用jupyter写一个粒子群算法

在Jupyter Notebook中编写粒子群优化（Particle Swarm Optimization，PSO）算法，首先需要导入必要的库，如`numpy`用于数值计算，以及可能的可视化库`matplotlib`。以下是简单的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt

# 初始化参数
def pso_init(swarm_size, dimensions, max_velocity, min_position, max_position):
    positions = np.random.uniform(min_position, max_position, (swarm_size, dimensions))
    velocities = np.random.uniform(-max_velocity, max_velocity, (swarm_size, dimensions))
    best_positions = positions.copy()
    personal_best_positions = positions.copy()
    return positions, velocities, best_positions, personal_best_positions

# 计算适应度函数
def fitness_function(positions, target):
    # 这里假设目标是一个简单的一维求最小值的问题
    return np.abs(positions - target).sum(axis=1)

# 更新粒子位置和速度
def update(p_pos, v_vel, g_best_pos, w=0.7, c1=2, c2=2, inertia_weight=0.9):
    r1, r2 = np.random.rand(*v_vel.shape), np.random.rand(*v_vel.shape)
    new_vel = w * v_vel + c1 * r1 * (g_best_pos - p_pos) + c2 * r2 * (personal_best_positions - p_pos)
    new_pos = np.clip(new_vel + p_pos, min_position, max_position)
    return new_pos, new_vel

# 主循环
def main(swarm_size, dimensions, max_iterations, max_velocity, min_position, max_position, target):
    positions, velocities, best_positions, personal_best_positions = pso_init(swarm_size, dimensions, max_velocity, min_position, max_position)
    
    for _ in range(max_iterations):
        velocities, positions = update(positions, velocities, best_positions)
        
        # 更新全局和个人最佳位置
        new_fitnesses = fitness_function(positions, target)
        better_indices = new_fitnesses < fitness_function(best_positions, target)
        best_positions[better_indices] = positions[better_indices]
        personal_best_positions[np.where(new_fitnesses < fitness_function(personal_best_positions, target))] = positions[np.where(new_fitnesses < fitness_function(personal_best_positions, target))]

    return best_positions, fitness_function(best_positions, target)

# 示例参数
swarm_size = 50
dimensions = 10
max_iterations = 100
max_velocity = 2
min_position = -50
max_position = 50
target = 0

best_solution, final_fitness = main(swarm_size, dimensions, max_iterations, max_velocity, min_position, max_position, target)
print("Best solution found:", best_solution)
print("Final fitness:", final_fitness)

# 可视化结果（如果需要）
plt.scatter(best_solution[:, 0], np.zeros_like(best_solution[:, 0]), s=100, c='r', label="Global Best")
plt.scatter(personal_best_positions[:, 0], np.zeros_like(personal_best_positions[:, 0]), s=50, c='b', label="Personal Best")
plt.xlabel("Position")
plt.ylabel("Fitness")
plt.legend()
plt.show()