"""
Paper: https://arxiv.org/pdf/2204.07867
Code: https://gitlab.com/qudo046/avt-331-l1-benchmarks
"""
from functools import partial
import warnings
import numpy as np
from smt_optim.benchmarks.base import BenchmarkProblem
[docs]
class Alos1(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 1
self.num_cstr = 0
self.num_fidelity = 2
self.num_obj = 1
self.bounds = np.array([
[0, 1],
])
# self.costs = [0.15/9, 1]
self.objective = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
# self.constraints = []
self.tags = [
"avt311",
]
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def f(self, x, fid=1):
if fid == 1:
return np.sin(30.0 * (x - 0.9) ** 4) * np.cos(2.0 * (x - 0.9)) + (x - 0.9) / 2.0
else:
return (self.f(x) - 1.0 + x) / (1.0 + 0.25 * x)
[docs]
class Alos(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Alos"
self.num_dim = 2
self.num_cstr = 0
self.num_fidelity = 2
self.num_obj = 1
self.bounds = np.array([
[0, 1],
[0, 1],
])
# self.costs = [0.15/9, 1]
self.objective = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
# self.constraints = []
self.tags = [
"avt311",
"n_variable",
]
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def set_dim(self, dim: int):
if "n_variable" in self.tags:
if dim < 2 or dim > 3:
warnings.warn("Alos is either a 2D or 3D benchmark problem.")
self.num_dim = dim
self.bounds = self.bounds[-1, :].reshape(1, 2)
self.bounds = self.bounds.repeat(dim, axis=0)
[docs]
def f(self, x, fid=1):
if fid == 1:
val = np.sin(21*(x[0] - 0.9)**4) * np.cos(2*(x[0] - 0.9)) + (x[0] - 0.7)/2
for i in range(1, self.num_dim):
prod = np.prod(x[:i+1])
val += (i+1) * x[i]**(i+1) * np.sin(prod)
return val
else:
val = self.f(x, fid=1)
num = val - 2 + np.sum(x)
term1 = 0.
for i in range(0, 2):
term1 += (i+1)*x[i]
term1 *= 0.25
term2 = 0.
for i in range(2, self.num_dim):
term2 += (i+1)*x[i]
term2 *= 0.25
denom = 5. + term1 - term2
return num/denom
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class MFRosenbrock(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 2 # could be variable with d -> [4, 7]
self.num_cstr = 0
self.num_fidelity = 3
self.num_obj = 1
self.bounds = np.array([[-2, 2]] * self.num_dim)
# self.costs = [0.1, 1]
self.objective = [
partial(self.f, fid=0),
partial(self.f, fid=1),
partial(self.f, fid=2),
]
# self.constraints = []
self.tags = [
"avt311",
"n_variable",
]
[docs]
def f(self, x, fid=2):
val = 0.
if fid == 2:
for i in range(self.num_dim-1):
val += 100*(x[i+1] - x[i]**2)**2 + (1 - x[i])**2
elif fid == 1:
for i in range(self.num_dim-1):
val += 50*(x[i+1] - x[i]**2)**2 + (-2 - x[i])**2
val -= 0.5*np.sum(x)
elif fid == 0:
sum_x = np.sum(x)
val = (self.f(x, fid=2) - 4. - 0.5*sum_x)/(10 + 0.25*sum_x)
else:
raise ValueError()
return val
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class MFRastrigin(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 2 # could be variable with d -> [4, 7]
self.num_cstr = 0
self.num_fidelity = 3
self.num_obj = 1
self.bounds = np.array([[-0.1, 0.2]] * self.num_dim)
# self.costs = [0.1, 1]
self.objective = [
partial(self.fi, phi=2_500),
partial(self.fi, phi=5_000),
partial(self.fi, phi=10_000),
]
# self.constraints = []
self.tags = [
"avt311",
"n_variable",
]
self.xStar = np.full(self.num_dim, 0.1)
self.theta = 0.2
self.Rmat = self.rotation_matrix(self.num_dim,
np.zeros((self.num_dim, self.num_dim-1)),
self.theta)
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def set_dim(self, dim: int):
if "n_variable" in self.tags:
self.num_dim = dim
self.bounds = self.bounds[-1, :].reshape(1, 2)
self.bounds = self.bounds.repeat(dim, axis=0)
self.xStar = np.full(self.num_dim, 0.1)
self.Rmat = self.rotation_matrix(self.num_dim,
np.zeros((self.num_dim, self.num_dim-1)),
self.theta)
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def f1(self, z):
return np.sum(z**2 + 1 - np.cos(10*np.pi*z))
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def z(self, x):
return self.Rmat @ (x - self.xStar)
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def resolution_error(self, z: np.ndarray, phi: float):
omega = 1 - phi/10_000
a = omega
w = 10*np.pi*omega
b = 0.5*np.pi*omega
return np.sum(a * np.cos(w*z + b + np.pi)**2)
[docs]
def rotation_matrix(self, n, v, theta):
"""
Aguilera-Perez algorithm
Parameters
----------
n : int
Dimension
v : (n, n-1) array
Input matrix
theta : float
Final rotation angle
Returns
-------
R : (n, n) array
Final rotation matrix
"""
v = v.copy().astype(float)
M = np.eye(n)
for c in range(n - 2):
for rr in range(n - 1, c, -1):
t = np.arctan2(v[rr, c], v[rr - 1, c])
R = np.eye(n)
# Givens rotation in (rr-1, rr)
coss = np.cos(t)
sins = np.sin(t)
R[rr, rr] = coss
R[rr, rr - 1] = sins
R[rr - 1, rr] = -sins
R[rr - 1, rr - 1] = coss
# v = R v
v1 = R @ v
v = v1
# M = R M
M1 = R @ M
M = M1
R = np.eye(n)
coss = np.cos(theta)
sins = np.sin(theta)
R[n - 1, n - 1] = coss
R[n - 1, n - 2] = sins
R[n - 2, n - 1] = -sins
R[n - 2, n - 2] = coss
B = R @ M
X = np.linalg.solve(M, B)
return X
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def fi(self, x: np.ndarray, phi: float):
z = self.z(x)
return self.f1(z) + self.resolution_error(z, phi)
[docs]
class Forrester(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 1 # could be variable with d -> [4, 7]
self.num_cstr = 0
self.num_fidelity = 4
self.num_obj = 1
self.bounds = np.array([[0, 1]] * self.num_dim)
# self.costs = [0.1, 1]
self.objective = [
partial(self.f, fid=0),
partial(self.f, fid=1),
partial(self.f, fid=2),
partial(self.f, fid=3),
]
# self.constraints = []
self.tags = [
"avt311",
]
[docs]
def f(self, x, fid=3):
if fid == 3:
f = ((6.0 * x - 2.0) ** 2.0) * np.sin(12.0 * x - 4.0)
elif fid == 2:
f = ((5.50 * x - 2.5) ** 2.0) * np.sin(12.0 * x - 4.0)
elif fid == 1:
f = 0.75 * self.f(x) + 5.0 * (x - 0.5) - 2.0
else:
f = 0.5 * self.f(x) + 10.0 * (x - 0.5) - 5.0
return f
[docs]
class DiscForrester(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 1 # could be variable with d -> [4, 7]
self.num_cstr = 0
self.num_fidelity = 2
self.num_obj = 1
self.bounds = np.array([[0, 1]] * self.num_dim)
# self.costs = [0.1, 1]
self.objective = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
# self.constraints = []
self.tags = [
"avt311",
]
[docs]
def f(self, x, fid=1):
if x <= 0.5:
f = ((6.0 * x - 2.0) ** 2.0) * np.sin(12.0 * x - 4.0)
elif x > 0.5:
f = 10 + ((6.0 * x - 2.0) ** 2.0) * np.sin(12.0 * x - 4.0)
if fid == 0:
if x <= 0.5:
f = 0.5 * f + 10.0 * (x - 0.5) - 5.0
elif x > 0.5:
f = 0.5 * f + 10.0 * (x - 0.5) - 7.0
return f
