python实现的遗传算法实例（一）
2016-01-28 14:52
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一、遗传算法介绍
遗传算法是通过模拟大自然中生物进化的历程，来解决问题的。大自然中一个种群经历过若干代的自然选择后，剩下的种群必定是适应环境的。把一个问题所有的解看做一个种群，经历过若干次的自然选择以后，剩下的解中是有问题的最优解的。当然，只能说有最优解的概率很大。这里，我们用遗传算法求一个函数的最大值。f(x) = 10 * sin( 5x ) + 7 * cos( 4x ), 0 <= x <= 10
1、将自变量x进行编码
取基因片段的长度为10, 则10位二进制位可以表示的范围是0到1023。基因与自变量转变的公式是x = b2d(individual) * 10 / 1023。构造初始的种群pop。每个个体的基因初始值是[0, 1, 0, 1, 0, 1, 0, 1, 0, 1]
2、计算目标函数值
根据自变量与基因的转化关系式，求出每个个体的基因对应的自变量，然后将自变量代入函数f（x），求出每个个体的目标函数值。
3、适应度函数
适应度函数是用来评估个体适应环境的能力，是进行自然选择的依据。本题的适应度函数直接将目标函数值中的负值变成0. 因为我们求的是最大值，所以要使目标函数值是负数的个体不适应环境，使其繁殖后代的能力为0.适应度函数的作用将在自然选择中体现。
4、自然选择
自然选择的思想不再赘述，操作使用轮盘赌算法。其具体步骤：假设种群中共5个个体，适应度函数计算出来的个体适应性列表是fitvalue = [1 ,3, 0, 2, 4] ，totalvalue = 10 ， 如果将fitvalue画到圆盘上，值的大小表示在圆盘上的面积。在转动轮盘的过程中，单个模块的面积越大则被选中的概率越大。选择的方法是将fitvalue转化为[1 ， 4 ，4 , 6 ，10], fitvalue / totalvalue = [0.1 , 0.4 , 0.4 , 0.6 , 1.0] . 然后产生5个0-1之间的随机数，将随机数从小到大排序，假如是[0.05
, 0.2 , 0.7 , 0.8 ,0.9]，则将0号个体、1号个体、4号个体、4号个体、4号个体拷贝到新种群中。自然选择的结果使种群更符合条件了。
5、繁殖
假设个体a、b的基因是a = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0]
b = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1]
这两个个体发生基因交换的概率pc = 0.6.如果要发生基因交换，则产生一个随机数point表示基因交换的位置，假设point = 4,则：
a = [1, 0, 0, 0, 0, 1, 1, 1, 0, 0]
b = [0, 0, 0, 1, 1, 0, 1, 1, 1, 1]
交换后为：
a = [1, 0, 0, 0, 1, 0, 1, 1, 1, 1]
b = [0, 0, 0, 1, 0, 1, 1, 1, 0, 0]
6、突变
遍历每一个个体，基因的每一位发生突变（0变为1,1变为0）的概率为0.001.突变可以增加解空间
二、代码
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text-decoration: none;"> 31</a> <a target=_blank id="L32" href="http://blog.csdn.net/u010902721/article/details/23531359#L32" rel="#L32" style="color: rgb(102, 102, 102); text-decoration: none;"> 32</a> | def b2d(b): #将二进制转化为十进制 x∈[0,10] t = 0 for j in range(len(b)): t += b[j] * (math.pow(2, j)) t = t * 10 / 1023 return t popsize = 50 #种群的大小#用遗传算法求函数最大值：#f(x)=10*sin(5x)+7*cos(4x) x∈[0,10] chromlength = 10 #基因片段的长度pc = 0.6 #两个个体交叉的概率pm = 0.001; #基因突变的概率results = [[]]bestindividual = []bestfit = 0fitvalue = []tempop = [[]]pop = [[0, 1, 0, 1, 0, 1, 0, 1, 0, 1] for i in range(popsize)]for i in range(100): #繁殖100代 objvalue = calobjvalue(pop) #计算目标函数值 fitvalue = calfitvalue(objvalue); #计算个体的适应值 [bestindividual, bestfit] = best(pop, fitvalue) #选出最好的个体和最好的函数值 results.append([bestfit,b2d(bestindividual)]) #每次繁殖，将最好的结果记录下来 selection(pop, fitvalue) #自然选择，淘汰掉一部分适应性低的个体 crossover(pop, pc) #交叉繁殖 mutation(pop, pc) #基因突变 results.sort() print(results[-1]) #打印函数最大值和对应的 |
来自CODE的代码片
GA.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> | def best(pop, fitvalue): #找出适应函数值中最大值，和对应的个体 px = len(pop) bestindividual = [] bestfit = fitvalue[0] for i in range(1,px): if(fitvalue[i] > bestfit): bestfit = fitvalue[i] bestindividual = pop[i] return [bestindividual, bestfit] |
来自CODE的代码片
best.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> <a target=_blank id="L10" href="http://blog.csdn.net/u010902721/article/details/23531359#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a> <a target=_blank id="L11" href="http://blog.csdn.net/u010902721/article/details/23531359#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a> | def calfitvalue(objvalue):#转化为适应值，目标函数值越大越好，负值淘汰。 fitvalue = [] temp = 0.0 Cmin = 0; for i in range(len(objvalue)): if(objvalue[i] + Cmin > 0): temp = Cmin + objvalue[i] else: temp = 0.0 fitvalue.append(temp) return fitvalue |
来自CODE的代码片
calfitvalue.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> <a target=_blank id="L10" href="http://blog.csdn.net/u010902721/article/details/23531359#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a> <a target=_blank id="L11" href="http://blog.csdn.net/u010902721/article/details/23531359#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a> | import math def decodechrom(pop): #将种群的二进制基因转化为十进制（0,1023） temp = []; for i in range(len(pop)): t = 0; for j in range(10): t += pop[i][j] * (math.pow(2, j)) temp.append(t) return temp def calobjvalue(pop): #计算目标函数值 temp1 = []; objvalue = []; temp1 = decodechrom(pop) for i in range(len(temp1)): x = temp1[i] * 10 / 1023 #（0,1023）转化为 （0,10） objvalue.append(10 * math.sin(5 * x) + 7 * math.cos(4 * x)) return objvalue #目标函数值objvalue[m] 与个体基因 pop[m] 对应 |
来自CODE的代码片
calobjvalue.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> <a target=_blank id="L10" href="http://blog.csdn.net/u010902721/article/details/23531359#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a> <a target=_blank id="L11" href="http://blog.csdn.net/u010902721/article/details/23531359#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a> | import random def crossover(pop, pc): #个体间交叉，实现基因交换 poplen = len(pop) for i in range(poplen - 1): if(random.random() < pc): cpoint = random.randint(0,len(pop[0])) temp1 = [] temp2 = [] temp1.extend(pop[i][0 : cpoint]) temp1.extend(pop[i+1][cpoint : len(pop[i])]) temp2.extend(pop[i+1][0 : cpoint]) temp2.extend(pop[i][cpoint : len(pop[i])]) pop[i] = temp1 pop[i+1] = temp2 |
来自CODE的代码片
crossover.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> <a target=_blank id="L10" href="http://blog.csdn.net/u010902721/article/details/23531359#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a> <a target=_blank id="L11" href="http://blog.csdn.net/u010902721/article/details/23531359#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a> | import random def mutation(pop, pm): #基因突变 px = len(pop) py = len(pop[0]) for i in range(px): if(random.random() < pm): mpoint = random.randint(0,py-1) if(pop[i][mpoint] == 1): pop[i][mpoint] = 0 else: pop[i][mpoint] = 1 |
来自CODE的代码片
mutation.py
<a target=_blank id="L1" href="http://blog.csdn.net/u010902721/article/details/23531359#L1" rel="#L1" style="color: rgb(102, 102, 102); text-decoration: none;"> 1</a> <a target=_blank id="L2" href="http://blog.csdn.net/u010902721/article/details/23531359#L2" rel="#L2" style="color: rgb(102, 102, 102); text-decoration: none;"> 2</a> <a target=_blank id="L3" href="http://blog.csdn.net/u010902721/article/details/23531359#L3" rel="#L3" style="color: rgb(102, 102, 102); text-decoration: none;"> 3</a> <a target=_blank id="L4" href="http://blog.csdn.net/u010902721/article/details/23531359#L4" rel="#L4" style="color: rgb(102, 102, 102); text-decoration: none;"> 4</a> <a target=_blank id="L5" href="http://blog.csdn.net/u010902721/article/details/23531359#L5" rel="#L5" style="color: rgb(102, 102, 102); text-decoration: none;"> 5</a> <a target=_blank id="L6" href="http://blog.csdn.net/u010902721/article/details/23531359#L6" rel="#L6" style="color: rgb(102, 102, 102); text-decoration: none;"> 6</a> <a target=_blank id="L7" href="http://blog.csdn.net/u010902721/article/details/23531359#L7" rel="#L7" style="color: rgb(102, 102, 102); text-decoration: none;"> 7</a> <a target=_blank id="L8" href="http://blog.csdn.net/u010902721/article/details/23531359#L8" rel="#L8" style="color: rgb(102, 102, 102); text-decoration: none;"> 8</a> <a target=_blank id="L9" href="http://blog.csdn.net/u010902721/article/details/23531359#L9" rel="#L9" style="color: rgb(102, 102, 102); text-decoration: none;"> 9</a> <a target=_blank id="L10" href="http://blog.csdn.net/u010902721/article/details/23531359#L10" rel="#L10" style="color: rgb(102, 102, 102); text-decoration: none;"> 10</a> <a target=_blank id="L11" href="http://blog.csdn.net/u010902721/article/details/23531359#L11" rel="#L11" style="color: rgb(102, 102, 102); text-decoration: none;"> 11</a> <a target=_blank id="L12" href="http://blog.csdn.net/u010902721/article/details/23531359#L12" rel="#L12" style="color: rgb(102, 102, 102); text-decoration: none;"> 12</a> <a target=_blank id="L13" href="http://blog.csdn.net/u010902721/article/details/23531359#L13" rel="#L13" style="color: rgb(102, 102, 102); text-decoration: none;"> 13</a> <a target=_blank id="L14" href="http://blog.csdn.net/u010902721/article/details/23531359#L14" rel="#L14" style="color: rgb(102, 102, 102); text-decoration: none;"> 14</a> <a target=_blank id="L15" href="http://blog.csdn.net/u010902721/article/details/23531359#L15" rel="#L15" style="color: rgb(102, 102, 102); text-decoration: none;"> 15</a> <a target=_blank id="L16" href="http://blog.csdn.net/u010902721/article/details/23531359#L16" rel="#L16" style="color: rgb(102, 102, 102); text-decoration: none;"> 16</a> <a target=_blank id="L17" href="http://blog.csdn.net/u010902721/article/details/23531359#L17" rel="#L17" style="color: rgb(102, 102, 102); text-decoration: none;"> 17</a> <a target=_blank id="L18" href="http://blog.csdn.net/u010902721/article/details/23531359#L18" rel="#L18" style="color: rgb(102, 102, 102); text-decoration: none;"> 18</a> <a target=_blank id="L19" href="http://blog.csdn.net/u010902721/article/details/23531359#L19" rel="#L19" style="color: rgb(102, 102, 102); text-decoration: none;"> 19</a> <a target=_blank id="L20" href="http://blog.csdn.net/u010902721/article/details/23531359#L20" rel="#L20" style="color: rgb(102, 102, 102); text-decoration: none;"> 20</a> <a target=_blank id="L21" href="http://blog.csdn.net/u010902721/article/details/23531359#L21" rel="#L21" style="color: rgb(102, 102, 102); text-decoration: none;"> 21</a> <a target=_blank id="L22" href="http://blog.csdn.net/u010902721/article/details/23531359#L22" rel="#L22" style="color: rgb(102, 102, 102); text-decoration: none;"> 22</a> <a target=_blank id="L23" href="http://blog.csdn.net/u010902721/article/details/23531359#L23" rel="#L23" style="color: rgb(102, 102, 102); text-decoration: none;"> 23</a> <a target=_blank id="L24" href="http://blog.csdn.net/u010902721/article/details/23531359#L24" rel="#L24" style="color: rgb(102, 102, 102); text-decoration: none;"> 24</a> <a target=_blank id="L25" href="http://blog.csdn.net/u010902721/article/details/23531359#L25" rel="#L25" style="color: rgb(102, 102, 102); text-decoration: none;"> 25</a> <a target=_blank id="L26" href="http://blog.csdn.net/u010902721/article/details/23531359#L26" rel="#L26" style="color: rgb(102, 102, 102); text-decoration: none;"> 26</a> <a target=_blank id="L27" href="http://blog.csdn.net/u010902721/article/details/23531359#L27" rel="#L27" style="color: rgb(102, 102, 102); text-decoration: none;"> 27</a> <a target=_blank id="L28" href="http://blog.csdn.net/u010902721/article/details/23531359#L28" rel="#L28" style="color: rgb(102, 102, 102); text-decoration: none;"> 28</a> <a target=_blank id="L29" href="http://blog.csdn.net/u010902721/article/details/23531359#L29" rel="#L29" style="color: rgb(102, 102, 102); text-decoration: none;"> 29</a> <a target=_blank id="L30" href="http://blog.csdn.net/u010902721/article/details/23531359#L30" rel="#L30" style="color: rgb(102, 102, 102); text-decoration: none;"> 30</a> <a target=_blank id="L31" href="http://blog.csdn.net/u010902721/article/details/23531359#L31" rel="#L31" style="color: rgb(102, 102, 102); text-decoration: none;"> 31</a> <a target=_blank id="L32" href="http://blog.csdn.net/u010902721/article/details/23531359#L32" rel="#L32" style="color: rgb(102, 102, 102); text-decoration: none;"> 32</a> | import random def sum(fitvalue): total = 0 for i in range(len(fitvalue)): total += fitvalue[i] return total def cumsum(fitvalue): for i in range(len(fitvalue)): t = 0; j = 0; while(j <= i): t += fitvalue[j] j = j + 1 fitvalue[i] = t; def selection(pop, fitvalue): #自然选择（轮盘赌算法） newfitvalue = [] totalfit = sum(fitvalue) for i in range(len(fitvalue)): newfitvalue.append(fitvalue[i] / totalfit) cumsum(newfitvalue) ms = []; poplen = len(pop) for i in range(poplen): ms.append(random.random()) #random float list ms ms.sort() fitin = 0 newin = 0 newpop = pop while newin < poplen: if(ms[newin] < newfitvalue[fitin]): newpop[newin] = pop[fitin] newin = newin + 1 else: fitin = fitin + 1 pop = newpop |
来自CODE的代码片
selection.py
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