Basic: Sobol sequencesΒΆ

In this example we will show the difference between a 2-d Sobol sequence and sampling uniformly at random in 2 dimensions. We will use the sobol and random-search solvers. The Sobol sequence has lower discrepancy, i.e., the generated samples are spread out better in the sampling space.

This example requires matplotlib to generate figures.

#uncomment the following line when you run this notebook interactively
%matplotlib inline
import matplotlib.pyplot as plt
import optunity
import random

Basic configuration and a dummy objective function. We don’t care about the returned function value, just the spread of samples.

def f(x1, x2):
return 0.0

We run the random search solver and Sobol sequence solver.

_, info_random, _ = optunity.minimize(f, num_evals=200, x1=[0, 1], x2=[0, 2], solver_name='random search')
plt.plot(info_random.call_log['args']['x1'], info_random.call_log['args']['x2'], 'bo')
plt.xlabel('x1')
plt.ylabel('x2')
plt.title('Random search')
plt.show()
_, info_sobol, _ = optunity.minimize(f, num_evals=200, x1=[0, 1], x2=[0, 2], solver_name='sobol')
plt.plot(info_sobol.call_log['args']['x1'], info_sobol.call_log['args']['x2'], 'ro')
plt.xlabel('x1')
plt.ylabel('x2')
plt.title('Sobol sequence')
plt.show()