一、实验目的
熟悉和掌握遗传算法的原理、流程和编码策略，并利用遗传求解函数优化问题，理解求解流程并测试主要参数对结果的影响。
二、实验原理
遗传算法的基本思想正是基于模仿生物界遗传学的遗传过程。它把问题的参数用基因代表，把问题的解用染色体代表（在计算机里用二进制码表示），从而得到一个由具有不同染色体的个体组成的群体。这个群体在问题特定的环境里生存竞争，适者有最好的机会生存和个体组成的群体。后代随机化地继承了父代的最好特征，并也在生存环境的控制支配下继续这一过程，群体的染色体都将逐渐适应环境，不断进化，最后收敛到一族最适应环境的类似个体，即得到问题最优的解。
三、实验条件
python3,anaconda3,pycharm
四、实验内容
import matplotlib.pyplot as plt
import random
import math
#计算函数
def f(args):
return f2(args)
def f1(args):
return (3 - (math.sin(2*args[0]))**2 - (math.sin(2*args[1]))**2)
def f2(args):
x = 1
for i in range(len(args)):
z = 0
for j in range(5):
z += (j+1) * math.cos(((j+1)+1)*args[i]+(j+1))
x *= z
return x
#适应函数
def s(x):
return s2(x)
def s1(x):
return math.exp(-abs(x-1))
def s2(x):
return math.exp(-abs(x+187))
# 计算2进制序列代表的数值
'''
解码并计算值
group 染色体
chrom_length 染色体长度
max_value, min_value 上下限
div 分界点
'''
def b2d(b, chrom_length, max_value, min_value, div):
rwno = []
#因为染色体里面有多个变量，所以需要div来分割
for i in range(len(div)):
if i == 0:
star = 0
end = div[i]
else:
star = div[i-1] + 1
end = div[i]
t = 0
for j in range(star, end): # 分隔参数[1,2,3||4,5,6]
t += b[j] * (math.pow(2, j - star))
t = t * max_value / (math.pow(2, end - star + 1) - 1) - min_value
rwno.append(t)
return rwno # 这是一个list
'''
计算当前函数值
group 染色体
chrom_length 染色体长度
max_value，min_value 最大最小值
divid 分割
'''
def calobjvalue(group, chrom_length, max_value, min_value, divid):
obj_value = []
for i in range(len(group)):
x = b2d(group[i], chrom_length, max_value, min_value, divid)#这里面可能是多个变量
obj_value.append(f(x))
return obj_value
# 获取适应值
def calfitvalue(obj_value):
fit_value = []
for i in range(len(obj_value)):
temp = s(obj_value[i]) # 调用适应函数计算
fit_value.append(temp)
return fit_value
#累计适应值方便计算平均
def sum_fit(fit_value):
total = 0
for i in range(len(fit_value)):
total += fit_value[i]
return total
# 转轮盘选择法
def selection(group, fit_value):
newfit_value = [] #[ [[染色体], [锚点]],... ]
newgroup = [] #[ [父], [母], [父], [母],....]
# 适应度总和
total_fit = sum_fit(fit_value)
# 设置各个的锚点
t = 0
for i in range(len(group)):
t += fit_value[i]/total_fit
newfit_value.append([group[i], t])
# 转轮盘选择法
for i in range(len(newfit_value)):
parents = len(newfit_value) # 初始化指针
r = random.random() #指针
for j in range(len(newfit_value)):#看看指针指到睡了
if newfit_value[j][1] > r:
parents = j
break
newgroup.append(newfit_value[parents][0])
return newgroup
# 交配
def crossover(group, fit_value, pc):
parents_group = selection(group, fit_value) #[ [[父], [母]],....]
group_len = len(parents_group)
for i in range(0, group_len, 2):
if(random.random() < pc): # 看看是否要交配
cpoint = random.randint(0, len(parents_group[0])) # 随机交叉点
temp1 = []
temp2 = []
temp1.extend(parents_group[i][0:cpoint])
temp1.extend(parents_group[i+1][cpoint:len(parents_group[i])])
temp2.extend(parents_group[i+1][0:cpoint])
temp2.extend(parents_group[i][cpoint:len(parents_group[i])])
group[i] = temp1
group[i+1] = temp2
# 基因突变
def mutation(group, pm):
px = len(group)
py = len(group[0])
for i in range(px): # 遍历
if(random.random() < pm):
mpoint = random.randint(0, py-1) # 取要变异哪个
if(group[i][mpoint] == 1):
group[i][mpoint] = 0
else:
group[i][mpoint] = 1
'''
找出最优解和最优解的基因编码
group 种群染色去
fit_value 种群适应
'''
def best(group, fit_value):
px = len(group)
best_in = group[0]
best_fit = fit_value[0]
for i in range(1, px):
if(fit_value[i] > best_fit):
best_fit = fit_value[i]
best_in = group[i]
#print(best_in)
return [best_in, best_fit]
'''
创建初代种群
group_size 种群大小
chrom_length 染色体长度
'''
def getfisrtgroup(group_size, chrom_length):
#print('初代种群：')
group = []
for i in range(group_size):
temp = []
for j in range(chrom_length):
temp.append(random.randint(0, 1))
group.append(temp)
#print(group)
return group
generation = 50 # 繁衍代数（数量越小，出结果脍，迭代次数越少）
group_size = 400 # 染色体数量，偶数
max_value = 20 # 范围
min_value = 10 # 偏移修正
chrom_length = 800 # 染色体长度
divid = [399, chrom_length-1] # 输入值分界点， 最后一位必须是染色体长度
pc = 0.7 # 交配概率
pm = 0.1 # 变异概率
results = [] # 存储每一代的最优解
fit_value = [] # 个体适应度
points = [] #多个最优解
#生成初代
group = getfisrtgroup(group_size, chrom_length)
for i in range(generation):
if i > 100:
pm = 0.01
if i > 1000:
pm = 0.001
obj_value = calobjvalue(group, chrom_length, max_value, min_value, divid) # 个体评价
fit_value = calfitvalue(obj_value) # 获取群体适应值
best_individual, best_fit = best(group, fit_value) # 返回最优基因, 最优适应值
xx = b2d(best_individual, chrom_length, max_value, min_value, divid)
if( abs(f(xx)+186.730909) < 0.000001):#找到最优解
flag = false
for p in points:
if( (abs(xx[0]-p[0]) < 0.1) and (abs(xx[1]-p[1]) < 0.1) ):#剔除重复解
flag = true
break
if flag == false:
print(xx)
points.append(xx)
results.append([i, best_fit, b2d(best_individual, chrom_length, max_value, min_value, divid), best_individual]) #加进坐标里
crossover(group, fit_value, pc) # 交配
mutation(group, pm) # 变异
#results.sort(key=lambda x:x[1])
rank = sorted(results, key=lambda x:x[1])
#print('\n', rank[-1])
#print(results)
x = b2d(rank[-1][3], chrom_length, max_value, min_value, divid)
#最终结果
print("f(x) = " , f(x) , "x = " , x , " 染色体 = ", rank[-1][3], " 适应值 = ", rank[-1][1], "代数：", rank[-1][0])
#输出适应图
x = []
y = []
for i in range(generation):
x.append(i)
y.append(results[i][1])
plt.plot(x, y)
plt.show()
五、实验结果
