24581e+00 0.000e+00 1 1.727 1.396
13 12.800 2.24581e+00 0.000e+00 1 1.871 1.483
14 13.000 2.24581e+00 0.000e+00 1 1.861 1.434
15 14.000 2.24581e+00 0.000e+00 2 1.773 1.626
16 14.200 2.24581e+00 0.000e+00 1 1.873 2.441
17 14.400 2.24581e+00 0.000e+00 1 1.816 1.540
18 14.600 2.24581e+00 0.000e+00 1 2.463 1.737
19 15.600 2.24581e+00 0.000e+00 2 1.954 1.771
20 16.600 2.24581e+00 0.000e+00 2 2.022 2.061
iter budget fmin rscv fidelity gp_time acq_time
21 17.600 2.24581e+00 0.000e+00 2 2.129 1.949
22 18.600 2.24581e+00 0.000e+00 2 2.000 1.912
23 19.600 2.24581e+00 0.000e+00 2 2.055 1.708
24 20.600 2.24581e+00 0.000e+00 2 2.304 1.819
data_x = []
for lvl in range(state.problem.num_fidelity):
samples = state.dataset.get_by_fidelity(lvl)
data_x.append(np.empty((len(samples), state.problem.num_dim)))
for idx, s in enumerate(samples):
data_x[lvl][idx, :] = s.x
sample = state.get_best_sample(ctol=1e-4)
print(f"best sample = \n{sample}")
X = np.linspace(problem.bounds[0, 0], problem.bounds[0, 1], 201)
XX, YY = np.meshgrid(X, X)
data = np.vstack((XX.ravel(), YY.ravel())).T
z = np.empty(data.shape[0])
c = np.empty(data.shape[0])
for i in range(data.shape[0]):
z[i] = problem.objective[-1](data[i, :])
c[i] = problem.constraints[0][-1](data[i, :])
Z = z.reshape(XX.shape)
C = c.reshape(XX.shape)
fig, ax = plt.subplots()
ax.set_title(problem.name)
ax.contour(XX, YY, Z, levels=20)
ax.contourf(XX, YY, np.where(C <= 0, np.nan, C), levels=0, colors="C7", alpha=0.15)
ax.contour(XX, YY, C, levels=[0], colors="C7")
ax.scatter(data_x[0][:, 0], data_x[0][:, 1], 10, color="C7", marker="o", alpha=0.5, label="DoE lvl 1/2", zorder=10)
ax.scatter(data_x[1][:, 0], data_x[1][:, 1], 20, color="C8", marker="s", alpha=0.5, label="DoE lvl 2/2", zorder=20)
ax.scatter(sample.x[0], sample.x[1], 75, c="C3", marker="*", label=r"MFSEGO $f_{\min}$", zorder=30)
ax.set_xlabel(r"$x_1$")
ax.set_ylabel(r"$x_2$")
ax.legend()
ax.set_aspect("equal")
plt.show()
best sample =
======= sample data =======
x = [-0.02562273 0.10992281]
obj = [2.24581415]
cstr = [-0.44438207]
eval_time = [2.38599023e-06 1.12300040e-06]
------- meta data -------
iter = 10
budget = 11.399999999999999
fidelity = 1
rscv = 0.0
===========================
