如何正確設置此優化 model 的動畫？

Question

我已經實現了一個簡單的隨機、基於群體的優化方法——灰狼優化器。 我在使用camera package 在每次迭代中正確捕獲 Matplotlib 圖時遇到了一些麻煩。

我正在為目標 function f(x,y) = x^2 + y^2 運行 GWO。 我只能看到候選解決方案收斂到最小值，但輪廓 plot 沒有出現。

您有什么建議，如何在后台顯示輪廓 plot？

GWO算法實現

%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

Function 來電

# 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

行x = np.linspace(LB[0],LB[1],1000)是否應該x = np.linspace(LB[0],UB[1],1000) ？ 根據您當前對x的定義， x是一個僅填充值 10 的數組，這意味着您不太可能找到輪廓。 您可能想要做的另一件事是將cont = plt.contour(X1,X2,Z,20,linewidths=0.75)線移動到plot_search_agent_positions function 內，以確保在 Z6F1C25ED1523962F1BBF9DEE9BE509 的每次迭代中繪制輪廓進行這些更改后，代碼如下所示：

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)

output 給出：