【Python代码】智能优化之遗传算法
import numpy as npimport matplotlib.pyplot as pltfrom matplotlib import cmfrom mpl_toolkits.mplot3d import Axes3DDNA_SIZE = 24POP_SIZE = 200CROSSOVER_RATE = 0.8MUTATION_RATE = 0.005N_GENERATIONS = 50X_BOUND = [-3, 3]Y_BOUND = [-3, 3]def F(x, y): return 3*(1-x)**2*np.exp(-(x**2)-(y+1)**2)- 10*(x/5 - x**3 - y**5)*np.exp(-x**2-y**2)- 1/3**np.exp(-(x+1)**2 - y**2)def plot_3d(ax): X = np.linspace(*X_BOUND, 100) Y = np.linspace(*Y_BOUND, 100) X,Y = np.meshgrid(X, Y) Z = F(X, Y) ax.plot_surface(X,Y,Z,rstride=1,cstride=1,cmap=cm.coolwarm) ax.set_zlim(-10,10) ax.set_xlabel(&#39;x&#39;) ax.set_ylabel(&#39;y&#39;) ax.set_zlabel(&#39;z&#39;) plt.pause(3) plt.show()def get_fitness(pop): x,y = translateDNA(pop) pred = F(x, y) return (pred - np.min(pred)) + 1e-3 #减去最小的适应度是为了防止适应度出现负数，通过这一步fitness的范围为,最后在加上一个很小的数防止出现为0的适应度def translateDNA(pop): #pop表示种群矩阵，一行表示一个二进制编码表示的DNA，矩阵的行数为种群数目 x_pop = pop[:,1::2]#奇数列表示X y_pop = pop[:,::2] #偶数列表示y #pop:(POP_SIZE,DNA_SIZE)*(DNA_SIZE,1) --> (POP_SIZE,1) x = x_pop.dot(2**np.arange(DNA_SIZE)[::-1])/float(2**DNA_SIZE-1)*(X_BOUND-X_BOUND)+X_BOUND y = y_pop.dot(2**np.arange(DNA_SIZE)[::-1])/float(2**DNA_SIZE-1)*(Y_BOUND-Y_BOUND)+Y_BOUND return x,ydef crossover_and_mutation(pop, CROSSOVER_RATE = 0.8): new_pop = [] for father in pop: #遍历种群中的每一个个体，将该个体作为父亲 child = father #孩子先得到父亲的全部基因（这里我把一串二进制串的那些0，1称为基因） if np.random.rand() < CROSSOVER_RATE: #产生子代时不是必然发生交叉，而是以一定的概率发生交叉 mother = pop #再种群中选择另一个个体，并将该个体作为母亲 cross_points = np.random.randint(low=0, high=DNA_SIZE*2) #随机产生交叉的点 child = mother #孩子得到位于交叉点后的母亲的基因 mutation(child) #每个后代有一定的机率发生变异 new_pop.append(child) return new_popdef mutation(child, MUTATION_RATE=0.003): if np.random.rand() < MUTATION_RATE: #以MUTATION_RATE的概率进行变异 mutate_point = np.random.randint(0, DNA_SIZE) #随机产生一个实数，代表要变异基因的位置 child = child^1 #将变异点的二进制为反转def select(pop, fitness): # nature selection wrt pop&#39;s fitness idx = np.random.choice(np.arange(POP_SIZE), size=POP_SIZE, replace=True, p=(fitness)/(fitness.sum()) ) return popdef print_info(pop): fitness = get_fitness(pop) max_fitness_index = np.argmax(fitness) print(&#34;max_fitness:&#34;, fitness) x,y = translateDNA(pop) print(&#34;最优的基因型：&#34;, pop) print(&#34;(x, y):&#34;, (x, y))if __name__ == &#34;__main__&#34;: fig = plt.figure() ax = Axes3D(fig) plt.ion()#将画图模式改为交互模式，程序遇到plt.show不会暂停，而是继续执行 plot_3d(ax) pop = np.random.randint(2, size=(POP_SIZE, DNA_SIZE*2)) #matrix (POP_SIZE, DNA_SIZE) for _ in range(N_GENERATIONS):#迭代N代 x,y = translateDNA(pop) if &#39;sca&#39; in locals(): sca.remove() sca = ax.scatter(x, y, F(x,y), c=&#39;black&#39;, marker=&#39;o&#39;);plt.show();plt.pause(0.1) pop = np.array(crossover_and_mutation(pop, CROSSOVER_RATE)) #F_values = F(translateDNA(pop), translateDNA(pop))#x, y --> Z matrix fitness = get_fitness(pop) pop = select(pop, fitness) #选择生成新的种群 print_info(pop) plt.ioff() plot_3d(ax)
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