"""
Reference: Efficient global optimization of constrained mixed variable problems
"""
import numpy as np
import smt.design_space as ds
from smt_optim.benchmarks.base import BenchmarkProblem
# MixVarBranin 4D (2 cont., 2 cat.)
# MixVarAugmentedBranin 12D (10 cont., 2 cat.)
# MixVarAugmentedBranin 12D (10 cont., 2 cat.)
# MixVarGoldstein (2 cont., 2 cat.)
[docs]
class MixVarBranin(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "MixVarBranin"
self.num_dim = 4
self.num_obj = 1
self.num_cstr = 1
self.num_fidelity = 1
self.design_space = ds.DesignSpace([
ds.FloatVariable(0, 1),
ds.FloatVariable(0, 1),
ds.CategoricalVariable([0, 1]),
ds.CategoricalVariable([0, 1]),
])
self.constraints = [self.constraint]
[docs]
def h(self, x):
term1 = 15 * x[1] - (5 / (4 * np.pi ** 2)) * (15 * x[0] - 5) ** 2 \
+ (5 / np.pi) * (15 * x[0] - 5) - 6
term2 = 10 * (1 - 1 / (8 * np.pi)) * np.cos(15 * x[0] - 5)
value = (term1 ** 2 + term2 + 10 - 54.8104) / 51.9496
return value
[docs]
def objective(self, x):
h_val = self.h(x[:2])
z = x[2:]
if z[0] == 0 and z[1] == 0:
return h_val
elif z[0] == 0 and z[1] == 1:
return 0.4 * h_val
elif z[0] == 1 and z[1] == 0:
return -0.75 * h_val + 3.0
elif z[0] == 1 and z[1] == 1:
return -0.5 * h_val + 1.4
return np.nan
[docs]
def constraint(self, x):
z = x[2:]
g = np.nan
if z[0] == 0 and z[1] == 0:
g = x[0] * x[1] - 0.4
elif z[0] == 0 and z[1] == 1:
g = 1.5 * x[0] * x[1] - 0.4
elif z[0] == 1 and z[1] == 0:
g = 1.5 * x[0] * x[1] - 0.2
elif z[0] == 1 and z[1] == 1:
g = 1.2 * x[0] * x[1] - 0.3
return -g
[docs]
class MixVarGoldstein(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "MixVarGoldstein"
self.num_dim = 4
self.num_obj = 1
self.num_cstr = 1
self.num_fidelity = 1
self.design_space = ds.DesignSpace([
ds.FloatVariable(0, 100),
ds.FloatVariable(0, 100),
ds.CategoricalVariable([0, 1, 2]),
ds.CategoricalVariable([0, 1, 2]),
])
self.constraints = [self.constraint]
self.x3_table = np.array([
[20, 50, 80],
[20, 50, 80],
[20, 50, 80],
])
self.x4_table = np.array([
[20, 20, 20],
[50, 50, 50],
[80, 80, 80],
])
self.c1_table = np.array([
[2, -2, 1],
[2, -2, 1],
[2, -2, 1],
])
self.c2_table = np.array([
[0.5, 0.5, 0.5],
[-1, -1, -1],
[-2, -2, -2],
])
[docs]
def h(self, x):
x1, x2, x3, x4 = x
value = (
53.3108
+ 0.184901 * x1
- 5.02914e-6 * x1**3
+ 7.72522e-8 * x1**4
- 0.0870775 * x2
- 0.106959 * x3
+ 7.98772e-6 * x3**3
+ 0.00242482 * x4
+ 1.32851e-6 * x4**3
- 0.00146393 * x1 * x2
- 0.00301588 * x1 * x3
- 0.00272291 * x1 * x4
+ 0.0017004 * x2 * x3
+ 0.0038428 * x2 * x4
- 0.000198969 * x3 * x4
+ 1.86025e-5 * x1 * x2 * x3
- 1.88719e-6 * x1 * x2 * x4
+ 2.50923e-5 * x1 * x3 * x4
- 5.62199e-5 * x2 * x3 * x4
)
return value
[docs]
def objective(self, x):
x1, x2 = x[0], x[1]
z1, z2 = int(x[2]), int(x[3])
x3 = self.x3_table[z2, z1]
x4 = self.x4_table[z2, z1]
return self.h([x1, x2, x3, x4])
[docs]
def constraint(self, x):
x1, x2 = x[0], x[1]
z1, z2 = int(x[2]), int(x[3])
c1 = self.c1_table[z2, z1]
c2 = self.c2_table[z2, z1]
value = (
c1 * np.sin(x1 / 10.0) ** 3
+ c2 * np.cos(x2 / 20.0) ** 2
)
return -value
[docs]
class MultiFidelityMixVarBranin(BenchmarkProblem):
def __init__(self):
super().__init__()
self.name = "MultiFidelityMixVarBranin"
self.num_dim = 4
self.num_obj = 1
self.num_cstr = 1
self.num_fidelity = 2
self.design_space = ds.DesignSpace([
ds.FloatVariable(0, 1),
ds.FloatVariable(0, 1),
ds.CategoricalVariable([0, 1]),
ds.CategoricalVariable([0, 1]),
])
self.children = MixVarBranin()
self.objective = [self.objective_lf, self.children.objective]
self.constraints = [
[self.constraint_lf, self.children.constraint]
]
[docs]
def objective_lf(self, x):
return self.children.objective(x) - np.cos(0.5*x[0]) - x[1]**3
[docs]
def constraint_lf(self, x):
return self.children.constraint(x) - 0.1 * np.sin(10*x[0] + 5*x[1])
if __name__ == "__main__":
import numpy as np
import matplotlib.pyplot as plt
# Instantiate your problem
problem = MixVarBranin()
# Continuous domain of the Branin function
x1 = np.linspace(0.0, 1.0, 300)
x2 = np.linspace(0.0, 1.0, 300)
X1, X2 = np.meshgrid(x1, x2)
# All 4 combinations of z1, z2
z_combinations = [
(0, 0),
(0, 1),
(1, 0),
(1, 1),
]
fig = plt.figure(figsize=(14, 10))
for i, (z1, z2) in enumerate(z_combinations, start=1):
F = np.zeros_like(X1)
for r in range(X1.shape[0]):
for c in range(X1.shape[1]):
x = np.array([X1[r, c], X2[r, c], z1, z2])
F[r, c] = problem.objective(x)
ax = fig.add_subplot(2, 2, i, projection="3d")
surf = ax.plot_surface(X1, X2, F, cmap="viridis", edgecolor="none")
ax.set_title(f"z1={z1}, z2={z2}")
ax.set_xlabel("x1")
ax.set_ylabel("x2")
ax.set_zlabel("f(x1, x2, z1, z2)")
fig.colorbar(surf, ax=ax, shrink=0.7, pad=0.1)
plt.tight_layout()
plt.show()
