经典遗传算法(SGA)解非线性最优化问题的python代码实现

# -*- coding: utf-8 -*- """ 程序功能：实现经典的遗传算法，测试函数为经典的非线性问题： max f(x1,x2)=21.5+x1*sin(4*pi*x1)+x2*sin(20*pi*x2) s.t. -3.0<=x1<=12.1 4.1<=x2<=5.8 说明： 1.采用经典的二进制编码，选择算子为轮盘赌选择，交叉算子为单点交叉，变异算子为反转（单点）变异 2.可调的参数为：gen,upper,lower,pc,pm,pop_num,delta,fun（165-172行） 3.修改函数请改25,231,232,234行，231,232行和upper,lower保持一致 4.此代码与之前的sga主程序不同 作者：(晓风)wangchao email: [email protected] 最初建立时间：2018.10.10 最近修改时间：2018.10.24 GA的简单实现 """ import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D import math #目标函数 def aimfun(x): y=21.5+x[0]*math.sin(4*math.pi*x[0])+x[1]*math.sin(20*math.pi*x[1]) return y #获得染色体长度 def getchromolen(delta, upper,lower): maxlen=25 chromo_len=[] for j in range(len(upper)): a=(upper[j]-lower[j])/delta[j] for i in range(maxlen): if (2**i < a) and (a < (2**(i+1))): chromo_len.append(i+1) break return chromo_len #解码 def decode(x,chromo_len,upper,lower): y=[] index=0 for i in range(len(chromo_len)): a = lower[i]+(int(x[index:(index+chromo_len[i])],2))*(upper[i]-lower[i])/(2**chromo_len[i]-1) y.append(a) index = index+chromo_len[i] return y #初始化种群 def init(pop_num,chromo_len): population=[] for i in range(pop_num): pop='' for k in chromo_len: for j in range(k): pop=pop+str(np.random.randint(0,2)) population.append(pop) return population #适应度函数 def fitnessfun(population,aimfun,chromo_len,upper,lower,fun): value=[] for i in range(len(population)): valuea=aimfun(decode(population[i],chromo_len,upper,lower)) value.append(valuea) if fun==0: minvalue=min(value) value=[(i-minvalue+0.0000001) for i in value] elif fun==1: maxvalue=max(value) value=[(maxvalue-i+0.0000001) for i in value] return value #轮盘赌选择 def roulettewheel(population,value,pop_num): fitness_sum=[] value_sum=sum(value) fitness=[i/value_sum for i in value] for i in range(len(population)):## if i==0: fitness_sum.append(fitness[i]) else: fitness_sum.append(fitness_sum[i-1]+fitness[i]) population_new=[] for j in range(pop_num):### r=np.random.uniform(0,1) for i in range(len(fitness_sum)):### if i==0: if r>=0 and r<=fitness_sum[i]: population_new.append(population[i]) else: if r>=fitness_sum[i-1] and r<=fitness_sum[i]: population_new.append(population[i]) return population_new #单点交叉 def crossover(population_new,pc,ncross): a=int(len(population_new)/2) parents_one=population_new[:a] parents_two=population_new[a:] np.random.shuffle(parents_one) np.random.shuffle(parents_two) offspring=[] for i in range(a): r=np.random.uniform(0,1) if r<=pc: point=np.random.randint(0,int(len(parents_one[i])/2)) off_one=parents_one[i][:point]+parents_two[i][point:] off_two=parents_two[i][:point]+parents_one[i][point:] ncross = ncross+1 else: off_one=parents_one[i] off_two=parents_two[i] offspring.append(off_one) offspring.append(off_two) return offspring #单点变异1 def mutation1(offspring,pm,nmut): for i in range(len(offspring)): r=np.random.uniform(0,1) if r<=pm: point=np.random.randint(0,len(offspring[i])) if point==0: if offspring[i][point]=='1': offspring[i]='0'+offspring[i][1:] else: offspring[i]='1'+offspring[i][1:] else: if offspring[i][point]=='1': offspring[i]=offspring[i][:(point-1)]+'0'+offspring[i][point:] else: offspring[i]=offspring[i][:(point-1)]+'1'+offspring[i][point:] nmut = nmut+1 return offspring #单点变异2 def mutation2(offspring,pm,nmut): for i in range(len(offspring)): for j in range(len(offspring[i])): r=np.random.uniform(0,1) if r<=pm: if j==0: if offspring[i][j]=='1': offspring[i]='0'+offspring[i][1:] else: offspring[i]='1'+offspring[i][1:] else: if offspring[i][j]=='1': offspring[i]=offspring[i][:(j-1)]+'0'+offspring[i][j:] else: offspring[i]=offspring[i][:(j-1)]+'1'+offspring[i][j:] nmut = nmut+1 return offspring #主程序---------------------------------------------------------------------------------------------------------------------------------- #参数设置----------------------------------------------------------------------- gen=1000#迭代次数 upper=[12.1,5.8]#自变量上界 lower=[-3.0,4.1]#自变量下界 pc=0.25#交叉概率 pm=0.01#变异概率 pop_num=10#种群大小 delta=[0.0001,0.0001]#编码精度 fun=0#0最大化，1最小化 #初始化------------------------------------------------------------------------- #获得编码长度 chromo_len = getchromolen(delta,upper,lower) #初始化种群 population=init(pop_num,chromo_len) #初始化交叉个数 ncross=0 #初始化变异个数 nmut=0 #储存每代种群的最优值及其对应的个体 t=[] best_ind=[] last=[]#储存最后一代个体的函数值 realvalue=[]#储存最后一代解码后的值 #循环--------------------------------------------------------------------------- for i in range(gen): print("迭代次数：") print(i) #适应度函数计算 value = fitnessfun(population,aimfun,chromo_len,upper,lower,fun) #轮盘赌选择 population=roulettewheel(population,value,pop_num) #交叉 offspring_c=crossover(population,pc,ncross) #变异 #offspring_m=mutation1(offspring,pm,nmut) offspring_m=mutation2(offspring_c,pm,nmut) population=offspring_m #储存当代的最优解 result=[] if i==gen-1: for j in range(len(population)): bb = decode(population[j],chromo_len,upper,lower) result.append(aimfun(bb)) realvalue.append(bb) last=result else: for j in range(len(population)): result.append(aimfun(decode(population[j],chromo_len,upper,lower))) maxre=max(result) h=result.index(max(result)) #将每代的最优解加入结果种群 t.append(maxre) best_ind.append(population[h]) #输出结果----------------------------------------------------------------------- best_value=max(t) hh=t.index(max(t)) print(best_value) print(decode(best_ind[hh],chromo_len,upper,lower)) #画出收敛曲线 plt.plot(t) plt.title('The curve of the optimal function value of each generation with the number of iterations',color='#123456') plt.xlabel('the number of iterations') plt.ylabel('the optimal function value of each generation') #画出函数与解的分布 fig = plt.figure() ax = Axes3D(fig) x1 = np.arange(-3,13,0.4) x2 = np.arange(4,6,0.0460) X, Y = np.meshgrid(x1,x2)#网格的创建，这个是关键 Z=21.5+X*np.sin(4*np.pi*X)+Y*np.sin(20*np.pi*Y) plt.xlabel('x1') plt.ylabel('x2') ax.set_zlabel('