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Я реализовал простой рандомизированный метод оптимизации на основе популяции- оптимизатор Серого волка. У меня возникли некоторые проблемы с правильным захватом графиков Matplotlib на каждой итерации с использованием camera пакета.

Я запускаю GWO для целевой функции f(x,y) = x^2 y^2. Я вижу только возможные решения, сходящиеся к минимумам, но контурный график не отображается.

У вас есть какие-либо предложения, как я могу отобразить контурный график в фоновом режиме?

Реализация алгоритма GWO

 %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] lt; fitness[alpha]:  alpha, beta = 1, alpha  else:  beta = 1   if fitness[2] gt; fitness[alpha] and fitness[2] lt; fitness[beta]:  beta, delta = 2, beta  elif fitness[2] lt; fitness[alpha]:  alpha,beta,delta = 2,alpha,beta  else:  delta = 2   for i in range(3,len(fitness)):  if fitness[i] lt;= fitness[alpha]:  alpha, beta,delta = i, alpha, beta  elif fitness[i] gt; fitness[alpha] and fitness[i]lt;= fitness[beta]:  beta,delta = i,beta  elif fitness[i] gt; fitness[beta] and fitness[i]lt;= 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 lt; 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  

Вызов функции

 # 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)  

Возможно ли x = np.linspace(LB[0],LB[1],1000) , чтобы вместо этого была строка x = np.linspace(LB[0],UB[1],1000) ? С вашим текущим определением x , x является массивом, заполненным только значением -10 , что означает, что вы вряд ли найдете контур. Еще одна вещь, которую вы, возможно, захотите сделать, — это переместить cont = plt.contour(X1,X2,Z,20,linewidths=0.75) линию внутри вашей plot_search_agent_positions функции, чтобы убедиться, что контур отображается на каждой итерации анимации. Как только вы внесете эти изменения, код будет выглядеть следующим образом:

 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] lt; fitness[alpha]:  alpha, beta = 1, alpha  else:  beta = 1   if fitness[2] gt; fitness[alpha] and fitness[2] lt; fitness[beta]:  beta, delta = 2, beta  elif fitness[2] lt; fitness[alpha]:  alpha,beta,delta = 2,alpha,beta  else:  delta = 2   for i in range(3,len(fitness)):  if fitness[i] lt;= fitness[alpha]:  alpha, beta,delta = i, alpha, beta  elif fitness[i] gt; fitness[alpha] and fitness[i]lt;= fitness[beta]:  beta,delta = i,beta  elif fitness[i] gt; fitness[beta] and fitness[i]lt;= 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 lt; 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)  

И результат дает: