@[TOC](粒子群算法python实现: 较复杂(即多元)情况)

求解一个较复杂的函数

 def function(x):
    #2004年考研题(我这里只求极小值):x^2-6xy+10^2-2yz-z^2+18=0,求z=z(x,y)的极值点和极值
    #此题答案极小值3，极小值点(9,3)
    #因为看答案知道z+y>0，所以只试z+y>0的情况
    z=(18+x[0]**2-6*x[0]*x[1]+11*x[1]**2)**0.5-x[1]#化成x1，x2即y表示z的形式
    return z

实现

class Particle:
    def __init__(self, dim, max_opsition=100, max_velocity=0.05):
        self.position = [random.uniform(-max_opsition, max_opsition) for i in range(dim)] #粒子初始位置
        self.velocity = [random.uniform(-max_velocity, max_velocity) for i in range(dim)]  # 粒子初始速度
        self.particle_best = [0.0 for i in range(dim)]  # 初始粒子最优解

    def set_position(self, i, value):
        self.position[i] = value

    def get_position(self):
        return self.position

    def set_particle_best(self, value):
        self.particle_best = value

    def get_particle_best(self):
        return self.particle_best

    def set_velocity(self, i, value):
        self.velocity[i] = value

    def get_velocity(self):
        return self.velocity
        
import random

particle_num = 100 #粒子数目
dim = 2
particles = [Particle(dim=2) for i in range(particle_num)] # 初始粒子
global_best = [0.0 for i in range(dim)] # 全局最优解

def update(particles,global_best,iter_num,W,n1,n2,max_velocity,function): 
    """
    状态更新
    """
    for j in range(iter_num):
        for i in range(len(particles)):
            
            # 计算每个粒子的最适应度，就是代个解看它的y是多少，如果y小于当前的最优解的值，就更新最优解为这个解
            if function(particles[i].get_position()) < function(particles[i].get_particle_best()):
                particles[i].set_particle_best(particles[i].get_position())
            # 更新全局最优解同理
            if function(particles[i].get_position()) < function(global_best):
                global_best = particles[i].get_position()
                
            for k in range(dim):
                # 套速度更新的公式
                particles[i].set_velocity(k, W * particles[i].get_velocity()[k] + \
                                          n1 * random.random() * (particles[i].get_particle_best()[k] - particles[i].get_position()[k]) \
                                          + n2 * random.random() * (global_best[k] - particles[i].get_position()[k]))
                # 限制速度，别让它飞了
                if particles[i].get_velocity()[k] > max_velocity:
                    particles[i].get_velocity()[k] = max_velocity
                elif particles[i].get_velocity()[k] < -max_velocity:
                    particles[i].get_velocity()[k] = -max_velocity
                # 套位置更新的公式
                particles[i].set_position(k,particles[i].get_position()[k] +  particles[i].get_velocity()[k])
    return global_best

W = 1 #惯性权重
n1 = 2 #认知学习因子
n2 = 2 #社会学习因子
max_velocity = 0.05 #速度限制
iter_num = 2000 #迭代次数

result=update(particles,global_best,iter_num,W,n1,n2,max_velocity,function)
print(result) #极值点，输出约为(9,3)
print(function(result)) #极小值, 输出约为3