"""
Paper: https://arxiv.org/pdf/2204.07867
Code: https://gitlab.com/qudo046/avt-331-l1-benchmarks
"""
from functools import partial
import math
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.bounds = np.array([
[0, 1],
])
# self.costs = [0.15/9, 1]
self.objectives = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
self.constraints = []
self.tags = [
"avt311"
]
[docs]
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 Alos2(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 2
self.num_cstr = 0
self.num_fidelity = 2
self.bounds = np.array([
[0, 1],
[0, 1],
])
# self.costs = [0.15/9, 1]
self.objectives = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
self.constraints = []
self.tags = [
"avt311"
]
[docs]
def f(self, x, fid=1):
if fid == 1:
return math.sin(21.0*(x[0]-0.9)**4)*math.cos(2.0*(x[0]-0.9))+(x[0]-0.7)/2.0+ 2.0*x[1]**2*math.sin(x[0]*x[1])
else:
return (self.f(x)-2.0+x[0]+x[1])/(5.0+0.25*x[0]+0.5*x[1])
[docs]
class Alos3(BenchmarkProblem):
def __init__(self):
super().__init__()
self.num_dim = 3
self.num_cstr = 0
self.num_fidelity = 2
self.bounds = np.array([[0, 1]] * self.num_dim)
# self.costs = [0.15/9, 1]
self.objectives = [
partial(self.f, fid=0),
partial(self.f, fid=1),
]
self.constraints = []
self.tags = [
"avt311"
]
[docs]
def f(self, x, fid=1):
if fid == 1:
return math.sin(21.0 * (x[0] - 0.9) ** 4) * math.cos(2.0 * (x[0] - 0.9)) + (x[0] - 0.7) / 2.0 + 2.0 * x[1] ** 2 * math.sin(x[0] * x[1]) + 3.0 * x[2] ** 3 * math.sin(x[0] * x[1] * x[2])
else:
return (f(x) - 2.0 + x[0] + x[1] + x[2]) / (5.0 + 0.25 * x[0] + 0.5 * x[1] - 0.75 * x[2])
[docs]
class MFRosenbrock2D(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.bounds = np.array([[-2, 2]] * self.num_dim)
# self.costs = [0.1, 1]
self.objectives = [
partial(self.f, fid=0),
partial(self.f, fid=1),
partial(self.f, fid=2),
]
self.constraints = []
self.tags = [
"avt311"
]
[docs]
def f(self, x, fid=2):
f = 0
# high fidelity
if fid == 2:
for k in range(self.num_dim - 1):
f += 100.0 * (x[k + 1] - x[k] ** 2) ** 2 + (1.0 - x[k]) ** 2
# medium fidelity
elif fid == 1:
for k in range(self.num_dim - 1):
f += 50.0 * (x[k + 1] - x[k] ** 2) ** 2 + (-2.0 - x[k]) ** 2 - 0.5 * x[k]
f -= 0.5 * x[self.num_dim - 1]
# low fidelity
if fid == 0:
for k in range(self.num_dim - 1):
f += 100.0 * (x[k + 1] - x[k] ** 2) ** 2 + (1.0 - x[k]) ** 2
b0 = 4.0
bi = [0.5 for x in range(self.num_dim)]
a0 = 10.0
ai = [0.25 for x in range(self.num_dim)] # Be careful that the denom != 0
# subtract additive terms
delta = b0
for i in range(self.num_dim):
delta = delta + bi[i] * x[i]
uval = f - delta
# divide by multiplicative terms
fac = a0
for i in range(self.num_dim):
fac = fac + ai[i] * x[i]
uval = uval / fac
f = uval
return f
[docs]
class MFRastrigin2D(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.bounds = np.array([[-0.1, 0.2]] * self.num_dim)
# self.costs = [0.1, 1]
self.objectives = [
partial(self.f, fid=0),
partial(self.f, fid=1),
partial(self.f, fid=2),
]
self.constraints = []
self.tags = [
"avt311"
]
self.xStar = [0.1 for x in range(self.num_dim)]
self.Xtrasla = [0.0 for x in range(self.num_dim)]
self.Theta = 0.2
self.Rmat = [[math.cos(self.Theta), -math.sin(self.Theta)], [math.sin(self.Theta), math.cos(self.Theta)]]
[docs]
def f(self, x, fid=2):
for k in range(self.num_dim):
self.Xtrasla[k] = x[k] - self.xStar[k]
z = [0.0 for x in range(self.num_dim)]
for k in range(self.num_dim):
for j in range(self.num_dim):
z[k] += self.Rmat[k][j] * self.Xtrasla[j]
f = 0.0
for k in range(self.num_dim):
f += (z[k] ** 2.0 + 1.0 - math.cos(10.0 * math.pi * z[k]))
if fid == 2:
Phi = 10000.0
elif fid == 1:
Phi = 5000.0
else:
Phi = 2500.0
TH = 1.0 - 0.0001 * Phi
a = TH
w = 10.0 * math.pi * TH
b = 0.5 * math.pi * TH
er = 0.0
for k in range(self.num_dim):
er += a * (math.cos(w * z[k] + b + math.pi) ** 2.0)
f += er
return f
[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.bounds = np.array([[0, 1]] * self.num_dim)
# self.costs = [0.1, 1]
self.objectives = [
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) * math.sin(12.0 * x - 4.0)
elif fid == 2:
f = ((5.50 * x - 2.5) ** 2.0) * math.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.bounds = np.array([[0, 1]] * self.num_dim)
# self.costs = [0.1, 1]
self.objectives = [
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) * math.sin(12.0 * x - 4.0)
elif x > 0.5:
f = 10 + ((6.0 * x - 2.0) ** 2.0) * math.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
