python - 如何正确地为这个优化模型制作动画

Question

我实现了一种简单的随机化、基于群体的优化方法——灰狼优化器。我在使用 camera 包在每次迭代中正确捕获 Matplotlib 图时遇到了一些问题。

我正在为目标函数 f(x,y) = x^2 + y^2 运行 GWO。我只能看到候选解收敛到最小值，但没有显示等值线图。

你有什么建议吗，我怎样才能在后台显示等高线图？

GWO 算法实现

%matplotlib notebook
import matplotlib.pyplot as plt
import numpy as np
from celluloid import Camera
import ffmpeg
import pillow

# X : Position vector of the initial population
# n : Initial population size

def gwo(f,max_iterations,LB,UB):
    
    fig = plt.figure()
    camera = Camera(fig)
    
    def random_population_uniform(m,a,b):
        dims = len(a)
        x = [list(a + np.multiply(np.random.rand(dims),b - a)) for i in range(m)]
        return np.array(x)

    def search_agent_fitness(fitness):
        alpha = 0
        if fitness[1] < fitness[alpha]:
            alpha, beta = 1, alpha
        else:
            beta = 1

        if fitness[2] > fitness[alpha] and fitness[2] < fitness[beta]:
            beta, delta = 2, beta
        elif fitness[2] < fitness[alpha]:
            alpha,beta,delta = 2,alpha,beta
        else:
            delta = 2

        for i in range(3,len(fitness)):
            if fitness[i] <= fitness[alpha]:
                alpha, beta,delta = i, alpha, beta
            elif fitness[i] > fitness[alpha] and fitness[i]<= fitness[beta]:
                beta,delta = i,beta
            elif fitness[i] > fitness[beta] and fitness[i]<= fitness[delta]:
                delta = i

        return alpha, beta, delta
    
    
    def plot_search_agent_positions(f,X,alpha,beta,delta,a,b):
        
    
        # Plot the positions of search agents

        x = X[:,0]
        y = X[:,1]
        
        
        s = plt.scatter(x,y,c='gray',zorder=1)
        s = plt.scatter(x[alpha],y[alpha],c='red',zorder=1)
        s = plt.scatter(x[beta],y[beta],c='blue',zorder=1)
        s = plt.scatter(x[delta],y[delta],c='green',zorder=1)
        
        camera.snap()
    

    
    # Initialize the position of the search agents
    X = random_population_uniform(50,np.array(LB),np.array(UB))
    
    n = len(X)

    l = 1
    
    # Plot the first image on screen
    x = np.linspace(LB[0],LB[1],1000)
    y = np.linspace(LB[0],UB[1],1000)

    X1,X2 = np.meshgrid(x,y)


    Z = f(X1,X2)
    cont = plt.contour(X1,X2,Z,20,linewidths=0.75)
    
    while (l < max_iterations):
            # Take the x,y coordinates of the initial population
            x = X[:,0]
            y = X[:,1]

            # Calculate the objective function for each search agent 
            fitness = list(map(f,x,y))

            # Update alpha, beta and delta
            alpha,beta,delta = search_agent_fitness(fitness)
            
            # Plot search agent positions
            plot_search_agent_positions(f,X,alpha,beta,delta,LB,UB)
            
            # a decreases linearly from 2 to 0
            a = 2 - l *(2 / max_iterations)

            # Update the position of search agents including the Omegas
            for i in range(n):
                x_prey = X[alpha]

                r1 = np.random.rand(2) #r1 is a random vector in [0,1] x [0,1]
                r2 = np.random.rand(2) #r2 is a random vector in [0,1] x [0,1]
                A1 = 2*a*r1 - a
                C1 = 2*r2

                D_alpha = np.abs(C1 * x_prey - X[i])
                X_1 = x_prey - A1*D_alpha
                
                x_prey = X[beta]
                r1 = np.random.rand(2) 
                r2 = np.random.rand(2) 
                A2 = 2*a*r1 - a
                C2 = 2*r2

                D_beta = np.abs(C2 * x_prey - X[i])
                X_2 = x_prey - A2*D_beta

                x_prey = X[delta]
                r1 = np.random.rand(2) 
                r2 = np.random.rand(2) 
                A3 = 2*a*r1 - a
                C3 = 2*r2

                D_delta = np.abs(C3 * x_prey - X[i])
                X_3 = x_prey - A3*D_delta

                X[i] = (X_1 + X_2 + X_3)/3

            l = l + 1
            

    return X[alpha],camera

函数调用

# define the objective function
def f(x,y):
    return x**2 + y**2

minimizer,camera = gwo(f,7,[-10,-10],[10,10])

animation = camera.animate(interval = 1000, repeat = True,
                           repeat_delay = 500)

Answer 1

x = np.linspace(LB[0],LB[1],1000) 行是否可能是 x = np.linspace(LB[0], UB[1],1000) 代替？根据您当前对 x 的定义，x 是一个仅填充值 -10 的数组，这意味着您不太可能找到轮廓。您可能想要做的另一件事是将 cont = plt.contour(X1,X2,Z,20,linewidths=0.75) 行移动到您的 plot_search_agent_positions 函数中以确保在动画的每次迭代中绘制轮廓。进行这些更改后，代码如下所示:

import matplotlib.pyplot as plt
import numpy as np
from celluloid import Camera
import ffmpeg
import PIL
from matplotlib import animation, rc
from IPython.display import HTML, Image # For GIF
from scipy.interpolate import griddata

rc('animation', html='html5')

# X : Position vector of the initial population
# n : Initial population size

def gwo(f,max_iterations,LB,UB):
    
    fig = plt.figure()
    fig.gca(aspect='equal')
    camera = Camera(fig)
    
    def random_population_uniform(m,a,b):
        dims = len(a)
        x = [list(a + np.multiply(np.random.rand(dims),b - a)) for i in range(m)]
        return np.array(x)

    def search_agent_fitness(fitness):
        alpha = 0
        if fitness[1] < fitness[alpha]:
            alpha, beta = 1, alpha
        else:
            beta = 1

        if fitness[2] > fitness[alpha] and fitness[2] < fitness[beta]:
            beta, delta = 2, beta
        elif fitness[2] < fitness[alpha]:
            alpha,beta,delta = 2,alpha,beta
        else:
            delta = 2

        for i in range(3,len(fitness)):
            if fitness[i] <= fitness[alpha]:
                alpha, beta,delta = i, alpha, beta
            elif fitness[i] > fitness[alpha] and fitness[i]<= fitness[beta]:
                beta,delta = i,beta
            elif fitness[i] > fitness[beta] and fitness[i]<= fitness[delta]:
                delta = i

        return alpha, beta, delta
    
    
    def plot_search_agent_positions(f,X,alpha,beta,delta,a,b,X1,X2,Z):
        
    
        # Plot the positions of search agents

        x = X[:,0]
        y = X[:,1]
        
        
        s = plt.scatter(x,y,c='gray',zorder=1)
        s = plt.scatter(x[alpha],y[alpha],c='red',zorder=1)
        s = plt.scatter(x[beta],y[beta],c='blue',zorder=1)
        s = plt.scatter(x[delta],y[delta],c='green',zorder=1)
        Z=f(X1,X2)
        cont=plt.contour(X1,X2,Z,levels=20,colors='k',norm=True)
        plt.clabel(cont, cont.levels, inline=True, fontsize=10)
        camera.snap()
    

    
    # Initialize the position of the search agents
    X = random_population_uniform(50,np.array(LB),np.array(UB))
    
    n = len(X)

    l = 1
    
    # Plot the first image on screen
    x = np.linspace(LB[0],UB[1],1000)
    y = np.linspace(LB[0],UB[1],1000)

    X1,X2 = np.meshgrid(x,y)
    Z=f(X1,X2)

    while (l < max_iterations):
            # Take the x,y coordinates of the initial population
            x = X[:,0]
            y = X[:,1]

            # Calculate the objective function for each search agent 
            fitness = list(map(f,x,y))

            # Update alpha, beta and delta
            alpha,beta,delta = search_agent_fitness(fitness)
            
            # Plot search agent positions
            plot_search_agent_positions(f,X,alpha,beta,delta,LB,UB,X1,X2,Z)
            
            # a decreases linearly from 2 to 0
            a = 2 - l *(2 / max_iterations)

            # Update the position of search agents including the Omegas
            for i in range(n):
                x_prey = X[alpha]

                r1 = np.random.rand(2) #r1 is a random vector in [0,1] x [0,1]
                r2 = np.random.rand(2) #r2 is a random vector in [0,1] x [0,1]
                A1 = 2*a*r1 - a
                C1 = 2*r2

                D_alpha = np.abs(C1 * x_prey - X[i])
                X_1 = x_prey - A1*D_alpha
                
                x_prey = X[beta]
                r1 = np.random.rand(2) 
                r2 = np.random.rand(2) 
                A2 = 2*a*r1 - a
                C2 = 2*r2

                D_beta = np.abs(C2 * x_prey - X[i])
                X_2 = x_prey - A2*D_beta

                x_prey = X[delta]
                r1 = np.random.rand(2) 
                r2 = np.random.rand(2) 
                A3 = 2*a*r1 - a
                C3 = 2*r2

                D_delta = np.abs(C3 * x_prey - X[i])
                X_3 = x_prey - A3*D_delta

                X[i] = (X_1 + X_2 + X_3)/3

            l = l + 1
            

    return X[alpha],camera
    # define the objective function
def f(x,y):
    return x**2 + y**2

minimizer,camera = gwo(f,7,[-10,-10],[10,10])

animation = camera.animate(interval = 1000, repeat = True,repeat_delay = 500)

输出给出: