用python解决用粒子群算法求最小值

粒子群优化算法（Particle Swarm Optimization, PSO）是一种常用的优化算法，它模拟鸟群或鱼群等生物的群体行为，通过不断地迭代寻找最优解。下面是使用Python实现粒子群算法求解最小值的代码示例：

import random

class Particle:
    def __init__(self, dim, max_iter):
        # 粒子的维度
        self.dim = dim
        # 最大迭代次数
        self.max_iter = max_iter
        # 当前迭代次数
        self.iter = 0
        # 粒子的位置和速度
        self.position = [random.uniform(-10, 10) for _ in range(dim)]
        self.velocity = [random.uniform(-1, 1) for _ in range(dim)]
        # 粒子的最佳位置和最佳适应度值
        self.best_position = self.position
        self.best_fitness = self.fitness()

    # 计算粒子的适应度值
    def fitness(self):
        # 这里以 Rosenbrock 函数为例
        x = self.position
        return sum(100.0 * (x[i + 1] - x[i] ** 2) ** 2 + (1 - x[i]) ** 2 for i in range(self.dim - 1))

    # 更新粒子的位置和速度
    def update(self, global_best_position, omega, phi_p, phi_g):
        r_p = [random.uniform(0, 1) for _ in range(self.dim)]
        r_g = [random.uniform(0, 1) for _ in range(self.dim)]
        for i in range(self.dim):
            self.velocity[i] = omega * self.velocity[i] + phi_p * r_p[i] * (self.best_position[i] - self.position[i]) + phi_g * r_g[i] * (global_best_position[i] - self.position[i])
            self.position[i] += self.velocity[i]
        self.iter += 1
        fitness = self.fitness()
        if fitness < self.best_fitness:
            self.best_position = self.position
            self.best_fitness = fitness

class PSO:
    def __init__(self, dim, size, max_iter):
        # 粒子的维度
        self.dim = dim
        # 粒子的数量
        self.size = size
        # 最大迭代次数
        self.max_iter = max_iter
        # 全局最佳位置和最佳适应度值
        self.global_best_position = [random.uniform(-10, 10) for _ in range(dim)]
        self.global_best_fitness = float('inf')
        # 初始化粒子群
        self.particles = [Particle(dim, max_iter) for _ in range(size)]

    # 运行 PSO 算法
    def run(self, omega=0.5, phi_p=0.5, phi_g=0.5):
        for i in range(self.max_iter):
            for particle in self.particles:
                if particle.best_fitness < self.global_best_fitness:
                    self.global_best_position = particle.best_position
                    self.global_best_fitness = particle.best_fitness
            for particle in self.particles:
                particle.update(self.global_best_position, omega, phi_p, phi_g)
            print('Iteration {}: global best fitness = {}'.format(i + 1, self.global_best_fitness))

if __name__ == '__main__':
    pso = PSO(dim=2, size=30, max_iter=100)
    pso.run()

上面的代码实现了一个简单的二维粒子群算法，在 Rosenbrock 函数上寻找最小值。你可以根据实际情况修改代码中的函数和参数来适应不同的问题。