import numpy as np
import random
import matplotlib.pyplot as plt
#目标函数
def function(x):
y = 0
for i in range(len(x)):
y = y + (x[i]**2 - 10 * np.cos(2 * np.pi * x[i]) + 10 )
return y
#选择函数，三个参数：种群个体、种群数量、适应度值
def select(population,population_size,fitness):
#fitness_proportion用来保存每个个体的选择概率
fitness_proportion = []
#计算适应度之和
fitness_sum = 0
for i in range(population_size):
fitness_sum += fitness[i]
#计算每个个体的选择概率
for i in range(population_size):
fitness_proportion.append(fitness[i] / fitness_sum)
#pie_fitness保存每个个体的累计概率
pie_fitness = []
cumsum = 0.0
for i in range(population_size):
pie_fitness.append(cumsum + fitness_proportion[i]) #pie_fitness为由1到i个个体相加的适应度和组成的list
cumsum += fitness_proportion[i] #所有个体生存率之和
# 生成随机数在轮盘上选点[0, 1)
random_selection = []
for i in range(population_size):
random_selection.append(random.random()) #返回随机生成的一个实数，它在[0,1)范围内。
# 选择新种群
new_population = []
random_selection_id = 0
while random_selection_id < population_size:
#随机数处于个体对应的累计区间时，则将这个个体赋给新种群
for i in range(population_size):
if random_selection[random_selection_id] < pie_fitness[i]:
new_population.append(population[i])
break
random_selection_id += 1
population = new_population
return population
#交叉函数，四个参数：种群个体、种群数量、交叉概率、维度信息
def crosscover(population,population_size,pc,dimen):
for i in range(0, population_size - 1, 2): #每两个一对
#如果生成的随机数小于交叉概率
if random.random() < pc:
# 随机选择交叉点,random.randint(0, dimen-1),返回[0,dimen-1]之间的整数
change_point = random.randint(0, dimen-1)
temp1 = []
temp2 = []
#两个个体在交叉点进行交换
temp1.extend(population[i][0: change_point])
temp1.extend(population[i + 1][change_point:])
temp2.extend(population[i + 1][0: change_point])
temp2.extend(population[i][change_point:])
population[i] = temp1
population[i + 1] = temp2
population = np.array(population)
return population
#变异函数，四个参数：种群个体、种群数量、变异概率、维度信息
def mutation(population,population_size,pm,dimen):
for i in range(population_size):
#如果随机生成的数小于变异概率
if random.random() < pm:
#随机生成个体中需要进行变异的数的数量mutation_num
mutation_num = random.randint(0, dimen-1)
#随机选择个体中mutation_num个数进行重新赋值
for j in range(mutation_num):
mutation_point = random.randint(0, dimen-1)
population[i][mutation_point] = np.random.uniform(low=-50, high=50)
population = np.array(population)
return population
#解的取值范围
rangepop=[-50,50]
#种群数量
pn = 50
#迭代次数
iterators = 1000
#交叉概率
pc = 0.6
#变异概率
pm = 0.05
#解的维度信息
dimen = 20
#种群，为数组形式
pop = np.zeros((pn,dimen))
#种群个体适应度值，为数组形式
fitness=np.zeros(pn)
#随机初始化种群
for j in range(pn):
pop[j] = np.random.uniform(low=-50, high=50,size=(1, dimen))
#计算适应度值
fitness[j] = function(pop[j])
#获取当前最优解bestpop和最优适应度值bestfit
bestpop, bestfit = pop[fitness.argmax()].copy(), fitness.max()
#bestfitness保存每次迭代中的最优适应度值，为数组形式
bestfitness=np.zeros(iterators)
#开始迭代训练
for i in range(iterators):
#选择操作
parents = select(pop,pn,fitness)
#交叉操作
crossover1 = crosscover(parents,pn,pc,dimen)
#变异操作
pop = mutation(crossover1,pn,pm,dimen)
#将上一次迭代的最优适应度值和新的适应度值比较，选择更大的适应度值作为新的最优适应度值，对应的个体作为当前最优解
for j in range(pn):
#确保个体取值在取值范围内[-50,50]内
pop[pop < rangepop[0]] = rangepop[0]
pop[pop > rangepop[1]] = rangepop[1]
#计算新个体适应度值
fitness[j] = function(pop[j])
#比较最优适应度值
if fitness[j] > bestfit:
bestfit = fitness[j]
bestpop = pop[j]
bestfitness[i] = bestfit
print("当前迭代次数:", i+1)
print("最优适应度值是:", bestfitness[i])
print("迭代结束后:")
print("最优解是:", bestpop)
print("最优适应度值是:", bestfitness[-1])
fig=plt.figure(figsize=(15, 10), dpi=300)
plt.title('The Change of Best Fitness',fontdict={'weight':'normal','size': 30})
x=range(1,1001,1)
plt.plot(x,bestfitness,color="red",linewidth=3.0, linestyle="-")
plt.tick_params(labelsize=25)
plt.xlim(0,1001)
plt.ylim(20000,50000)
plt.xlabel("Epoch",fontdict={'weight':'normal','size': 30})
plt.ylabel("Fitness value",fontdict={'weight':'normal','size': 30})
plt.xticks(range(0,1001,100))
plt.yticks(range(20000,50000,5000))
plt.savefig("GA.png")
plt.show()
