用python绘制评估优化算法性能的测试函数

雨点打透心脏的1/2处 2022-05-23 22:40 332阅读 0赞

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][Link 1]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：  
![这里写图片描述][70]

![这里写图片描述][70 1]

![这里写图片描述][70 2]

![这里写图片描述][70 3]

![这里写图片描述][70 4]

![这里写图片描述][70 5]

![这里写图片描述][70 6]

![这里写图片描述][70 7]

感觉图像的颜色还不是很好看，等之后优化了来改

[Link 1]: https://en.wikipedia.org/wiki/Test_functions_for_optimization#cite_ref-1
[70]: /images/20220524/0ad9224104b04374910258746baecc29.png
[70 1]: /images/20220524/54f2ab9b5b7843ae888002a09c3ee40a.png
[70 2]: /images/20220524/32fc21e5445f4e47a1fe2f813f607478.png
[70 3]: /images/20220524/c94226f8eb974514ba8f6b717fc01497.png
[70 4]: /images/20220524/5146a20a3d004c6d99fe891959b4f73b.png
[70 5]: /images/20220524/4076f7edd37745f38330eeebeb166e92.png
[70 6]: /images/20220524/91507a02a1ae4cd183836e23f9e391cf.png
[70 7]: /images/20220524/40556cf99a294dd0adbaa36fba77fe0b.png