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import os
import io
import matplotlib.pyplot as plt
plt.switch_backend('agg')
from scipy.misc import imread
import numpy as np
import imageio
solution = [10, 10]
def schaffer(x, y):
x -= solution[0]
y -= solution[1]
return 0.5 + ((np.sin((x ** 2) - (y ** 2)) ** 2) - 0.5) \
/ \
((1 + 0.001 * ((x ** 2) + (y ** 2))) ** 2)
def f(w):
return -(schaffer(w[0], w[1]) - schaffer(solution[0], solution[1])) ** 2
def main():
plt.switch_backend('agg')
N = 2
xmean = np.random.randn(N)
sigma = 0.3
stopeval = 1e3 * N ** 2
stopfitness = 1e-10
λ = 64 # 4+int(3*np.log(N))
mu = λ // 4
weights = np.log(mu + 1 / 2) - np.log(np.asarray(range(1, mu + 1))).astype(np.float32)
weights = weights / np.sum(weights)
mueff = (np.sum(weights) ** 2) / np.sum(weights ** 2)
cc = (4 + mueff / N) / (N + 4 + 2 * mueff / N)
cs = (mueff + 2) / (N + mueff + 5)
c1 = 2 / ((N + 1.3) ** 2 + mueff)
cmu = min(1 - c1, 2 * (mueff - 2 + 1 / mueff) / ((N + 2) ** 2 + mueff))
damps = 1 + 2 * max(0, ((mueff - 1) / (N + 1)) ** 0.5 - 1) + cs
pc = np.zeros(N).astype(np.float32)
ps = np.zeros(N).astype(np.float32)
B = np.eye(N, N).astype(np.float32)
D = np.ones(N).astype(np.float32)
C = B * np.diag(D ** 2) * B.T
invsqrtC = B * np.diag(D ** -1) * B.T
eigeneval = 0
chiN = N ** 0.5 * (1 - 1 / (4 * N) + 1 / (21 * N ** 2))
counteval = 0
generation = 0
solution_found = False
graphs = []
while counteval < stopeval:
arx = np.zeros((λ, N))
arfitness = np.zeros(λ)
for k in range(λ):
arx[k] = xmean + sigma * B.dot(D * np.random.randn(N))
arfitness[k] = f(arx[k])
counteval += 1
plt.ylim(-1, 20)
plt.xlim(-1, 20)
plt.plot(solution[0], solution[1], "b.")
plt.plot(arx[:, 0], arx[:, 1], "r.")
plt.plot(np.mean(arx[:, 0]), np.mean(arx[:, 1]), "g.")
buf = io.BytesIO()
plt.savefig(buf, format='png')
plt.clf()
buf.seek(0)
img = imread(buf)
buf.close()
graphs.append(img)
arindex = np.argsort(-arfitness)
arfitness = arfitness[arindex]
xold = xmean
xmean = weights.dot(arx[arindex[0:mu]])
ps = (1 - cs) * ps + np.sqrt(cs * (2 - cs) * mueff) * invsqrtC.dot((xmean - xold) / sigma)
hsig = np.linalg.norm(ps) / np.sqrt(1 - (1 - cs) ** (2 * counteval / λ)) / chiN < 1.4 + 2 / (N + 1)
pc = (1 - cc) * pc + hsig * np.sqrt(cc * (2 - cc) * mueff) * ((xmean - xold) / sigma)
artmp = (1 / sigma) * (arx[arindex[0:mu]] - xold)
C = (1 - c1 - cmu) * C + c1 * (pc.dot(pc.T) + (1 - hsig) * cc * (2 - cc) * C) + cmu * artmp.T.dot(
np.diag(weights)).dot(artmp)
sigma = sigma * np.exp((cs / damps) * (np.linalg.norm(ps) / chiN - 1))
if counteval - eigeneval > λ / (c1 + cmu) / N / 10:
eigeneval = counteval
C = np.triu(C) + np.triu(C, 1).T
D, B = np.linalg.eig(C)
D = np.sqrt(D)
invsqrtC = B.dot(np.diag(D ** -1).dot(B.T))
generation += 1
if arfitness[0] >= -stopfitness:
solution_found = True
break
if solution_found:
print("Solution found at generation #" + str(generation))
else:
print("Solution not found")
if not os.path.exists("result"):
os.makedirs("result")
imageio.mimsave('result/cma-es.gif', graphs)
if __name__ == '__main__':
main()