目录

实例：

求解函数的最大值y=xsin(10x)+xsin(2x),自变量取值：0--5，用Python画出的图像如下

(注：此代码好像有一些感觉不对的地方，首先:没有保留那些适应度低的个体

pop = select(pop, fitness) '''这一行代码，压根就是把适应度低的个体给干没了。'''

for parent in pop:

child = crossover(parent, pop_copy)

child = mutate(child)

parent[:] = child '''这个for循环，没有对交叉变异后的个体进行适应度筛选啊'''

)

代码讲解：

'''

1初始化种群：返回一个元素为 二进制的矩阵，每一行代表一个个体，每个个体由二进制数字表示x值

2：代表二进制，POP_SIZE：矩阵行数，DNA_SIZE：矩阵列数。

'''

pop = np.random.randint(2, size=(POP_SIZE, DNA_SIZE))

'''

2，计算适应度并且原则优良种群，(有放回的抽取)，循环很多代

pop:代表二进制种群,translateDNA(pop):将其转化十进制，在计算适应度，在select选择优良种群

'''

F_values = F(translateDNA(pop)) #求函数值

fitness = get_fitness(F_values) #得到使用度，这里例子函数值就是适应度

pop = select(pop, fitness)

#此时的pop是经过筛选的好的总群，也是一个二进制表现方式，里面有很多一样的个体，因为使用放回抓取

'''

3,经过一波筛选后，接下来该交叉变异了，为了得到更好的x值，因为初始化的x值使得个体分布不均匀

'''

pop_copy = pop.copy() #复制一份优良种群，用于交叉变异

for parent in pop:

child = crossover(parent, pop_copy) #交叉

child = mutate(child) #交叉后的种群在进行变异

parent[:] = child

#将child赋值给parent

难度较大的代码：

crossover() mutate() parent[:] = child

'''

crossover

交叉：parent：表示每一个二进制个体，pop：优良的种群，如100个个体

返回交叉后的一个个体，也是二进制表示方式

这个函数的功能就是

parent[cross_points] = pop[i_, cross_points]

'''

def crossover(parent, pop): # mating process (genes crossover)

if np.random.rand() < CROSS_RATE:

i_ = np.random.randint(0, POP_SIZE, size=1) # select another individual from pop

# 从0-POP_SIZE，随机选择一个数字，

cross_points = np.random.randint(0, 2, size=DNA_SIZE).astype(np.bool)

#array([ True, False, False, True, True, False, False, True, True,

#True])

#随机生成一个10个元素的数组，元素为0和1，在转化成bool型

# choose crossover points

parent[cross_points] = pop[i_, cross_points]

#这个语句有难度：

'''

将parent为True的元素，将被改变，False的元素不变.将被改变的元素改变成 pop矩阵第 i_ 行里面被选择为true的元素，

注意，parent的是cross_points, pop 也是cross_points，必须保持一致，才可以实现交叉生成一个新的个体，这个个体是父母基因的交叉结果

'''

# mating and produce one child

return parent #将新个体返回出去

'''

变异：将交叉后得到的个体，(这个个体不一定就是好的个体，很可能是不好的适应度不高的个体)

进行变异，

核心代码：

child[point] = 1 if child[point] == 0 else 0

'''

def mutate(child):

for point in range(DNA_SIZE):

if np.random.rand() < MUTATION_RATE:

child[point] = 1 if child[point] == 0 else 0

'''

point是把child这个个体基因遍历一遍，按照几率进行将0变成1，

注意:并不是将所有的0变成1，而是有几率的 if np.random.rand() < MUTATION_RATE:

'''

return child

全部代码：

"""

Visualize Genetic Algorithm to find a maximum point in a function.

Visit my tutorial website for more: https://morvanzhou.github.io/tutorials/

"""

import numpy as np

import matplotlib.pyplot as plt

DNA_SIZE = 10 # DNA length

POP_SIZE = 100 # population size

CROSS_RATE = 0.8 # mating probability (DNA crossover)

MUTATION_RATE = 0.003 # mutation probability

N_GENERATIONS = 200

X_BOUND = [0, 5] # x upper and lower bounds

def F(x): return np.sin(10*x)*x + np.cos(2*x)*x # to find the maximum of this function

# find non-zero fitness for selection

def get_fitness(pred): return pred + 1e-3 - np.min(pred)

# convert binary DNA to decimal and normalize it to a range(0, 5)

def translateDNA(pop): return pop.dot(2 ** np.arange(DNA_SIZE)[::-1]) / float(2**DNA_SIZE-1) * X_BOUND[1]

def select(pop, fitness): # nature selection wrt pop's fitness

idx = np.random.choice(np.arange(POP_SIZE), size=POP_SIZE, replace=True,

p=fitness/fitness.sum())

return pop[idx]

def crossover(parent, pop): # mating process (genes crossover)

if np.random.rand() < CROSS_RATE:

i_ = np.random.randint(0, POP_SIZE, size=1) # select another individual from pop

cross_points = np.random.randint(0, 2, size=DNA_SIZE).astype(np.bool) # choose crossover points

parent[cross_points] = pop[i_, cross_points] # mating and produce one child

return parent

def mutate(child):

for point in range(DNA_SIZE):

if np.random.rand() < MUTATION_RATE:

child[point] = 1 if child[point] == 0 else 0

return child

pop = np.random.randint(2, size=(POP_SIZE, DNA_SIZE)) # initialize the pop DNA

plt.ion() # something about plotting

x = np.linspace(*X_BOUND, 200)

plt.plot(x, F(x))

for _ in range(N_GENERATIONS):

F_values = F(translateDNA(pop)) # compute function value by extracting DNA

# something about plotting

if 'sca' in globals(): sca.remove()

sca = plt.scatter(translateDNA(pop), F_values, s=200, lw=0, c='red', alpha=0.5); plt.pause(0.05)

# GA part (evolution)

fitness = get_fitness(F_values)

print("Most fitted DNA: ", pop[np.argmax(fitness), :])

pop = select(pop, fitness)

pop_copy = pop.copy()

for parent in pop:

child = crossover(parent, pop_copy)

child = mutate(child)

parent[:] = child # parent is replaced by its child

plt.ioff(); plt.show()