##题目： 用遗传算法求函数f(a,b)=2a x sin(8PI x b) + b x cos(13PI x a)最大值，a:[-3,7]，b:[-4:10] ##实现步骤：python
- 初始化种群
- 计算种群中每一个个体的适应值
- 淘汰部分个体（这里是求最大值，f值存在正值，因此淘汰全部负值）
- 轮盘算法对种群进行选择
- 进行交配、变异，交叉点、变异点随机
##分析： 为了方便，先将自变量范围调整为[0,10]、[0,14] 有两个变量，种群中每一个个体用一个列表表示，两个列表项，每项是一个二进制字符串（分别由a、b转化而来） 种群之间交配时须要肯定交叉点，先将个体染色体中的两个二进制字符串拼接，再肯定一个随机数做为交叉点 为了程序的数据每一步都比较清晰正确，我在select、crossover、mutation以后分别都进行了一次适应值的从新计算 ##具体代码：算法
import math
import random
def sum(list):
total = 0.0
for line in list:
total += line
return total
def rand(a, b):
number = random.uniform(a,b)
return math.floor(number*100)/100
PI = math.pi
def fitness(x1,x2):
return 2*(x1-3)*math.sin(8*PI*x2)+(x2-4)*math.cos(13*PI*x1)
def todecimal(str):
parta = str[0:4]
partb = str[4:]
numerical = int(parta,2)
partb = partb[::-1]
for i in range(len(partb)):
numerical += int(partb[i])*math.pow(0.5,(i+1))
return numerical
def tobinarystring(numerical):
numa = math.floor(numerical)
numb = numerical - numa
bina = bin(numa)
bina = bina[2:]
result = "0"*(4-len(bina))
result += bina
for i in range(7):
numb *= 2
result += str(math.floor(numb))
numb = numb - math.floor(numb)
return result
class Population:
def __init__(self):
self.pop_size = 500 # 设定种群个体数为500
self.population = [[]] # 种群个体的二进制字符串集合，每一个个体的字符串由一个列表组成[x1,x2]
self.individual_fitness = [] # 种群个体的适应度集合
self.chrom_length = 22 # 一个染色体22位
self.results = [[]] # 记录每一代最优个体，是一个三元组(value,x1_str,x2_str)
self.pc = 0.6 # 交配几率
self.pm = 0.01 # 变异几率
self.distribution = [] # 用于种群选择时的轮盘
def initial(self):
for i in range(self.pop_size):
x1 = rand(0,10)
x2 = rand(0,14)
x1_str = tobinarystring(x1)
x2_str = tobinarystring(x2)
self.population.append([x1_str,x2_str]) # 添加一个个体
fitness_value = fitness(x1,x2)
self.individual_fitness.append(fitness_value) # 记录该个体的适应度
self.population = self.population[1:]
self.results = self.results[1:]
def eliminate(self):
for i in range(self.pop_size):
if self.individual_fitness[i]<0:
self.individual_fitness[i] = 0.0
def getbest(self):
"取得当前种群中的一个最有个体加入results集合"
index = self.individual_fitness.index(max(self.individual_fitness))
x1_str = self.population[index][0]
x2_str = self.population[index][1]
value = self.individual_fitness[index]
self.results.append((value,x1_str,x2_str,))
def select(self):
"轮盘算法，用随机数作个体选择，选择以后会更新individual_fitness对应的数值"
"第一步先要初始化轮盘"
"选出新种群以后更新individual_fitness"
total = sum(self.individual_fitness)
begin = 0
for i in range(self.pop_size):
temp = self.individual_fitness[i]/total+begin
self.distribution.append(temp)
begin = temp
new_population = []
new_individual_fitness = []
for i in range(self.pop_size):
num = random.random() # 生成一个0~1之间的浮点数
j = 0
for j in range(self.pop_size):
if self.distribution[j]<num:
continue
else:
break
index = j if j!=0 else (self.pop_size-1)
new_population.append(self.population[index])
new_individual_fitness.append(self.individual_fitness[index])
self.population = new_population
self.individual_fitness = new_individual_fitness
def crossover(self):
"选择好新种群以后要进行交配"
"注意这只是一次种群交配，种群每一次交配过程，会让每两个相邻的染色体进行信息交配"
for i in range(self.pop_size-1):
if random.random()<self.pc:
cross_position = random.randint(1,self.chrom_length-1)
i_x1x2_str = self.population[i][0]+self.population[i][1] # 拼接起第i个染色体的两个二进制字符串
i1_x1x2_str = self.population[i+1][0]+self.population[i+1][1] # 拼接起第i+1个染色体的两个二进制字符串
str1_part1 = i_x1x2_str[:cross_position]
str1_part2 = i_x1x2_str[cross_position:]
str2_part1 = i1_x1x2_str[:cross_position]
str2_part2 = i1_x1x2_str[cross_position:]
str1 = str1_part1+str2_part2
str2 = str2_part1+str1_part2
self.population[i] = [str1[:11],str1[11:]]
self.population[i+1] = [str2[:11],str2[11:]]
"而后更新individual_fitness"
for i in range(self.pop_size):
x1_str = self.population[i][0]
x2_str = self.population[i][1]
x1 = todecimal(x1_str)
x2 = todecimal(x2_str)
self.individual_fitness[i] = fitness(x1,x2)
def mutation(self):
"个体基因变异"
for i in range(self.pop_size):
if random.random()<self.pm:
x1x2_str = self.population[i][0]+self.population[i][1]
pos = random.randint(0,self.chrom_length-1)
bit = "1" if x1x2_str[pos]=="0" else "0"
x1x2_str = x1x2_str[:pos]+bit+x1x2_str[pos+1:]
self.population[i][0] = x1x2_str[:11]
self.population[i][1] = x1x2_str[11:]
"而后更新individual_fitness"
for i in range(self.pop_size):
x1_str = self.population[i][0]
x2_str = self.population[i][1]
x1 = todecimal(x1_str)
x2 = todecimal(x2_str)
self.individual_fitness[i] = fitness(x1, x2)
def solving(self,times):
"进行times次数的整个种群交配变异"
"先得到初代的最优个体"
self.getbest()
for i in range(times):
"每一代的染色体个体和适应值，须要先淘汰，而后选择，再交配、变异，最后获取最优个体。而后进入下一代"
self.eliminate()
self.select()
self.crossover()
self.mutation()
self.getbest()
def returnbest(self):
self.results.sort()
return self.results[len(self.results)-1]
if __name__ == '__main__':
demo = Population()
demo.initial()
demo.solving(100)
answer = demo.returnbest()
value = answer[0]
x1 = todecimal(answer[1])
x2 = todecimal(answer[2])
print(x1,x2,value)
参考文章app