粒子群算法的Python简单实现

需要优化的目标函数

\[target = x^2+y^2+z^2\]

def target(nparray):
    return nparray[0]**2 + nparray[1]**2 + nparray[2]**2

初始化条件

N = 30 #个体数量
D = 3  #目标函数的维数
M = 1000 #迭代次数
c1 = 0.5 #加速常数1
c2 = 0.5 #加速常数2
w = 0.6 #惯性因子

初始化每个粒子的位置和速度

import numpy as np
import random

X = np.zeros((N, D))
V = np.zeros((N, D))
y = np.zeros((N, D))

for i in range(N): #行
    for j in range(D): #列
        X[i][j] = random.random()
        V[i][j] = random.random()

计算每个粒子的适应度

P = np.zeros(N) #P为个体历史最优解

for i in range(N):
    P[i] = target(X[i])
    y[i] = X[i]
    #print(target(X[i]))

初始化pg，pg为全局最优解

pg = X[0]
for i in range(1,N):
    if float(target(X[i])) < float(target(pg)):
        pg = X[i]

算法主要循环

for t in range(M):
    for i in range(N):
        V[i] = w*V[i] + c1*random.random()*(y[i]-X[i]) + c2*random.random()*(pg-X[i])
        X[i] = X[i] + V[i]
        if target(X[i])<P[i]:
            P[i] = target(X[i])
            y[i] = X[i]
        if P[i]<target(pg):
            pg = y[i]
    #Pbest[t] = target(pg)

pg

array([ 9.74182970e-163, -1.51205792e-162, -5.62277013e-163])

target(pg)

0.0