粒子群算法Python

粒子群算法（Particle Swarm Optimization，PSO）是一种基于群体智能的优化算法，通过模拟鸟群或鱼群等生物群体的行为，来寻找最优解。下面是一个使用Python实现粒子群算法的例子：

import random

class Particle:
    def __init__(self, dim):
        self.position = [random.uniform(-5, 5) for _ in range(dim)]
        self.velocity = [random.uniform(-1, 1) for _ in range(dim)]
        self.best_position = self.position.copy()
        self.best_fitness = float('inf')

    def update_velocity(self, global_best_position, w, c1, c2):
        for i in range(len(self.velocity)):
            r1 = random.random()
            r2 = random.random()
            cognitive_component = c1 * r1 * (self.best_position[i] - self.position[i])
            social_component = c2 * r2 * (global_best_position[i] - self.position[i])
            self.velocity[i] = w * self.velocity[i] + cognitive_component + social_component

    def update_position(self):
        for i in range(len(self.position)):
            self.position[i] += self.velocity[i]
            if self.position[i] < -5:
                self.position[i] = -5
            elif self.position[i] > 5:
                self.position[i] = 5

    def evaluate_fitness(self):
        # 计算适应度函数值，这里以目标函数的值作为适应度
        fitness = sum([x ** 2 for x in self.position])
        if fitness < self.best_fitness:
            self.best_fitness = fitness
            self.best_position = self.position.copy()

def particle_swarm_optimization(dim, num_particles, max_iterations):
    particles = [Particle(dim) for _ in range(num_particles)]
    global_best_position = None
    global_best_fitness = float('inf')

    for _ in range(max_iterations):
        for particle in particles:
            particle.evaluate_fitness()
            if particle.best_fitness < global_best_fitness:
                global_best_fitness = particle.best_fitness
                global_best_position = particle.best_position.copy()

        for particle in particles:
            particle.update_velocity(global_best_position, 0.5, 1, 1)
            particle.update_position()

    return global_best_position, global_best_fitness

# 示例使用
dim = 2  # 维度
num_particles = 20  # 粒子数量
max_iterations = 100  # 最大迭代次数

best_position, best_fitness = particle_swarm_optimization(dim, num_particles, max_iterations)
print("Best position: ", best_position)
print("Best fitness: ", best_fitness)

这个例子中，我们定义了一个粒子类（Particle），每个粒子有自己的位置（position）、速度（velocity）、最佳位置（best_position）和最佳适应度（best_fitness）。粒子群算法的核心是通过更新速度和位置来搜索最优解。在每次迭代中，粒子根据自身的最佳位置和全局最佳位置来更新速度，然后根据新的速度更新位置。最终，算法会返回全局最佳位置和最佳适应度。