粒子群优化算法python

粒子群优化算法（Particle Swarm Optimization，PSO）是一种基于群体智能的优化算法，常用于求解优化问题。下面是一个简单的Python实现：

import random
import math

class Particle:
    def __init__(self, dim, lb, ub):
        self.position = [random.uniform(lb, ub) for i in range(dim)]
        self.velocity = [random.uniform(lb, ub) for i 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, r2 = random.uniform(0, 1), random.uniform(0, 1)
            cognitive = c1 * r1 * (self.best_position[i] - self.position[i])
            social = c2 * r2 * (global_best_position[i] - self.position[i])
            self.velocity[i] = w * self.velocity[i] + cognitive + social

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

    def evaluate(self, obj_func):
        fitness = obj_func(self.position)
        if fitness < self.best_fitness:
            self.best_fitness = fitness
            self.best_position = self.position.copy()

class PSO:
    def __init__(self, obj_func, dim, size, lb, ub, max_iter):
        self.obj_func = obj_func
        self.dim = dim
        self.size = size
        self.lb = lb
        self.ub = ub
        self.max_iter = max_iter
        self.particles = [Particle(dim, lb, ub) for i in range(size)]
        self.global_best_fitness = float('inf')
        self.global_best_position = [0] * dim

    def optimize(self):
        for iter in range(self.max_iter):
            for particle in self.particles:
                particle.evaluate(self.obj_func)
                if particle.best_fitness < self.global_best_fitness:
                    self.global_best_fitness = particle.best_fitness
                    self.global_best_position = particle.best_position.copy()
            for particle in self.particles:
                particle.update_velocity(self.global_best_position, 0.7, 1.5, 1.5)
                particle.update_position(self.lb, self.ub)

        return self.global_best_position, self.global_best_fitness

其中，Particle类表示粒子，包含位置、速度、最佳位置和最佳适应度；PSO类表示粒子群优化算法，包含目标函数、维度、粒子数、搜索范围、最大迭代次数、粒子列表和全局最佳位置和适应度。optimize方法是优化函数，其中先遍历所有粒子并计算其适应度和最佳位置，然后更新全局最佳位置。接着更新所有粒子的速度和位置，最后返回全局最佳位置和适应度。

使用方法如下：

def sphere(x):
    return sum([xi ** 2 for xi in x])

pso = PSO(sphere, 30, 50, -100, 100, 100)
best_position, best_fitness = pso.optimize()
print(best_position, best_fitness)

这里定义了一个目标函数sphere，是一个标准的多维球形函数。然后创建一个PSO对象，设置维度为30，粒子数为50，搜索范围为-100到100，最大迭代次数为100。最后调用optimize方法求解最优解。