### PSO算法在Python中的实现 粒子群优化(Particle Swarm Optimization, PSO)是一种基于群体智能的全局优化方法，灵感来源于鸟群觅食行为。该算法通过模拟鸟类的社会行为来寻找最优解。 #### 导入必要的库 为了实现PSO算法，在Python中通常会导入一些常用的科学计算库： ```python import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D ``` #### 定义适应度函数 定义一个简单的二维Rosenbrock函数作为目标函数用于测试PSO性能[^1]: ```python def fitness_function(positions): x, y = positions[:, 0], positions[:, 1] return (1 - x)**2 + 100 * (y - x**2)**2 ``` #### 初始化参数并创建种群 设置基本参数如最大迭代次数、粒子数量等，并随机初始化位置和速度向量: ```python class ParticleSwarmOptimization: def __init__(self, num_particles=30, max_iter=100, w=0.7298, c1=1.49618, c2=1.49618): self.num_particles = num_particles self.max_iter = max_iter self.w = w # inertia weight 惯性权重 self.c1 = c1 # cognitive component 认知部分系数 self.c2 = c2 # social component 社交部分系数 # Initialize particles' position and velocity randomly within bounds [-5, 5] self.positions = np.random.uniform(-5, 5, size=(num_particles, 2)) self.velocities = np.zeros_like(self.positions) # Evaluate initial particle's fitness values self.personal_best_positions = self.positions.copy() self.fitness_values = fitness_function(self.positions) # Find global best from personal bests of all particles idx_min_fitness = np.argmin(self.fitness_values) self.global_best_position = self.personal_best_positions[idx_min_fitness].copy() def optimize(self): fig = plt.figure(figsize=(8, 6)) ax = fig.add_subplot(111, projection='3d') for iteration in range(self.max_iter): r1, r2 = np.random.rand(), np.random.rand() # Random factors # Update velocities based on previous experience and neighbors’ experiences. self.velocities = ( self.w * self.velocities + self.c1 * r1 * (self.personal_best_positions - self.positions) + self.c2 * r2 * (self.global_best_position - self.positions)) # Apply boundary conditions to the updated velocities self.positions += self.velocities self.positions[self.positions < -5] = -5 self.positions[self.positions > 5] = 5 current_fitness = fitness_function(self.positions) # Update personal best if better solution found improved_indices = current_fitness < self.fitness_values self.personal_best_positions[improved_indices] = self.positions[improved_indices] self.fitness_values[improved_indices] = current_fitness[improved_indices] # Update global best after updating each individual’s personal best new_global_best_idx = np.argmin(current_fitness) if current_fitness[new_global_best_idx] < fitness_function([self.global_best_position]): self.global_best_position = self.positions[new_global_best_idx].copy() # Plotting every few iterations... if iteration % 10 == 0 or iteration == self.max_iter - 1: plot_swarm(ax, self.positions, iteration) print(f"Global Best Position Found at Iteration {iteration}: ", self.global_best_position) def plot_swarm(axis, swarm_pos, iter_num=None): X, Y = np.meshgrid(np.linspace(-5, 5), np.linspace(-5, 5)) Z = fitness_function(np.array([X.ravel(), Y.ravel()]).T).reshape(X.shape) axis.clear() surf = axis.plot_surface(X, Y, Z, alpha=.3, cmap=plt.cm.jet) scatter = axis.scatter(swarm_pos[:, 0], swarm_pos[:, 1], fitness_function(swarm_pos), marker="o", color="black", s=20) if iter_num is not None: title = f"Iteration #{iter_num}" else: title = "Particle Positions" axis.set_title(title) plt.pause(.1) plt.show() ``` 此代码片段展示了如何构建一个基础版本的PSO求解器以及可视化其进化过程。注意这里仅选择了Rosenbrock函数为例；实际应用时可根据具体需求调整适应度函数和其他超参数配置。