"""
Reference: https://www.sfu.ca/~ssurjano/optimization.html
"""
import numpy as np
from smt_optim.benchmarks.base import BenchmarkProblem
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class Ackley(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Ackley"
self.num_dim: int | str = "variable"
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[0, 40],
])
self.a = 20
self.b = 0.2
self.c = 2*np.pi
self.exp1 = np.exp(1)
self.tags = [
"sfu",
"n_variable",
]
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def objective(self, x):
sum1 = 0
sum2 = 0
for i in range(self.num_dim):
sum1 += x[i]**2
sum2 += np.cos(self.c*x[i])
term1 = -self.a * np.exp(-self.b * np.sqrt(sum1 / self.num_dim))
term2 = -np.exp(sum2 / self.num_dim)
return term1 + term2 + self.a + self.exp1
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class Bukin6(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Bukin6"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-15, 5],
[-3, 3],
])
self.tags = [
"sfu",
]
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def objective(self, x):
term1 = 100 * np.sqrt(abs(x[1] - 0.01*x[0]**2))
term2 = 0.01 * abs(x[0] + 10)
return term1 + term2
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class CrossInTray(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "CrossInTray"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-5.12, 5.12],
[-5.12, 5.12],
])
self.tags = [
"sfu",
]
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def objective(self, x):
fact1 = np.sin(x[0]) * np.sin(x[1])
fact2 = np.exp(abs(100 - np.sqrt(x[0] ** 2 + x[1] ** 2) / np.pi))
return -0.0001 * (abs(fact1 * fact2) + 1) ** 0.1
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class DropWave(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "DropWave"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-10, 10],
[-10, 10],
])
self.tags = [
"sfu",
]
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def objective(self, x):
frac1 = 1 + np.cos(12 * np.sqrt(x[0] ** 2 + x[1] ** 2))
frac2 = 0.5 * (x[0] ** 2 + x[1] ** 2) + 2
return -frac1 / frac2
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class EggHolder(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "EggHolder"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-512, 512],
[-514, 512],
])
self.tags = [
"sfu",
]
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def objective(self, x):
term1 = -(x[1] + 47) * np.sin(np.sqrt(abs(x[1] + x[0] / 2 + 47)))
term2 = -x[0] * np.sin(np.sqrt(abs(x[0] - (x[1] + 47))))
return term1 + term2
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class GramacyLee(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "GramacyLee"
self.num_dim = 1
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[0.5, 2.5],
])
self.tags = [
"sfu",
]
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def objective(self, x):
term1 = np.sin(10 * np.pi * x) / (2 * x)
term2 = (x - 1) ** 4
return term1 + term2
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class Griewank(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Griewank"
self.num_dim: int | str = "variable"
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-600, 600],
])
self.tags = [
"sfu",
"n_variable",
]
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def objective(self, x):
term1 = 0
term2 = 1
for i in range(self.num_dim):
term1 += x[i] ** 2 / 4000
term2 *= np.cos(x[i] / np.sqrt(float(i+1)))
return term1 - term2 + 1
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class HolderTable(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "HolderTable"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-10, 10],
[-10, 10],
])
self.tags = [
"sfu",
]
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def objective(self, x):
fact1 = np.sin(x[0]) * np.cos(x[1])
fact2 = np.exp(abs(1 - np.sqrt(x[0] ** 2 + x[1] ** 2) / np.pi))
return -abs(fact1 * fact2)
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class Langermann(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Langermann"
self.num_dim = 2 # could be variable
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[0, 10],
[0, 10],
])
self.tags = [
"sfu",
]
self.m = 5
self.c = np.array([1, 2, 5, 2, 3])
self.A = np.array([
[3, 5],
[5, 2],
[2, 1],
[1, 4],
[7, 9],
])
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def objective(self, x):
outer = 0
for i in range(self.m):
inner = 0
for j in range(self.num_dim):
inner += (x[j] - self.A[i, j]) ** 2
new = self.c[i] * np.exp(-inner / np.pi) * np.cos(np.pi * inner)
outer += new
return outer
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class Levy(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Levy"
self.num_dim: int | str = "variable"
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-10, 10],
])
self.tags = [
"sfu",
"n_variable",
]
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def objective(self, x):
w = np.empty(self.num_dim)
for i in range(self.num_dim):
w[i] = 1 + (x[i] - 1) / 4
term1 = (np.sin(np.pi * w[0])) ** 2
term3 = (w[self.num_dim-1] - 1) ** 2 * (1 + (np.sin(2 * np.pi * w[self.num_dim-1])) ** 2)
term2 = 0
for i in range(self.num_dim-1):
new = (w[i] - 1) ** 2 * (1 + 10 * (np.sin(np.pi * w[i] + 1)) ** 2)
term2 += new
return term1 + term2 + term3
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class Levy13(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Levy"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-10, 10],
[-10, 10],
])
self.tags = [
"sfu",
]
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def objective(self, x):
term1 = (np.sin(3 * np.pi * x[0])) ** 2
term2 = (x[0] - 1) ** 2 * (1 + (np.sin(3 * np.pi * x[1])) ** 2)
term3 = (x[1] - 1) ** 2 * (1 + (np.sin(2 * np.pi * x[1])) ** 2)
return term1 + term2 + term3
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class Rastrigin(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Rastrigin"
self.num_dim: int | str = "variable"
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-5.12, 5.12],
])
self.tags = [
"sfu",
"n_variable",
]
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def objective(self, x):
term1 = 0
for i in range(self.num_dim):
term1 += (x[i] ** 2 - 10 * np.cos(2 * np.pi * x[i]))
return 10 * self.num_dim + term1
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class Schaffer2(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Schaffer2"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-100, 100],
[-100, 100]
])
self.tags = [
"sfu",
]
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def objective(self, x):
fact1 = (np.sin(x[0] ** 2 - x[1] ** 2)) ** 2 - 0.5
fact2 = (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2
return 0.5 + fact1 / fact2
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class Schaffer4(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Schaffer4"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-100, 100],
[-100, 100]
])
self.tags = [
"sfu",
]
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def objective(self, x):
fact1 = (np.cos(np.sin(abs(x[0] ** 2 - x[1] ** 2)))) ** 2 - 0.5
fact2 = (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2
return 0.5 + fact1 / fact2
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class Schwefel(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Schwefel"
self.num_dim: int | str = "variable"
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-500, 500],
])
self.tags = [
"sfu",
"n_variable",
]
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def objective(self, x):
term1 = 0
for i in range(self.num_dim):
term1 += x[i] * np.sin(np.sqrt(abs(x[i])))
return 418.9829 * self.num_dim - term1
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class Shubert(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "Shubert"
self.num_dim = 2
self.num_obj = 1
self.num_cstr = 0
self.num_fidelity = 1
self.bounds = np.array([
[-5.12, 5.12],
[-5.12, 5.12],
])
self.tags = [
"sfu",
]
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def objective(self, x):
sum1 = 0
sum2 = 0
for i in range(5):
new1 = i * np.cos((i + 1) * x[0] + i)
new2 = i * np.cos((i + 1) * x[1] + i)
sum1 += new1
sum2 += new2
return sum1 * sum2
