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 npimport matplotlib.pyplot as pltfrom mpl_toolkits.mplot3d import Axes3Ddef 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", -20z_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：

感觉图像的颜色还不是很好看，等之后优化了来改

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