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Copy path3 Tree-Structured Parzen Estimator.py
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3 Tree-Structured Parzen Estimator.py
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import numpy as np
import matplotlib.pyplot as plt
from memory_profiler import memory_usage
import time
from hyperopt import fmin, tpe, hp, Trials
# Define benchmark functions
def ackley(x):
x = np.array(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):
x = np.array(x)
return (x[0] + 2 * x[1] - 7)**2 + (2 * x[0] + x[1] - 5)**2
def rastrigin(x):
x = np.array(x)
A = 10
return A * len(x) + np.sum(x**2 - A * np.cos(2 * np.pi * x))
def rosenbrock(x):
x = np.array(x)
return np.sum(100 * (x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2)
def schwefel(x):
x = np.array(x)
return 418.9829 * len(x) - np.sum(x * np.sin(np.sqrt(np.abs(x))))
def sphere(x):
x = np.array(x)
return np.sum(x**2)
def michalewicz(x):
x = np.array(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):
x = np.array(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):
x = np.array(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):
x = np.array(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):
x = np.array(x)
return np.sum((x - 1)**2) - np.sum(x[:-1] * x[1:])
def dixon_price(x):
x = np.array(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):
x = np.array(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):
x = np.array(x)
return 1 + np.sum(x**2 / 4000) - np.prod(np.cos(x / np.sqrt(np.arange(1, len(x) + 1))))
def levy(x):
x = np.array(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):
x = np.array(x)
return 0.26 * (x[0]**2 + x[1]**2) - 0.48 * x[0] * x[1]
def goldstein_price(x):
x = np.array(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):
x = np.array(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):
x = np.array(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):
x = np.array(x)
return np.sum(np.abs(x))
def tpe_optimization(func, bounds, max_iter=200):
space = [hp.uniform(f"x{i}", b[0], b[1]) for i, b in enumerate(bounds)]
def objective(x):
return func(x)
trials = Trials()
best = fmin(objective, space, algo=tpe.suggest, max_evals=max_iter, trials=trials, rstate=np.random.default_rng(42))
return best, [t['result']['loss'] for t in trials.trials]
# Prepare 20 functions
functions = [
("1. Ackley", ackley, [(-5, 5)] * 2),
("2. Booth", booth, [(-5, 5)] * 2),
("3. Rastrigin", rastrigin, [(-5, 5)] * 2),
("4. Rosenbrock", rosenbrock, [(-5, 5)] * 2),
("5. Schwefel", schwefel, [(-500, 500)] * 2),
("6. Sphere", sphere, [(-5, 5)] * 2),
("7. Michalewicz", michalewicz, [(0, np.pi)] * 2),
("8. Zakharov", zakharov, [(-5, 5)] * 2),
("9. Eggholder", eggholder, [(-512, 512)] * 2),
("10. Beale", beale, [(-4.5, 4.5)] * 2),
("11. Trid", trid, [(-5, 5)] * 2),
("12. Dixon-Price", dixon_price, [(-5, 5)] * 2),
("13. Cross-in-Tray", cross_in_tray, [(-10, 10)] * 2),
("14. Griewank", griewank, [(-600, 600)] * 2),
("15. Levy", levy, [(-10, 10)] * 2),
("16. Matyas", matyas, [(-10, 10)] * 2),
("17. Goldstein-Price", goldstein_price, [(-2, 2)] * 2),
("18. Powell", powell, [(-5, 5)] * 4),
("19. Bird", bird, [(-2 * np.pi, 2 * np.pi)] * 2),
("20. Pyramid", pyramid, [(-5, 5)] * 2)
]
# Prepare the plot
fig, axes = plt.subplots(4, 4, figsize=(20, 20))
axes = axes.ravel()
# Run TPE Optimization and display results for all functions
for idx, (name, func, bounds) in enumerate(functions):
print(f"\nRunning {name}...")
start_time = time.time()
memory_before = memory_usage()[0]
best_x, costs = tpe_optimization(func, bounds, max_iter=200)
memory_after = memory_usage()[0]
end_time = time.time()
print(f"Function: {name}")
print(f"Best Cost: {min(costs) 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)")
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()