差分进化算法DE-python实现

算法原理请看https://blog.csdn.net/ztf312/article/details/78432711

下面是python 实现

# -*- coding: cp936 -*-
import numpy as np
import matplotlib.pyplot as plt
import math
import random

# Rastrigr 函数
def object_function(x):
    f = 0
    for i in range(0,len(x)):
        f = f + (x[i] ** 2 - (10 * math.cos(2 * np.pi * x[i])) + 10)
    return f
# 参数
def initpara():
    NP = 100   # 种群数量
    F = 0.6   # 缩放因子
    CR = 0.7   # 交叉概率
    generation = 2000   # 遗传代数
    len_x = 10
    value_up_range = 5.12
    value_down_range = -5.12
    return NP, F, CR, generation, len_x, value_up_range, value_down_range
# 种群初始化
def initialtion(NP):
    np_list = []   # 种群，染色体
    for i in range(0,NP):
        x_list = []   # 个体，基因
        for j in range(0,len_x):
            x_list.append(value_down_range + random.random() * (value_up_range - value_down_range))
        np_list.append(x_list)
    return np_list
# 列表相减
def substract(a_list,b_list):
    a = len(a_list)
    new_list = []
    for i in range(0,a):
        new_list.append(a_list[i]-b_list[i])
    return new_list
# 列表相加
def add(a_list,b_list):
    a = len(a_list)
    new_list = []
    for i in range(0,a):
        new_list.append(a_list[i]+b_list[i])
    return new_list
# 列表的数乘
def multiply(a,b_list):
    b = len(b_list)
    new_list = []
    for i in range(0,b):
        new_list.append(a * b_list[i])
    return new_list
# 变异
def mutation(np_list):
    v_list = []
    for i in range(0,NP):
        r1 = random.randint(0,NP-1)
        while r1 == i:
            r1 = random.randint(0,NP-1)
        r2 = random.randint(0,NP-1)
        while r2 == r1 | r2 == i:
            r2 = random.randint(0,NP-1)
        r3 = random.randint(0,NP-1)
        while r3 == r2 | r3 == r1 | r3 == i:
            r3 = random.randint(0,NP-1)
        
        v_list.append(add(np_list[r1], multiply(F, substract(np_list[r2],np_list[r3]))))
    return v_list
# 交叉
def crossover(np_list,v_list):
    u_list = []
    for i in range(0,NP):
        vv_list = []
        for j in range(0,len_x):
            if (random.random() <= CR) | (j == random.randint(0,len_x - 1)):
                vv_list.append(v_list[i][j])
            else:
                vv_list.append(np_list[i][j])
        u_list.append(vv_list)
    return u_list
# 选择
def selection(u_list,np_list):
    for i in range(0,NP):
        if object_function(u_list[i]) <= object_function(np_list[i]):
            np_list[i] = u_list[i]
        else:
            np_list[i] = np_list[i]
    return np_list
# 主函数
NP, F, CR, generation, len_x, value_up_range, value_down_range = initpara()
np_list = initialtion(NP)
min_x = []
min_f = []
for i in range(0,NP):
    xx = []
    xx.append(object_function(np_list[i]))
min_f.append(min(xx))
min_x.append(np_list[xx.index(min(xx))])
for i in range(0,generation):
    v_list = mutation(np_list)
    u_list = crossover(np_list,v_list)
    np_list = selection(u_list,np_list)
    for i in range(0,NP):
        xx = []
        xx.append(object_function(np_list[i]))
    min_f.append(min(xx))
    min_x.append(np_list[xx.index(min(xx))])
# 输出
min_ff = min(min_f)
min_xx = min_x[min_f.index(min_ff)]
print('the minimum point is x ')
print(min_xx)
print('the minimum value is y ')
print(min_ff)
# 画图
x_label = np.arange(0,generation+1,1)
plt.plot(x_label,min_f,color = 'blue')
plt.xlabel('iteration')
plt.ylabel('fx')
plt.savefig('./iteration-f.png')
plt.show()

下面是输出结果：

he minimum point is x 
[6.571458044073247e-10, -1.6132099500206647e-09, 5.479208933390588e-10, 1.4316602937984918e-10, -1.0300811905852257e-09, -9.4552825214611e-11, 7.820675729557053e-10, -1.0017881437355374e-09, 7.502751928050157e-11, 8.595546094079207e-10]
the minimum value is y 
0.0