"""
Reference: Towards a multi-fidelity & multi-objective Bayesian optimization efficient algorithm
Rémy Charayron, Thierry Lefebvre, Nathalie Bartoli, Joseph Morlier
With multi-fidelity variant?
ZDT1, ZDT2, ZDT3, ZDT5 (w/ cstr)
DTLZ5
"""
import numpy as np
from smt_optim.benchmarks.base import BenchmarkProblem
[docs]
class ZDT1(BenchmarkProblem):
def __init__(self):
super().__init__()
# pareto-optimal front with g(x) = 1 (with discontinuity)
# num_dim from reference: 30
self.name: str = "ZDT1"
self.num_dim: int | str = "variable"
self.num_obj: int = 2
self.num_cstr: int = 0
self.num_fidelity = 1
self.tags = [
"n_variable",
"multi-obj",
"ZDT",
]
self.bounds = np.array(
[
[0, 1],
]
)
self.objective = [
self.f1,
self.f2,
]
[docs]
def f1(self, x):
return x[0]
[docs]
def g(self, x):
return 1 + 9 * np.sum(x[1:]) / (self.num_dim - 1)
[docs]
def h(self, f1, g):
return 1 - np.sqrt(f1 / g)
[docs]
def f2(self, x):
f1 = self.f1(x)
g = self.g(x)
return g * self.h(f1, g)
[docs]
class ZDT2(BenchmarkProblem):
def __init__(self):
super().__init__()
# pareto-optimal front with g(x) = 1 (with discontinuity)
# num_dim from reference: 30
self.name: str = "ZDT2"
self.num_dim: int | str = "variable"
self.num_obj: int = 2
self.num_cstr: int = 0
self.num_fidelity = 1
self.tags = [
"n_variable",
"multi-obj",
"ZDT",
]
self.bounds = np.array(
[
[0, 1],
]
)
self.objective = [
self.f1,
self.f2,
]
[docs]
def f1(self, x):
return x[0]
[docs]
def g(self, x):
return 1 + 9 * np.sum(x[1:]) / (self.num_dim - 1)
[docs]
def h(self, f1, g):
return 1 - (f1 / g) ** 2
[docs]
def f2(self, x):
f1 = self.f1(x)
g = self.g(x)
return g * self.h(f1, g)
[docs]
class ZDT3(BenchmarkProblem):
def __init__(self):
super().__init__()
# pareto-optimal front with g(x) = 1 (with discontinuity)
# num_dim from reference: 30
self.name: str = "ZDT3"
self.num_dim: int | str = "variable"
self.num_obj: int = 2
self.num_cstr: int = 0
self.num_fidelity = 1
self.tags = [
"n_variable",
"multi-obj",
"ZDT",
]
self.bounds = np.array(
[
[0, 1],
]
)
self.objective = [
self.f1,
self.f2,
]
[docs]
def f1(self, x):
return x[0]
[docs]
def g(self, x):
return 1 + 9 * np.sum(x[1:]) / (self.num_dim - 1)
[docs]
def h(self, f1, g):
return 1 - np.sqrt(f1 / g) - f1 / g * np.sin(10 * np.pi * f1)
[docs]
def f2(self, x):
f1 = self.f1(x)
g = self.g(x)
return g * self.h(f1, g)
[docs]
class ZDT4(BenchmarkProblem):
def __init__(self):
super().__init__()
# pareto-optimal front with g(x) = 1.25 (with discontinuity)
# num_dim from reference: 10
self.name: str = "ZDT4"
self.num_dim: int | str = "variable"
self.num_obj: int = 2
self.num_cstr: int = 0
self.num_fidelity = 1
self.tags = [
"n_variable",
"multi-obj",
"ZDT",
]
# custom set_dim class method
self.bounds = np.array(
[
[np.nan, np.nan],
]
)
self.objective = [
self.f1,
self.f2,
]
[docs]
def set_dim(self, dim):
if dim == 1:
raise Exception("ZDT4 dimension must be greater than 1.")
if "n_variable" in self.tags:
self.num_dim = dim
self.bounds = np.empty((dim, 2))
self.bounds[0, :] = [0, 1]
self.bounds[1:, :] = [-5, 5]
else:
raise Exception("Not a variable dimension problem.")
[docs]
def f1(self, x):
return x[0]
[docs]
def g(self, x):
return (
1 + 10 * (self.num_dim - 1) + np.sum(x[1:] - 10 * np.cos(4 * np.pi * x[1:]))
)
[docs]
def h(self, f1, g):
return 1 - np.sqrt(f1 / g)
[docs]
def f2(self, x):
f1 = self.f1(x)
g = self.g(x)
return g * self.h(f1, g)
# TODO: implement ZDT45 and ZDT46
if __name__ == "__main__":
import numpy as np
import matplotlib.pyplot as plt
# Instantiate your problem
problem = ZDT4()
problem.set_dim(2)
x1 = np.linspace(0, 1, 101)
x2 = np.linspace(0, 0, 101)
XX, YY = np.meshgrid(x1, x2)
data = np.vstack((XX.ravel(), YY.ravel())).T
f1 = np.empty(data.shape[0])
f2 = np.empty(data.shape[0])
for i in range(data.shape[0]):
f1[i] = problem.f1(data[i, :])
f2[i] = problem.f2(data[i, :])
F1 = f1.reshape(XX.shape)
F2 = f2.reshape(XX.shape)
fig, ax = plt.subplots()
ax.scatter(F1, F2, 5)
plt.show()
