1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
|
import numpy as np
from cmaes.cmasop import CMASoP
def example1():
"""
example with benchmark on sets of points
"""
# number of total dimensions
dim = 10
# number of dimensions in each subspace
subspace_dim = 2
# number of points in each subspace
point_num = 10
# objective function
def quadratic(x):
coef = 1000 ** (np.arange(dim) / float(dim - 1))
return np.sum((x * coef) ** 2)
# sets_of_points (on [-5, 5])
discrete_subspace_num = dim // subspace_dim
sets_of_points = (
2 * np.random.rand(discrete_subspace_num, point_num, subspace_dim) - 1
) * 5
# add the optimal solution (for benchmark function)
sets_of_points[:, -1] = np.zeros(subspace_dim)
np.random.shuffle(sets_of_points)
# optimizer (CMA-ES-SoP)
optimizer = CMASoP(
sets_of_points=sets_of_points,
mean=np.random.rand(dim) * 4 + 1,
sigma=2.0,
)
best_eval = np.inf
eval_count = 0
for generation in range(200):
solutions = []
for _ in range(optimizer.population_size):
# Ask a parameter
x, enc_x = optimizer.ask()
value = quadratic(enc_x)
# save best eval
best_eval = np.min((best_eval, value))
eval_count += 1
solutions.append((x, value))
# Tell evaluation values.
optimizer.tell(solutions)
print(f"#{generation} ({best_eval} {eval_count})")
if best_eval < 1e-4 or optimizer.should_stop():
break
def example2():
"""
example with benchmark on mixed variable (sets of points and continuous variable)
"""
# number of total dimensions
dim = 10
# number of dimensions in each subspace
subspace_dim = 2
# number of points in each subspace
point_num = 10
# objective function
def quadratic(x):
coef = 1000 ** (np.arange(dim) / float(dim - 1))
return np.sum((x * coef) ** 2)
# sets_of_points (on [-5, 5])
# almost half of the subspaces are continuous spaces
discrete_subspace_num = (dim // 2) // subspace_dim
sets_of_points = (
2 * np.random.rand(discrete_subspace_num, point_num, subspace_dim) - 1
) * 5
# add the optimal solution (for benchmark function)
sets_of_points[:, -1] = np.zeros(subspace_dim)
np.random.shuffle(sets_of_points)
# optimizer (CMA-ES-SoP)
optimizer = CMASoP(
sets_of_points=sets_of_points,
mean=np.random.rand(dim) * 4 + 1,
sigma=2.0,
)
best_eval = np.inf
eval_count = 0
for generation in range(200):
solutions = []
for _ in range(optimizer.population_size):
# Ask a parameter
x, enc_x = optimizer.ask()
value = quadratic(enc_x)
# save best eval
best_eval = np.min((best_eval, value))
eval_count += 1
solutions.append((x, value))
# Tell evaluation values.
optimizer.tell(solutions)
print(f"#{generation} ({best_eval} {eval_count})")
if best_eval < 1e-4 or optimizer.should_stop():
break
def example3():
"""
example with benchmark on mixed variable
(continuous variable and sets of points with different numbers of dimensions and points)
"""
# numbers of dimensions in each subspace
subspace_dim_list = [2, 3, 5]
cont_dim = 10
# numbers of points in each subspace
point_num_list = [10, 20, 40]
# number of total dimensions
dim = int(np.sum(subspace_dim_list) + cont_dim)
# objective function
def quadratic(x):
coef = 1000 ** (np.arange(dim) / float(dim - 1))
return np.sum((coef * x) ** 2)
# sets_of_points (on [-5, 5])
discrete_subspace_num = len(subspace_dim_list)
sets_of_points = [
(2 * np.random.rand(point_num_list[i], subspace_dim_list[i]) - 1) * 5
for i in range(discrete_subspace_num)
]
# add the optimal solution (for benchmark function)
for i in range(discrete_subspace_num):
sets_of_points[i][-1] = np.zeros(subspace_dim_list[i])
np.random.shuffle(sets_of_points[i])
# optimizer (CMA-ES-SoP)
optimizer = CMASoP(
sets_of_points=sets_of_points,
mean=np.random.rand(dim) * 4 + 1,
sigma=2.0,
)
best_eval = np.inf
eval_count = 0
for generation in range(400):
solutions = []
for _ in range(optimizer.population_size):
# Ask a parameter
x, enc_x = optimizer.ask()
value = quadratic(enc_x)
# save best eval
best_eval = np.min((best_eval, value))
eval_count += 1
solutions.append((x, value))
# Tell evaluation values.
optimizer.tell(solutions)
print(f"#{generation} ({best_eval} {eval_count})")
if best_eval < 1e-4 or optimizer.should_stop():
break
if __name__ == "__main__":
example1()
example2()
# example3()
|
