111 lines
3.9 KiB
Python
111 lines
3.9 KiB
Python
import matplotlib
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import numpy as np
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from numpy.ma import cos
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import matplotlib.pyplot as plt
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from matplotlib import cm
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from mpl_toolkits.mplot3d import Axes3D
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import datetime
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matplotlib.use('Qt5Agg')
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DNA_SIZE = 24 # 编码长度
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POP_SIZE = 100 # 种群大小
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CROSS_RATE = 0.8 # 交叉率
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MUTA_RATE = 0.15 # 变异率
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Iterations = 1000 # 代次数
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X_BOUND = [0, 10] # X区间
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Y_BOUND = [0, 10] # Y区间
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def F(x, y): # 适应度函数
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return (6.452 * (x + 0.125 * y) * (cos(x) - cos(2 * y)) ** 2) / (
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0.8 + (x - 4.2) ** 2 + 2 * (y - 7) ** 2) + 3.226 * y
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def decodeDNA(pop): # 解码
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x_pop = pop[:, 1::2] # 奇数列表示X
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y_pop = pop[:, ::2] # 偶数列表示y
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x = x_pop.dot(2 ** np.arange(DNA_SIZE)[::-1]) / float(2 ** DNA_SIZE - 1) * (X_BOUND[1] - X_BOUND[0]) + X_BOUND[0]
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y = y_pop.dot(2 ** np.arange(DNA_SIZE)[::-1]) / float(2 ** DNA_SIZE - 1) * (Y_BOUND[1] - Y_BOUND[0]) + Y_BOUND[0]
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return x, y
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def getfitness(pop):
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x, y = decodeDNA(pop)
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temp = F(x, y)
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return (temp - np.min(temp)) + 0.0001 # 减去最小的适应度是为了防止适应度出现负数
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def select(pop, fitness): # 根据适应度选择
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temp = np.random.choice(np.arange(POP_SIZE), size=POP_SIZE, replace=True, p=(fitness) / (fitness.sum()))
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return pop[temp]
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def crossmuta(pop, CROSS_RATE):
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new_pop = []
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for i in pop: # 遍历种群中的每一个个体，将该个体作为父代
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temp = i # 子代先得到父亲的全部基因
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if np.random.rand() < CROSS_RATE: # 以交叉概率发生交叉
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j = pop[np.random.randint(POP_SIZE)] # 从种群中随机选择另一个个体，并将该个体作为母代
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cpoints1 = np.random.randint(0, DNA_SIZE * 2 - 1) # 随机产生交叉的点
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cpoints2 = np.random.randint(cpoints1, DNA_SIZE * 2)
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temp[cpoints1:cpoints2] = j[cpoints1:cpoints2] # 子代得到位于交叉点后的母代的基因
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mutation(temp, MUTA_RATE) # 后代以变异率发生变异
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new_pop.append(temp)
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return new_pop
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def mutation(temp, MUTA_RATE):
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if np.random.rand() < MUTA_RATE: # 以MUTA_RATE的概率进行变异
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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
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temp[mutate_point] = temp[mutate_point] ^ 1 # 将变异点的二进制为反转
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def print_info(pop): # 用于输出结果
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fitness = getfitness(pop)
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maxfitness = np.argmax(fitness) # 返回最大值的索引值
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print("max_fitness:", fitness[maxfitness])
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x, y = decodeDNA(pop)
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print("最优的基因型：", pop[maxfitness])
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print("(x, y):", (x[maxfitness], y[maxfitness]))
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print("F(x,y)_max = ", F(x[maxfitness], y[maxfitness]))
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def plot_3d(ax):
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X = np.linspace(*X_BOUND, 100)
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Y = np.linspace(*Y_BOUND, 100)
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X, Y = np.meshgrid(X, Y)
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Z = F(X, Y)
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ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm)
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ax.set_zlim(-20, 100)
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ax.set_xlabel('x')
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ax.set_ylabel('y')
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ax.set_zlabel('z')
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plt.pause(0.01) # 缩短暂停时间
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# 移除 plt.show()
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start_t = datetime.datetime.now()
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if __name__ == "__main__":
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plt.ion() # 提前设置交互模式
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fig = plt.figure()
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ax = fig.add_subplot(111, projection='3d') # 修改3D坐标创建方式
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plot_3d(ax)
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pop = np.random.randint(2, size=(POP_SIZE, DNA_SIZE * 2))
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for _ in range(Iterations):
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x, y = decodeDNA(pop)
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if 'sca' in locals():
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sca.remove()
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sca = ax.scatter(x, y, F(x, y), c='red', marker='o', s=50) # 增大标记尺寸
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plt.draw() # 强制重绘
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plt.pause(0.01) # 保证足够的更新时间
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pop = np.array(crossmuta(pop, CROSS_RATE))
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fitness = getfitness(pop)
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pop = select(pop, fitness) # 选择生成新的种群
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end_t = datetime.datetime.now()
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print((end_t - start_t).seconds)
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print_info(pop)
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plt.ioff()
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plot_3d(ax)
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