1. 根据pso的伪代码，利用python实现算法

下面是 Python 实现的 PSO 算法，其中包括初始化粒子、更新位置和速度、更新全局最优和个体最优等步骤：

import random

# PSO 参数
POPULATION_SIZE = 20
MAX_ITERATION = 50
C1 = 1.5
C2 = 1.5
W = 0.7

# 优化目标函数
def objective_function(x):
    return (x-2)**2

# 初始化粒子群
def initialize_particles():
    particles = []
    for i in range(POPULATION_SIZE):
        position = random.uniform(-10, 10)
        velocity = 0
        particle = {'position': position, 'velocity': velocity, 'pbest': position, 'pbest_fitness': objective_function(position)}
        particles.append(particle)
    gbest = particles[0]['position']
    gbest_fitness = particles[0]['pbest_fitness']
    return particles, gbest, gbest_fitness

# 更新粒子位置和速度
def update_particles(particles, gbest):
    for i in range(POPULATION_SIZE):
        particle = particles[i]
        velocity = W * particle['velocity'] + C1 * random.random() * (particle['pbest'] - particle['position']) + C2 * random.random() * (gbest - particle['position'])
        position = particle['position'] + velocity
        particle['position'] = position
        particle['velocity'] = velocity

# 更新全局最优和个体最优
def update_bests(particles, gbest, gbest_fitness):
    for i in range(POPULATION_SIZE):
        particle = particles[i]
        fitness = objective_function(particle['position'])
        if fitness < particle['pbest_fitness']:
            particle['pbest'] = particle['position']
            particle['pbest_fitness'] = fitness
        if fitness < gbest_fitness:
            gbest = particle['position']
            gbest_fitness = fitness
    return gbest, gbest_fitness

# PSO 主函数
def pso():
    # 初始化粒子群
    particles, gbest, gbest_fitness = initialize_particles()

    # 迭代寻优
    for i in range(MAX_ITERATION):
        # 更新粒子位置和速度
        update_particles(particles, gbest)
        # 更新全局最优和个体最优
        gbest, gbest_fitness = update_bests(particles, gbest, gbest_fitness)
        # 打印当前的最优解
        print('iteration {}: gbest_fitness = {}'.format(i+1, gbest_fitness))

    return gbest, gbest_fitness

# 运行 PSO 算法
pso()

这个实现中，`initialize_particles` 函数用于初始化粒子群；`update_particles` 函数用于更新粒子位置和速度；`update_bests` 函数用于更新全局最优和个体最优。最后的 `pso` 函数是 PSO 的主函数，其中包括了初始化和迭代两个步骤。在迭代过程中，我们不断更新粒子位置和速度，并更新全局最优和个体最优。最后输出最优解和最优适应度。