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import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
def eggholder(x):
return (-(x[1] + 47) * np.sin(np.sqrt(abs(x[0]/2 + (x[1] + 47))))
-x[0] * np.sin(np.sqrt(abs(x[0] - (x[1] + 47)))))
bounds = [(-512, 512), (-512, 512)]
x = np.arange(-512, 513)
y = np.arange(-512, 513)
xgrid, ygrid = np.meshgrid(x, y)
xy = np.stack([xgrid, ygrid])
results = dict()
results['shgo'] = optimize.shgo(eggholder, bounds)
results['DA'] = optimize.dual_annealing(eggholder, bounds)
results['DE'] = optimize.differential_evolution(eggholder, bounds)
results['BH'] = optimize.basinhopping(eggholder, bounds)
results['shgo_sobol'] = optimize.shgo(eggholder, bounds, n=200, iters=5,
sampling_method='sobol')
fig = plt.figure(figsize=(4.5, 4.5))
ax = fig.add_subplot(111)
im = ax.imshow(eggholder(xy), interpolation='bilinear', origin='lower',
cmap='gray')
ax.set_xlabel('x')
ax.set_ylabel('y')
def plot_point(res, marker='o', color=None):
ax.plot(512+res.x[0], 512+res.x[1], marker=marker, color=color, ms=10)
plot_point(results['BH'], color='y') # basinhopping - yellow
plot_point(results['DE'], color='c') # differential_evolution - cyan
plot_point(results['DA'], color='w') # dual_annealing. - white
# SHGO produces multiple minima, plot them all (with a smaller marker size)
plot_point(results['shgo'], color='r', marker='+')
plot_point(results['shgo_sobol'], color='r', marker='x')
for i in range(results['shgo_sobol'].xl.shape[0]):
ax.plot(512 + results['shgo_sobol'].xl[i, 0],
512 + results['shgo_sobol'].xl[i, 1],
'ro', ms=2)
ax.set_xlim([-4, 514*2])
ax.set_ylim([-4, 514*2])
fig.tight_layout()
plt.show()
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