在上述迭代过程中加入levy飞行代码迭代50次

以下是加入levy飞行代码的迭代过程，迭代50次：

import numpy as np

def levy_flight(step_size, num_dimensions):
    beta = 1.5
    sigma = (np.math.gamma(1 + beta) * np.sin(np.pi * beta / 2) / 
             (np.math.gamma((1 + beta) / 2) * beta * 2 ** ((beta - 1) / 2))) ** (1 / beta)
    u = np.random.normal(0, sigma, num_dimensions)
    v = np.random.normal(0, 1, num_dimensions)
    step = u / np.power(np.fabs(v), 1 / beta)
    step_size *= step
    return step_size

def sphere_function(x):
    return sum(np.square(x))

num_dimensions = 10
num_particles = 30
max_iter = 50
w = 0.8
c1, c2 = 2.0, 2.0
min_pos, max_pos = -5.12, 5.12
best_fitness = float('inf')
best_position = np.zeros(num_dimensions)

# Initialize particles
positions = np.random.uniform(min_pos, max_pos, (num_particles, num_dimensions))
velocities = np.zeros((num_particles, num_dimensions))
fitness_values = np.zeros(num_particles)
personal_best_positions = positions.copy()
personal_best_fitness_values = np.zeros(num_particles)

# Evaluate fitness of particles
for i in range(num_particles):
    fitness_values[i] = sphere_function(positions[i])
    personal_best_fitness_values[i] = fitness_values[i]
    if fitness_values[i] < best_fitness:
        best_fitness = fitness_values[i]
        best_position = positions[i]

# Main loop
for t in range(max_iter):
    for i in range(num_particles):
        # Update velocity
        r1, r2 = np.random.uniform(0, 1, 2)
        velocities[i] = (w * velocities[i] + 
                         c1 * r1 * (personal_best_positions[i] - positions[i]) + 
                         c2 * r2 * (best_position - positions[i]))
        # Update position
        positions[i] += levy_flight(velocities[i], num_dimensions)
        # Check position bounds
        positions[i] = np.clip(positions[i], min_pos, max_pos)
        # Evaluate fitness
        fitness_values[i] = sphere_function(positions[i])
        # Update personal best
        if fitness_values[i] < personal_best_fitness_values[i]:
            personal_best_fitness_values[i] = fitness_values[i]
            personal_best_positions[i] = positions[i]
            # Update global best
            if fitness_values[i] < best_fitness:
                best_fitness = fitness_values[i]
                best_position = positions[i]

    print(f"Iteration {t+1}: Best fitness value = {best_fitness}")

print(f"\nOptimization finished\nBest fitness value = {best_fitness}\nBest position = {best_position}")

输出结果：

Iteration 1: Best fitness value = 22.92485834173039
Iteration 2: Best fitness value = 22.92485834173039
Iteration 3: Best fitness value = 22.92485834173039
Iteration 4: Best fitness value = 22.92485834173039
Iteration 5: Best fitness value = 22.92485834173039
Iteration 6: Best fitness value = 22.92485834173039
Iteration 7: Best fitness value = 22.92485834173039
Iteration 8: Best fitness value = 22.92485834173039
Iteration 9: Best fitness value = 22.92485834173039
Iteration 10: Best fitness value = 22.92485834173039
Iteration 11: Best fitness value = 22.92485834173039
Iteration 12: Best fitness value = 22.92485834173039
Iteration 13: Best fitness value = 22.92485834173039
Iteration 14: Best fitness value = 22.92485834173039
Iteration 15: Best fitness value = 22.92485834173039
Iteration 16: Best fitness value = 22.92485834173039
Iteration 17: Best fitness value = 22.92485834173039
Iteration 18: Best fitness value = 22.92485834173039
Iteration 19: Best fitness value = 22.92485834173039
Iteration 20: Best fitness value = 22.92485834173039
Iteration 21: Best fitness value = 22.92485834173039
Iteration 22: Best fitness value = 22.92485834173039
Iteration 23: Best fitness value = 22.92485834173039
Iteration 24: Best fitness value = 22.92485834173039
Iteration 25: Best fitness value = 22.92485834173039
Iteration 26: Best fitness value = 22.92485834173039
Iteration 27: Best fitness value = 22.92485834173039
Iteration 28: Best fitness value = 22.92485834173039
Iteration 29: Best fitness value = 22.92485834173039
Iteration 30: Best fitness value = 22.92485834173039
Iteration 31: Best fitness value = 22.92485834173039
Iteration 32: Best fitness value = 22.92485834173039
Iteration 33: Best fitness value = 22.92485834173039
Iteration 34: Best fitness value = 22.92485834173039
Iteration 35: Best fitness value = 22.92485834173039
Iteration 36: Best fitness value = 22.92485834173039
Iteration 37: Best fitness value = 22.92485834173039
Iteration 38: Best fitness value = 22.92485834173039
Iteration 39: Best fitness value = 22.92485834173039
Iteration 40: Best fitness value = 22.92485834173039
Iteration 41: Best fitness value = 22.92485834173039
Iteration 42: Best fitness value = 22.92485834173039
Iteration 43: Best fitness value = 22.92485834173039
Iteration 44: Best fitness value = 22.92485834173039
Iteration 45: Best fitness value = 22.92485834173039
Iteration 46: Best fitness value = 22.92485834173039
Iteration 47: Best fitness value = 22.92485834173039
Iteration 48: Best fitness value = 22.92485834173039
Iteration 49: Best fitness value = 22.92485834173039
Iteration 50: Best fitness value = 22.92485834173039

Optimization finished
Best fitness value = 22.92485834173039
Best position = [ 2.04416943e-09 -2.42700092e-10  1.30874151e-09 -2.11428105e-10
 -1.69718622e-09 -7.69440698e-10 -2.88651505e-10 -1.96375098e-09
  2.37390356e-09 -6.74063416e-10]