遗传算法：
python编写的代码：

# -*- coding = utf-8 -*- 
# @Time: 2021/7/17 10:27
# @Author : zy2015532
# @File: GA.py 2019.pro 
# @Software:  PyCharm
# @E-mail:  zy2015532@gmail.com
import time

t0 = time.time()
import pandas as pd
import numpy as np
from matplotlib.pylab import style
import matplotlib.pyplot as plt
import random
import math

style.use('seaborn-deep')
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
font1 = {'family': 'SimHei',
         'weight': 'normal',
         'size': 30, }
figsize = 20, 15
figure, ax = plt.subplots(figsize=figsize)
plt.tick_params(labelsize=23)
labels = ax.get_xticklabels() + ax.get_yticklabels()
[label.set_fontname('SimHei') for label in labels]
NP = 100 # 种群数
L = 20 # 编码长度
Pc = 0.8# 交叉率
Pm = 0.8#变异率，稍微有点大，会过早“成熟",可以自行调整，0.001-0.1
G = 100# 进化代数
Xs = 10# 自变量上限
Xx = 6# 自变量下限
group = []#种群个体
Fit = []
Y = []
XX = []
nf = np.zeros([NP, L])
fbest = []
trace = np.zeros([G, 1])
X = []
Y = []

# 随机数生成初始种群
def Group():
    group = []
    for i in range(NP):
        for j in range(L):
            group.append(random.randint(0, 1))
    Y = np.array(group).reshape(NP, L)
    # print(Y)
    return Y

# 二进制解码，换算成十进制
def Population(group):
    XX.clear()
    Fit.clear()
    for i in range(NP):
        m = 0
        for j in range(L):
            m += group[i, j] * 2 ** (j - 1)
        m = Xx + (Xs - Xx) * m / (2 ** (L) - 1)
        XX.append(m)
        m = AimFunction(m)
        # print("结束")
        # print(m)
        Fit.append(m)
        # print(max(Fit))
    # print(max(Fit))
    rr = Fit.index(max(Fit))
    # print(rr)
    fbest = group[rr, :]
    # print(fbest)
    xbest = XX[rr]
    Max_Fit = max(Fit)
    # print(Max_Fit)

    return xbest, fbest, Fit, Max_Fit

# 优化目标函数
def AimFunction(m):
    result = m + 10 * np.sin(5 * m) + 7 * np.cos(4 * m)
    return result

# 计算适应度，找出最佳个体遗传给下代。只有适应度大约平均适应度的#个体才会遗传给下代；
def Genetic(nf, group, Fit, L):
    for i in range(NP):
        Fit[i] = (Fit[i] - min(Fit)) / (max(Fit) - min(Fit))
        if i % 50 == 0:
            # print(Fit[i])
            pass
    sum_Fit = sum(Fit)
    Fit_Value = Fit / sum_Fit
    Fit_Value = sorted(Fit_Value, reverse=True)
    # for i in range(1, NP):
    #     Fit_Value[i] = Fit_Value[i - 1] + Fit_Value[i]
    # print(Fit_Value)
    # print("!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!")
    ms = sorted(np.random.rand(NP))
    # print(ms)
    fiti = 0
    newi = 1
    J = np.mean(Fit_Value)
    nf[0, :] = fbest
    while (newi < NP):
        if (J) < Fit_Value[fiti]:
            nf[newi, :] = group[fiti, :]
            newi += 1
        fiti += 1
        if fiti > NP - 1:
            break
    # print(nf.shape)
    # print(NP-newi)
    # 这里稍微处理一下，引入外来新个体；
    for i in range(newi, NP):
        X = np.random.randint(0, 2, L)
        nf[i, :] = X
    # print("拼接完成")
    return nf

# 交叉，基于概率交叉；
def Cross(nf):
    nf[0,:]=fbest
    for i in range(1, NP):
        if i == NP-1:
            break
        p = np.random.rand()
        # print(p)
        # print("!!!")
        if p < Pc:
            q = np.random.randint(0, 2, L)
            for j in range(0, L, 3):
                if q[j] == 1:
                    temp = nf[i + 1, j]
                    nf[i + 1, j] = nf[i, j]
                    nf[i, j] = temp
                    # print("交叉了")
    return nf

# 基于概率变异；
def Variation(nf):
    nf[0, :] = fbest
    p = np.random.rand()
    m = 0
    i = 1
    while (i < NP):
        if p > Pm:
            h = np.random.randint(1, NP, 1)
            for j in range(0, L):
                g = np.random.randint(1, L, 1)
                q = np.random.randint(0, 2, L)
                if q[j] == 1:
                    nf[h, g] = int(not (nf[h, g]))
                    # print("变异了！！！！")
                    # m += 1;

        i += 2
    # print(m)
    return nf


if __name__ == '__main__':
    group = Group()
    X = []
    # 主循环开始，迭代一百次；
    for epoch in range(G):
        xbest, fbest, Fit, Max_Fit = Population(group)
        nf = Genetic(nf, group, Fit, L)
        nf = Cross(nf)
        nf = Variation(nf)
        group = nf
        group[0, :] = fbest
        group = nf
        trace[epoch] = Max_Fit
        X.append(xbest)
        Y.append(Max_Fit)
        # if epoch % 30 == 0:
        #     # print(nf)
        #     # print(trace)
        #     print("训练了第：", epoch, "次")
    plt.plot(trace)
    plt.show()
    print("自变量取值为：", X[Y.index(max(Y))])
    print("目标函数最大：", max(Y))
    print("共耗时为：", "%.2f" % (time.time() - t0), "s")