-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy path0 Stochastic Gradient Descent.py
160 lines (129 loc) · 5.53 KB
/
0 Stochastic Gradient Descent.py
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
import numpy as np
import matplotlib.pyplot as plt
from memory_profiler import memory_usage
import time
# Define benchmark functions
def ackley(x):
a, b, c = 20, 0.2, 2 * np.pi
d = len(x)
sum1 = np.sum(x**2)
sum2 = np.sum(np.cos(c * x))
return -a * np.exp(-b * np.sqrt(sum1 / d)) - np.exp(sum2 / d) + a + np.exp(1)
def booth(x):
return (x[0] + 2 * x[1] - 7)**2 + (2 * x[0] + x[1] - 5)**2
def rastrigin(x):
A = 10
return A * len(x) + np.sum(x**2 - A * np.cos(2 * np.pi * x))
def rosenbrock(x):
return np.sum(100 * (x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2)
def schwefel(x):
return 418.9829 * len(x) - np.sum(x * np.sin(np.sqrt(np.abs(x))))
def sphere(x):
return np.sum(x**2)
def michalewicz(x):
m = 10
return -np.sum(np.sin(x) * np.sin(((np.arange(len(x)) + 1) * x**2) / np.pi)**(2 * m))
def zakharov(x):
sum1 = np.sum(x**2)
sum2 = np.sum(0.5 * (np.arange(len(x)) + 1) * x)
return sum1 + sum2**2 + sum2**4
def eggholder(x):
return -(x[1] + 47) * np.sin(np.sqrt(abs(x[0]/2 + (x[1] + 47)))) - x[0] * np.sin(np.sqrt(abs(x[0] - (x[1] + 47))))
def beale(x):
return (1.5 - x[0] + x[0]*x[1])**2 + (2.25 - x[0] + x[0]*x[1]**2)**2 + (2.625 - x[0] + x[0]*x[1]**3)**2
def trid(x):
return np.sum((x - 1)**2) - np.sum(x[:-1] * x[1:])
def dixon_price(x):
return (x[0] - 1)**2 + np.sum([(i + 1) * (2 * x[i]**2 - x[i-1])**2 for i in range(1, len(x))])
def cross_in_tray(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
def griewank(x):
return 1 + np.sum(x**2 / 4000) - np.prod(np.cos(x / np.sqrt(np.arange(1, len(x) + 1))))
def levy(x):
w = 1 + (x - 1) / 4
term1 = np.sin(np.pi * w[0])**2
term2 = np.sum((w[:-1] - 1)**2 * (1 + 10 * np.sin(np.pi * w[:-1] + 1)**2))
term3 = (w[-1] - 1)**2 * (1 + np.sin(2 * np.pi * w[-1])**2)
return term1 + term2 + term3
def matyas(x):
return 0.26 * (x[0]**2 + x[1]**2) - 0.48 * x[0] * x[1]
def goldstein_price(x):
term1 = 1 + ((x[0] + x[1] + 1)**2) * (19 - 14*x[0] + 3*x[0]**2 - 14*x[1] + 6*x[0]*x[1] + 3*x[1]**2)
term2 = 30 + ((2*x[0] - 3*x[1])**2) * (18 - 32*x[0] + 12*x[0]**2 + 48*x[1] - 36*x[0]*x[1] + 27*x[1]**2)
return term1 * term2
def powell(x):
term1 = (x[0] + 10*x[1])**2
term2 = 5 * (x[2] - x[3])**2
term3 = (x[1] - 2*x[2])**4
term4 = 10 * (x[0] - x[3])**4
return term1 + term2 + term3 + term4
def bird(x):
return np.sin(x[0]) * np.exp((1 - np.cos(x[1]))**2) + np.cos(x[1]) * np.exp((1 - np.sin(x[0]))**2) + (x[0] - x[1])**2
def pyramid(x):
return np.sum(np.abs(x))
def numerical_gradient(func, x, epsilon=1e-6):
grad = np.zeros_like(x)
for i in range(len(x)):
x1, x2 = x.copy(), x.copy()
x1[i] += epsilon
x2[i] -= epsilon
grad[i] = (func(x1) - func(x2)) / (2 * epsilon)
return grad
def stochastic_gradient_descent(func, x0, lr=0.01, max_iter=200):
x = np.array(x0)
costs = []
for _ in range(max_iter):
grad = numerical_gradient(func, x)
# Choose a random dimension to update (stochastic part)
idx = np.random.randint(0, len(x))
x[idx] -= lr * grad[idx]
costs.append(func(x))
return x, costs
# Prepare 20 functions
functions = [
("1. Ackley", ackley, np.random.uniform(-5, 5, 2)),
("2. Booth", booth, np.random.uniform(-5, 5, 2)),
("3. Rastrigin", rastrigin, np.random.uniform(-5, 5, 2)),
("4. Rosenbrock", rosenbrock, np.random.uniform(-5, 5, 2)),
("5. Schwefel", schwefel, np.random.uniform(-500, 500, 2)),
("6. Sphere", sphere, np.random.uniform(-5, 5, 2)),
("7. Michalewicz", michalewicz, np.random.uniform(0, np.pi, 2)),
("8. Zakharov", zakharov, np.random.uniform(-5, 5, 2)),
("9. Eggholder", eggholder, np.random.uniform(-512, 512, 2)),
("10. Beale", beale, np.random.uniform(-4.5, 4.5, 2)),
("11. Trid", trid, np.random.uniform(-5, 5, 2)),
("12. Dixon-Price", dixon_price, np.random.uniform(-5, 5, 2)),
("13. Cross-in-Tray", cross_in_tray, np.random.uniform(-10, 10, 2)),
("14. Griewank", griewank, np.random.uniform(-600, 600, 2)),
("15. Levy", levy, np.random.uniform(-10, 10, 2)),
("16. Matyas", matyas, np.random.uniform(-10, 10, 2)),
("17. Goldstein-Price", goldstein_price, np.random.uniform(-2, 2, 2)),
("18. Powell", powell, np.random.uniform(-5, 5, 4)),
("19. Bird", bird, np.random.uniform(-2 * np.pi, 2 * np.pi, 2)),
("20. Pyramid", pyramid, np.random.uniform(-5, 5, 2))
]
# Prepare the plot
fig, axes = plt.subplots(4, 4, figsize=(20, 20))
axes = axes.ravel()
# Run Stochastic Gradient Descent and display results for all functions
for idx, (name, func, x0) in enumerate(functions):
print(f"\nRunning {name}...")
start_time = time.time()
memory_before = memory_usage()[0]
best_x, costs = stochastic_gradient_descent(func, x0, lr=0.01, max_iter=100)
memory_after = memory_usage()[0]
end_time = time.time()
print(f"Function: {name}")
print(f"Best Cost: {costs[-1] if costs else 'N/A'}")
print(f"Convergence Time: {end_time - start_time} seconds")
print(f"Memory Usage: {max(0, memory_after - memory_before)} MB")
print("Complexity Class: O(n * d)")
if idx < len(axes):
axes[idx].plot(costs)
axes[idx].set_title(name)
axes[idx].set_xlabel("Iterations")
axes[idx].set_ylabel("Cost")
plt.tight_layout()
plt.show()