### 粒子群算法单目标优化Python实现 #### 初始化粒子群 为了实现粒子群优化(Particle Swarm Optimization, PSO)，首先定义一个`ParticleSwarmOptimizer`类用于管理群体中的所有粒子以及它们的行为。每个粒子代表搜索空间中的潜在解决方案。 ```python import numpy as np class Particle: def __init__(self, bounds, velo_range=(-1, 1)): self.position = [] self.velocity = [] self.best_pos = [] self.fitness_value = float('inf') self.best_fitness_val = float('inf') for i in range(len(bounds)): self.velocity.append(np.random.uniform(velo_range[0], velo_range[1])) self.position.append(np.random.uniform(bounds[i][0], bounds[i][1])) def evaluate(position): # 定义适应度函数，这里以Rosenbrock function为例 fitness = sum([100 * (position[i + 1] - position[i] ** 2)**2 + (1 - position[i])**2 for i in range(len(position)-1)]) return fitness ``` 此段代码创建了一个名为`Particle`的类来表示每一个粒子，并设置了初始位置和速度范围[^4]。 #### 更新粒子状态 接下来，在每次迭代过程中都需要更新粒子的状态——即调整其飞行方向（速度）与当前位置： ```python class ParticleSwarmOptimizer(): def __init__(self, particles_count=30, max_iter=100, w=0.7298, c1=1.49618, c2=1.49618): self.particles = [Particle(bounds) for _ in range(particles_count)] self.global_best_position = None self.global_best_fitness = float('inf') self.max_iterations = max_iter self.w = w # 惯性权重 self.c1 = c1 # 自我学习因子 self.c2 = c2 # 社会学习因子 def optimize(self): for iteration in range(self.max_iterations): for particle in self.particles: fit = evaluate(particle.position) if fit < particle.best_fitness_val: particle.best_fitness_val = fit particle.best_pos = list(particle.position) if fit < self.global_best_fitness: self.global_best_fitness = fit self.global_best_position = list(particle.position) for particle in self.particles: new_velocity = [] for i in range(len(particle.position)): r1 = np.random.rand() r2 = np.random.rand() cognitive_velocity = self.c1*r1*(particle.best_pos[i]-particle.position[i]) social_velocity = self.c2*r2*(self.global_best_position[i]-particle.position[i]) velocity_update = self.w*particle.velocity[i]+cognitive_velocity+social_velocity new_velocity.append(max(min(velocity_update,bounds[i][1]),bounds[i][0])) particle.velocity = new_velocity particle.position += np.array(new_velocity) opt = ParticleSwarmOptimizer() opt.optimize() print(f'Global Best Position: {opt.global_best_position}, Fitness Value:{opt.global_best_fitness}') ``` 上述代码展示了如何通过循环逐步改进粒子的位置直到达到最大迭代次数为止。在此期间，不断比较并保存个体最优(`best_pos`)及全局最优(`global_best_position`)解。最后输出寻得的最佳位置及其对应的适应度值。