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| import os
import matplotlib
matplotlib.use('TkAgg')
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
"""
目标函数：Rastrigin函数的最小值
"""
def objective_function(x: list):
A = 10
n = len(x)
return A * n + sum([xi ** 2 - A * np.cos(2 * np.pi * xi) for xi in x])
def simulated_annealing(initial_state: list, objective_function,
initial_temperature: float = 100, cool_rate: float = 0.95,
num_iterations: float = 1000, perturbation_scale: float = 0.1):
"""
模拟退火函数
:param initial_state:初始状态
:param objective_function:目标函数
:param initial_temperature:初始温度
:param cool_rate:冷却系数
:param num_iterations:迭代次数
:param perturbation_scale:扰动大小
:return:结果
"""
current_state = initial_state.copy()
best_state = initial_state.copy()
current_energy = objective_function(current_state)
best_energy = current_energy
energies = [current_energy]
temperatures = [initial_temperature]
states = [current_state.copy()]
best_states = []
temperature = initial_temperature
for iteration in range(num_iterations):
neighbor = current_state + np.random.normal(0, perturbation_scale, len(current_state))
neighbor_energy = objective_function(neighbor)
delta_energy = neighbor_energy - current_energy
if delta_energy < 0 or np.random.rand() < np.exp(-delta_energy / temperature):
current_state = neighbor
current_energy = neighbor_energy
if current_energy < best_energy:
best_state = current_state.copy()
best_energy = current_energy
temperature *= cool_rate
energies.append(current_energy)
temperatures.append(temperature)
states.append(current_state.copy())
best_states.append(best_state.copy())
if (iteration + 1) % 100 == 0:
print(f"Iteration {iteration + 1}/{num_iterations}, "
f"Current Energy: {current_energy:.4f}, "
f"Best Energy: {best_energy:.4f}, "
f"Temperature: {temperature:.4f}")
return {
'best_state': best_state,
'best_energy': best_energy,
'energies': np.array(energies),
'temperatures': np.array(temperatures),
'states': np.array(states),
'best_states_every_10': np.array(best_states)
}
seed = int.from_bytes(os.urandom(4), byteorder='big', signed=False)
print("种子", seed)
np.random.seed(seed)
initial_state = np.random.uniform(-5.12, 5.12, 2)
print("initial_state", initial_state)
result = simulated_annealing(
initial_state,
objective_function,
initial_temperature=100,
cool_rate=0.99,
num_iterations=2000,
perturbation_scale=0.5
)
best_state = result['best_state']
print("最终结果", best_state, "误差", np.sqrt(best_state[0] ** 2 + best_state[1] ** 2))
best_states = result['best_states_every_10']
x_opt = best_states[:, 0]
y_opt = best_states[:, 1]
x = np.linspace(-5.12, 5.12, 200)
y = np.linspace(-5.12, 5.12, 200)
X, Y = np.meshgrid(x, y)
Z = objective_function([X.ravel(), Y.ravel()]).reshape(X.shape)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(18, 6))
contour = ax1.contourf(X, Y, Z, levels=20, cmap='coolwarm')
fig.colorbar(contour, ax=ax1, label='目标函数值')
ax1.set_title(f'Rastrigin函数等高线图，种子={seed}')
ax1.set_xlabel('x1')
ax1.set_ylabel('x2')
ax1.scatter(result['best_state'][0], result['best_state'][1], c='green', s=100,
label='最终最优解', edgecolors='black', zorder=3)
ax1.scatter(initial_state[0], initial_state[1], c='yellow', s=100,
label='初始点', edgecolors='black', zorder=3)
ax1.plot(x_opt, y_opt, 'r-o', linewidth=2, markersize=4, label='优化路径', zorder=2)
for i, (xi, yi) in enumerate(best_states):
ax1.text(xi + 0.5, yi, f'{i + 1}', color='purple', fontsize=10,
ha='center', va='center', bbox=dict(facecolor='white', alpha=0.7), zorder=1)
ax1.set_aspect('equal', adjustable='box')
ax1.set_xlim(-5.12, 5.12)
ax1.set_ylim(-5.12, 5.12)
ax1.legend()
ax1.grid(True)
ax2.plot(result['energies'], label='能量变化', color='blue', linewidth=1)
ax2.set_title('能量变化')
ax2.set_xlabel('迭代次数')
ax2.set_ylabel('能量值')
ax2.legend()
ax2.grid(True)
plt.tight_layout()
plt.show()
|
