python绘制评估优化算法性能的测试函数

站长资源 2025/5/11 佚名

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南强小屋 Design By 杰米

测试函数主要是用来评估优化算法特性的，这里我用python3绘制了部分测试函数的图像。具体的测试函数可以结合维基百科来了解。想要显示某个测试函数的图片把代码结尾对应的注释去掉即可，具体代码如下：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D


def draw_pic(X, Y, Z, z_max, title, z_min=0):
 fig = plt.figure()
 ax = Axes3D(fig)
 ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.cm.hot)
 # ax.contourf(X, Y, Z, zdir='z', offset=-2, cmap=plt.cm.hot)
 ax.set_zlim(z_min, z_max)
 ax.set_title(title)
 # plt.savefig("./myProject/Algorithm/pic/%s.png" % title) # 保存图片
 plt.show()


def get_X_AND_Y(X_min, X_max, Y_min, Y_max):
 X = np.arange(X_min, X_max, 0.1)
 Y = np.arange(Y_min, Y_max, 0.1)
 X, Y = np.meshgrid(X, Y)
 return X, Y


# rastrigin测试函数
def Rastrigin(X_min = -5.52, X_max = 5.12, Y_min = -5.12, Y_max = 5.12):
 A = 10
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = 2 * A + X ** 2 - A * np.cos(2 * np.pi * X) + Y ** 2 - A * np.cos(2 * np.pi * Y)
 return X, Y, Z, 100, "Rastrigin function"


# Ackley测试函数
def Ackley(X_min = -5, X_max = 5, Y_min = -5, Y_max = 5):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = -20 * np.exp(-0.2 * np.sqrt(0.5 * (X**2 + Y**2))) -   np.exp(0.5 * (np.cos(2 * np.pi * X) + np.cos(2 * np.pi * Y))) + np.e + 20
 return X, Y, Z, 15, "Ackley function"


# Sphere测试函数
def Sphere(X_min = -3, X_max = 3, Y_min = -3, Y_max = 3):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = X**2 + Y**2
 return X, Y, Z, 20, "Sphere function"


# beale测试函数
def Beale(X_min = -4.5, X_max = 4.5, Y_min = -4.5, Y_max = 4.5):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = np.power(1.5 - X + X * Y, 2) + np.power(2.25 - X + X * (Y ** 2), 2)   + np.power(2.625 - X + X * (Y ** 3), 2)
 return X, Y, Z, 150000, "Beale function"


# Booth测试函数
def Booth(X_min = -10, X_max = 10, Y_min = -10, Y_max = 10):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = np.power(X + 2*Y - 7, 2) + np.power(2 * X + Y - 5, 2)
 return X, Y, Z, 2500, "Booth function"


# Bukin测试函数
def Bukin(X_min = -15, X_max = -5, Y_min = -3, Y_max = 3):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = 100 * np.sqrt(np.abs(Y - 0.01 * X**2)) + 0.01 * np.abs(X + 10)
 return X, Y, Z, 200, "Bukin function"


# Three-hump camel测试函数
def three_humpCamel(X_min = -5, X_max = 5, Y_min = -5, Y_max = 5):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = 2 * X**2 - 1.05 * X**4 + (1/6) * X**6 + X*Y + Y*2
 return X, Y, Z, 2000, "three-hump camel function"


# Hölder table测试函数
def Holder_table(X_min = -10, X_max = 10, Y_min = -10, Y_max = 10):
 X, Y = get_X_AND_Y(X_min, X_max, Y_min, Y_max)
 Z = -np.abs(np.sin(X) * np.cos(Y) * np.exp(np.abs(1 - np.sqrt(X**2 + Y**2)/np.pi)))
 return X, Y, Z, 0, "Hölder table function", -20



z_min = None
# X, Y, Z, z_max, title = Rastrigin()
# X, Y, Z, z_max, title = Ackley()
# X, Y, Z, z_max, title = Sphere()
# X, Y, Z, z_max, title = Beale()
X, Y, Z, z_max, title = Booth()
# X, Y, Z, z_max, title = Bukin()
# X, Y, Z, z_max, title = three_humpCamel()
# X, Y, Z, z_max, title, z_min = Holder_table()

draw_pic(X, Y, Z, z_max, title, z_min)

以下是上述代码绘制的测试函数的图像：