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| import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
def objective_function(x):
if x.ndim == 1:
x = x.reshape(1, -1)
A = 10
n = x.shape[1]
return A * n + np.sum(x**2 - A * np.cos(2 * np.pi * x), axis=1)
def analytical_gradient(x):
A = 10
return 2 * x + 2 * np.pi * A * np.sin(2 * np.pi * x)
def water_flow_erosion_optimizer(
func,
grad_func,
bounds,
n_droplets=50,
max_iterations=1000,
learning_rate=0.1,
erosion_rate=0.2,
decay_rate=0.95,
random_perturbation_scale=0.05,
grid_res=50,
verbose=False
):
dim = len(bounds)
if dim != 2 and verbose:
print("Warning: Visualization is only for 2D. Running optimization in %dD." % dim)
droplets = np.zeros((n_droplets, dim))
for d_idx in range(dim):
droplets[:, d_idx] = np.random.uniform(bounds[d_idx][0], bounds[d_idx][1], n_droplets)
min_b = np.array([b[0] for b in bounds])
max_b = np.array([b[1] for b in bounds])
water_level_grid = np.zeros((grid_res, grid_res))
def get_grid_idx(pos):
scaled_pos = (pos - min_b) / (max_b - min_b)
idx = np.floor(scaled_pos * grid_res).astype(int)
idx = np.clip(idx, 0, grid_res - 1)
return tuple(idx)
best_global_solution = droplets[0].copy()
best_global_value = func(best_global_solution).item()
history = []
if verbose:
print(f"Starting WFEO optimization with {n_droplets} droplets...")
for iteration in range(max_iterations):
for i in range(n_droplets):
current_pos = droplets[i].copy()
original_grad = grad_func(current_pos)
grid_idx = get_grid_idx(current_pos)
current_water_level = water_level_grid[grid_idx]
effective_grad = original_grad + current_water_level * np.sign(original_grad)
new_pos = current_pos - learning_rate * effective_grad
new_pos += np.random.normal(0, random_perturbation_scale, dim)
for d in range(dim):
new_pos[d] = np.clip(new_pos[d], bounds[d][0], bounds[d][1])
new_grid_idx = get_grid_idx(new_pos)
water_level_grid[new_grid_idx] += erosion_rate
droplets[i] = new_pos
current_droplet_value = func(new_pos).item()
if current_droplet_value < best_global_value:
best_global_value = current_droplet_value
best_global_solution = new_pos.copy()
water_level_grid *= decay_rate
history.append(best_global_value)
if verbose and iteration % 50 == 0:
print(f"Iteration {iteration}: Best value = {best_global_value:.4f}")
if verbose:
print("\nOptimization finished.")
return best_global_solution, best_global_value, history, water_level_grid
def run_tests(params, num_tests=5):
"""为一组参数运行多次测试，并返回结果。"""
print(f"\n--- Running Tests for Parameters: {params} ---")
bounds = [(-5.12, 5.12), (-5.12, 5.12)]
results = []
for i in range(num_tests):
_, final_value, _, _ = water_flow_erosion_optimizer(
objective_function,
analytical_gradient,
bounds,
**params,
verbose=False
)
results.append(final_value)
print(f"Test {i+1}: Final Best Value = {final_value:.4f}")
avg_value = np.mean(results)
std_value = np.std(results)
print(f"Average Final Value: {avg_value:.4f} ± {std_value:.4f}")
return avg_value, std_value, results
if __name__ == "__main__":
bounds = [(-5.12, 5.12), (-5.12, 5.12)]
params_baseline = {
'n_droplets': 100,
'max_iterations': 1000,
'learning_rate': 0.1,
'erosion_rate': 0.005,
'decay_rate': 0.995,
'random_perturbation_scale': 0.01,
'grid_res': 100
}
params_aggressive = {
'n_droplets': 200,
'max_iterations': 1000,
'learning_rate': 0.1,
'erosion_rate': 0.01,
'decay_rate': 0.99,
'random_perturbation_scale': 0.05,
'grid_res': 100
}
params_conservative = {
'n_droplets': 50,
'max_iterations': 1000,
'learning_rate': 0.05,
'erosion_rate': 0.001,
'decay_rate': 0.999,
'random_perturbation_scale': 0.005,
'grid_res': 100
}
print("--- 批量性能测试开始 ---")
avg_baseline, std_baseline, results_baseline = run_tests(params_baseline)
avg_aggressive, std_aggressive, results_aggressive = run_tests(params_aggressive)
avg_conservative, std_conservative, results_conservative = run_tests(params_conservative)
print("--- 批量性能测试结束 ---")
plt.figure(figsize=(8, 6))
plt.boxplot([results_baseline, results_aggressive, results_conservative],
labels=['Baseline', 'Aggressive', 'Conservative'])
plt.title('WFEO Performance Comparison Across Different Parameter Sets')
plt.ylabel('Final Best Value')
plt.xlabel('Parameter Strategy')
plt.grid(True)
plt.show()
print("\n--- 绘制一次详细运行结果（使用基准参数）---")
final_solution, final_value, opt_history, final_water_grid = water_flow_erosion_optimizer(
objective_function,
analytical_gradient,
bounds,
**params_baseline,
verbose=True
)
print(f"\nFinal Best Solution: {final_solution}")
print(f"Final Best Value: {final_value:.4f}")
fig = plt.figure(figsize=(15, 6))
ax1 = fig.add_subplot(121)
ax1.plot(opt_history)
ax1.set_title("Optimization Progress (Best Value per Iteration)")
ax1.set_xlabel("Iteration")
ax1.set_ylabel("Objective Function Value")
ax1.grid(True)
ax2 = fig.add_subplot(122, projection='3d')
x = np.linspace(bounds[0][0], bounds[0][1], 100)
y = np.linspace(bounds[1][0], bounds[1][1], 100)
X, Y = np.meshgrid(x, y)
points = np.stack([X.flatten(), Y.flatten()], axis=1)
Z = objective_function(points).reshape(X.shape)
ax2.plot_surface(X, Y, Z, cmap='viridis', alpha=0.7, rstride=1, cstride=1)
water_level_scale_factor = (np.max(Z) - np.min(Z)) / (np.max(final_water_grid) + 1e-9) * 0.1
Z_with_water = Z + final_water_grid * water_level_scale_factor
ax2.plot_surface(X, Y, Z_with_water, cmap='Blues', alpha=0.3, rstride=1, cstride=1)
ax2.scatter(final_solution[0], final_solution[1], final_value, color='red', s=100, label='Final Best', zorder=10)
ax2.set_title("Energy Landscape with Final Water Levels")
ax2.set_xlabel("X-axis")
ax2.set_ylabel("Y-axis")
ax2.set_zlabel("Energy")
ax2.legend()
plt.tight_layout()
plt.show()
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