In [1]:
import openturns as ot
import numpy as np
import matplotlib.pyplot as plt
from skgarden import RandomForestQuantileRegressor
from depimpact.plots import set_style_paper
from skopt import forest_minimize
from skopt.acquisition import gaussian_ei, gaussian_lcb, gaussian_pi
%matplotlib inline
%load_ext autoreload
%autoreload 2
set_style_paper()
In [2]:
from scipy.special import erfinv
def func(X, noise_lvl=0.2, nu=1., return_quantile=False, type_noise='uniform', alpha=0.05):
"""
"""
X = np.asarray(X)
n_sample = X.shape[0]
if type_noise == 'uniform':
noise = np.random.uniform(-noise_lvl, noise_lvl, n_sample)
elif type_noise == 'normal':
noise = np.random.normal(0., noise_lvl, n_sample)
else:
raise ValueError('Wrong type_noise')
y = X*np.cos(2*np.pi*X) + (X-nu)**2*noise
if return_quantile:
if type_noise == 'uniform':
q = 2*noise_lvl*alpha - noise_lvl
elif type_noise == 'normal':
q = noise_lvl*np.sqrt(2)*erfinv * (2*alpha - 1)
quantile = X*np.cos(2*np.pi*X) + (X-nu)**2*q
if n_sample == 1:
return y.item(), quantile.item()
else:
return y, quantile
else:
if n_sample == 1:
return y.item()
else:
return y
In [3]:
xmin, xmax = -np.pi/2, np.pi/2.
def plot_func(func, xmin, xmax, n_plot=100000, alpha=0.05, ax=None):
x_plot = np.linspace(xmin, xmax, n_plot)
y_true = func(x_plot, noise_lvl=0.)
y_noised, quant = func(x_plot, return_quantile=True, alpha=alpha)
id_min_true = y_true.argmin()
id_min_noised = quant.argmin()
if ax is None:
fig, ax = plt.subplots(figsize=(7, 4))
ax.plot(x_plot, y_true, 'g-', label='Mean')
ax.plot(x_plot, quant, 'k-', label='Quantile at $\\alpha=%d$ %%' % (alpha*100))
#ax.plot(x_plot[id_min_true], y_true[id_min_true], 'go', label='Excepted min')
#ax.plot(x_plot[id_min_noised], quant[id_min_noised], 'ro', label='Quantile min')
ax.set_xlim(xmin, xmax)
ax.set_xlabel('$x$')
ax.set_ylabel('$y$')
return ax
fig, ax = plt.subplots(figsize=(7, 4))
plot_func(func, xmin, xmax, ax=ax)
ax.legend(loc=0)
fig.tight_layout()
In [4]:
class ModifiedRandomForestQuantileRegressor(RandomForestQuantileRegressor):
def predict(self, X, return_std=False):
"""
"""
X = np.asarray(X)
alpha = 0.05
if return_std:
n_sample = X.shape[0]
n_estimators = self.n_estimators
pred = np.zeros((n_estimators, n_sample))
for i, tree in enumerate(self.estimators_):
pred[i] = tree.predict(X, quantile=alpha*100)
mean = pred.mean(axis=0)
std = pred.std(axis=0)
return mean, std
else:
mean = RandomForestQuantileRegressor.predict(self, X, quantile=alpha*100)
return mean
In [5]:
n_random_starts = 50
n_iter = 100
n_estimators = 200
min_samples_split = max(2, int(n_random_starts/10))
rfq = ModifiedRandomForestQuantileRegressor(n_estimators, min_samples_split=min_samples_split, n_jobs=7)
n_calls = n_random_start + n_iter
space = [(xmin, xmax)]
acq_func = 'EI'
opt_res = forest_minimize(func, space, acq_func=acq_func, base_estimator=rfq,
n_calls=n_calls, n_random_starts=n_random_starts, n_jobs=7, verbose=True)
Iteration No: 1 started. Evaluating function at random point.
Iteration No: 1 ended. Evaluation done at random point.
Time taken: 0.0011
Function value obtained: -1.4609
Current minimum: -1.4609
Iteration No: 2 started. Evaluating function at random point.
Iteration No: 2 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.0731
Current minimum: -1.4609
Iteration No: 3 started. Evaluating function at random point.
Iteration No: 3 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 1.0099
Current minimum: -1.4609
Iteration No: 4 started. Evaluating function at random point.
Iteration No: 4 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.7427
Current minimum: -1.4609
Iteration No: 5 started. Evaluating function at random point.
Iteration No: 5 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -1.4953
Current minimum: -1.4953
Iteration No: 6 started. Evaluating function at random point.
Iteration No: 6 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.4978
Current minimum: -1.4953
Iteration No: 7 started. Evaluating function at random point.
Iteration No: 7 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.2902
Current minimum: -1.4953
Iteration No: 8 started. Evaluating function at random point.
Iteration No: 8 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.4008
Current minimum: -1.4953
Iteration No: 9 started. Evaluating function at random point.
Iteration No: 9 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.5245
Current minimum: -1.4953
Iteration No: 10 started. Evaluating function at random point.
Iteration No: 10 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.5930
Current minimum: -1.4953
Iteration No: 11 started. Evaluating function at random point.
Iteration No: 11 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.4384
Current minimum: -1.4953
Iteration No: 12 started. Evaluating function at random point.
Iteration No: 12 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.0975
Current minimum: -1.4953
Iteration No: 13 started. Evaluating function at random point.
Iteration No: 13 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.8470
Current minimum: -1.4953
Iteration No: 14 started. Evaluating function at random point.
Iteration No: 14 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.5346
Current minimum: -1.4953
Iteration No: 15 started. Evaluating function at random point.
Iteration No: 15 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.3934
Current minimum: -1.4953
Iteration No: 16 started. Evaluating function at random point.
Iteration No: 16 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.0165
Current minimum: -1.4953
Iteration No: 17 started. Evaluating function at random point.
Iteration No: 17 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.4028
Current minimum: -1.4953
Iteration No: 18 started. Evaluating function at random point.
Iteration No: 18 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.7922
Current minimum: -1.4953
Iteration No: 19 started. Evaluating function at random point.
Iteration No: 19 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.1150
Current minimum: -1.4953
Iteration No: 20 started. Evaluating function at random point.
Iteration No: 20 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.3933
Current minimum: -1.4953
Iteration No: 21 started. Evaluating function at random point.
Iteration No: 21 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.9207
Current minimum: -1.4953
Iteration No: 22 started. Evaluating function at random point.
Iteration No: 22 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.4901
Current minimum: -1.4953
Iteration No: 23 started. Evaluating function at random point.
Iteration No: 23 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.9877
Current minimum: -1.4953
Iteration No: 24 started. Evaluating function at random point.
Iteration No: 24 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -1.2339
Current minimum: -1.4953
Iteration No: 25 started. Evaluating function at random point.
Iteration No: 25 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.1592
Current minimum: -1.4953
Iteration No: 26 started. Evaluating function at random point.
Iteration No: 26 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.8584
Current minimum: -1.4953
Iteration No: 27 started. Evaluating function at random point.
Iteration No: 27 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.2150
Current minimum: -1.4953
Iteration No: 28 started. Evaluating function at random point.
Iteration No: 28 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.0834
Current minimum: -1.4953
Iteration No: 29 started. Evaluating function at random point.
Iteration No: 29 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -1.2368
Current minimum: -1.4953
Iteration No: 30 started. Evaluating function at random point.
Iteration No: 30 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.4761
Current minimum: -1.4953
Iteration No: 31 started. Evaluating function at random point.
Iteration No: 31 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.9264
Current minimum: -1.4953
Iteration No: 32 started. Evaluating function at random point.
Iteration No: 32 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.0678
Current minimum: -1.4953
Iteration No: 33 started. Evaluating function at random point.
Iteration No: 33 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.0263
Current minimum: -1.4953
Iteration No: 34 started. Evaluating function at random point.
Iteration No: 34 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: -0.4902
Current minimum: -1.4953
Iteration No: 35 started. Evaluating function at random point.
Iteration No: 35 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: -0.3428
Current minimum: -1.4953
Iteration No: 36 started. Evaluating function at random point.
Iteration No: 36 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: 0.1639
Current minimum: -1.4953
Iteration No: 37 started. Evaluating function at random point.
Iteration No: 37 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: 1.0108
Current minimum: -1.4953
Iteration No: 38 started. Evaluating function at random point.
Iteration No: 38 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: 0.1171
Current minimum: -1.4953
Iteration No: 39 started. Evaluating function at random point.
Iteration No: 39 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: 0.4268
Current minimum: -1.4953
Iteration No: 40 started. Evaluating function at random point.
Iteration No: 40 ended. Evaluation done at random point.
Time taken: 0.0003
Function value obtained: 0.2904
Current minimum: -1.4953
Iteration No: 41 started. Evaluating function at random point.
Iteration No: 41 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.2535
Current minimum: -1.4953
Iteration No: 42 started. Evaluating function at random point.
Iteration No: 42 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.4043
Current minimum: -1.4953
Iteration No: 43 started. Evaluating function at random point.
Iteration No: 43 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 1.9195
Current minimum: -1.4953
Iteration No: 44 started. Evaluating function at random point.
Iteration No: 44 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -1.2208
Current minimum: -1.4953
Iteration No: 45 started. Evaluating function at random point.
Iteration No: 45 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.5002
Current minimum: -1.4953
Iteration No: 46 started. Evaluating function at random point.
Iteration No: 46 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.3010
Current minimum: -1.4953
Iteration No: 47 started. Evaluating function at random point.
Iteration No: 47 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.3379
Current minimum: -1.4953
Iteration No: 48 started. Evaluating function at random point.
Iteration No: 48 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: -0.0303
Current minimum: -1.4953
Iteration No: 49 started. Evaluating function at random point.
Iteration No: 49 ended. Evaluation done at random point.
Time taken: 0.0004
Function value obtained: 0.8372
Current minimum: -1.4953
Iteration No: 50 started. Evaluating function at random point.
Iteration No: 50 ended. Evaluation done at random point.
Time taken: 1.1746
Function value obtained: 0.6548
Current minimum: -1.4953
Iteration No: 51 started. Searching for the next optimal point.
Iteration No: 51 ended. Search finished for the next optimal point.
Time taken: 1.3088
Function value obtained: -0.9089
Current minimum: -1.4953
Iteration No: 52 started. Searching for the next optimal point.
Iteration No: 52 ended. Search finished for the next optimal point.
Time taken: 1.1791
Function value obtained: -0.5852
Current minimum: -1.4953
Iteration No: 53 started. Searching for the next optimal point.
Iteration No: 53 ended. Search finished for the next optimal point.
Time taken: 1.2678
Function value obtained: -0.8282
Current minimum: -1.4953
Iteration No: 54 started. Searching for the next optimal point.
Iteration No: 54 ended. Search finished for the next optimal point.
Time taken: 1.2837
Function value obtained: 0.0303
Current minimum: -1.4953
Iteration No: 55 started. Searching for the next optimal point.
Iteration No: 55 ended. Search finished for the next optimal point.
Time taken: 1.1831
Function value obtained: -0.6646
Current minimum: -1.4953
Iteration No: 56 started. Searching for the next optimal point.
Iteration No: 56 ended. Search finished for the next optimal point.
Time taken: 1.2067
Function value obtained: -0.4879
Current minimum: -1.4953
Iteration No: 57 started. Searching for the next optimal point.
Iteration No: 57 ended. Search finished for the next optimal point.
Time taken: 1.3093
Function value obtained: -1.0460
Current minimum: -1.4953
Iteration No: 58 started. Searching for the next optimal point.
Iteration No: 58 ended. Search finished for the next optimal point.
Time taken: 1.2352
Function value obtained: -1.4279
Current minimum: -1.4953
Iteration No: 59 started. Searching for the next optimal point.
Iteration No: 59 ended. Search finished for the next optimal point.
Time taken: 1.2672
Function value obtained: -1.0871
Current minimum: -1.4953
Iteration No: 60 started. Searching for the next optimal point.
Iteration No: 60 ended. Search finished for the next optimal point.
Time taken: 1.3010
Function value obtained: 0.2273
Current minimum: -1.4953
Iteration No: 61 started. Searching for the next optimal point.
Iteration No: 61 ended. Search finished for the next optimal point.
Time taken: 1.3254
Function value obtained: -1.1057
Current minimum: -1.4953
Iteration No: 62 started. Searching for the next optimal point.
Iteration No: 62 ended. Search finished for the next optimal point.
Time taken: 1.3371
Function value obtained: -0.1023
Current minimum: -1.4953
Iteration No: 63 started. Searching for the next optimal point.
Iteration No: 63 ended. Search finished for the next optimal point.
Time taken: 1.3595
Function value obtained: -0.9552
Current minimum: -1.4953
Iteration No: 64 started. Searching for the next optimal point.
Iteration No: 64 ended. Search finished for the next optimal point.
Time taken: 1.4625
Function value obtained: -0.1852
Current minimum: -1.4953
Iteration No: 65 started. Searching for the next optimal point.
Iteration No: 65 ended. Search finished for the next optimal point.
Time taken: 1.3719
Function value obtained: -0.6245
Current minimum: -1.4953
Iteration No: 66 started. Searching for the next optimal point.
Iteration No: 66 ended. Search finished for the next optimal point.
Time taken: 1.2628
Function value obtained: -1.2821
Current minimum: -1.4953
Iteration No: 67 started. Searching for the next optimal point.
Iteration No: 67 ended. Search finished for the next optimal point.
Time taken: 1.2808
Function value obtained: -0.5407
Current minimum: -1.4953
Iteration No: 68 started. Searching for the next optimal point.
Iteration No: 68 ended. Search finished for the next optimal point.
Time taken: 1.2821
Function value obtained: -0.6192
Current minimum: -1.4953
Iteration No: 69 started. Searching for the next optimal point.
Iteration No: 69 ended. Search finished for the next optimal point.
Time taken: 1.4636
Function value obtained: -1.5997
Current minimum: -1.5997
Iteration No: 70 started. Searching for the next optimal point.
Iteration No: 70 ended. Search finished for the next optimal point.
Time taken: 1.3913
Function value obtained: -1.6356
Current minimum: -1.6356
Iteration No: 71 started. Searching for the next optimal point.
Iteration No: 71 ended. Search finished for the next optimal point.
Time taken: 1.3944
Function value obtained: -0.5352
Current minimum: -1.6356
Iteration No: 72 started. Searching for the next optimal point.
Iteration No: 72 ended. Search finished for the next optimal point.
Time taken: 1.2850
Function value obtained: -1.6533
Current minimum: -1.6533
Iteration No: 73 started. Searching for the next optimal point.
Iteration No: 73 ended. Search finished for the next optimal point.
Time taken: 1.4027
Function value obtained: -0.9775
Current minimum: -1.6533
Iteration No: 74 started. Searching for the next optimal point.
Iteration No: 74 ended. Search finished for the next optimal point.
Time taken: 1.3270
Function value obtained: -1.0583
Current minimum: -1.6533
Iteration No: 75 started. Searching for the next optimal point.
Iteration No: 75 ended. Search finished for the next optimal point.
Time taken: 1.3353
Function value obtained: -0.7195
Current minimum: -1.6533
Iteration No: 76 started. Searching for the next optimal point.
Iteration No: 76 ended. Search finished for the next optimal point.
Time taken: 1.4211
Function value obtained: -1.1728
Current minimum: -1.6533
Iteration No: 77 started. Searching for the next optimal point.
Iteration No: 77 ended. Search finished for the next optimal point.
Time taken: 1.4878
Function value obtained: -1.3208
Current minimum: -1.6533
Iteration No: 78 started. Searching for the next optimal point.
Iteration No: 78 ended. Search finished for the next optimal point.
Time taken: 1.4465
Function value obtained: -0.3383
Current minimum: -1.6533
Iteration No: 79 started. Searching for the next optimal point.
Iteration No: 79 ended. Search finished for the next optimal point.
Time taken: 1.4306
Function value obtained: -1.0332
Current minimum: -1.6533
Iteration No: 80 started. Searching for the next optimal point.
Iteration No: 80 ended. Search finished for the next optimal point.
Time taken: 1.5530
Function value obtained: -0.8943
Current minimum: -1.6533
Iteration No: 81 started. Searching for the next optimal point.
Iteration No: 81 ended. Search finished for the next optimal point.
Time taken: 1.5657
Function value obtained: -0.9309
Current minimum: -1.6533
Iteration No: 82 started. Searching for the next optimal point.
Iteration No: 82 ended. Search finished for the next optimal point.
Time taken: 1.5718
Function value obtained: -0.2104
Current minimum: -1.6533
Iteration No: 83 started. Searching for the next optimal point.
Iteration No: 83 ended. Search finished for the next optimal point.
Time taken: 1.3783
Function value obtained: -0.5705
Current minimum: -1.6533
Iteration No: 84 started. Searching for the next optimal point.
Iteration No: 84 ended. Search finished for the next optimal point.
Time taken: 1.3836
Function value obtained: -0.5858
Current minimum: -1.6533
Iteration No: 85 started. Searching for the next optimal point.
Iteration No: 85 ended. Search finished for the next optimal point.
Time taken: 1.3832
Function value obtained: -1.0241
Current minimum: -1.6533
Iteration No: 86 started. Searching for the next optimal point.
Iteration No: 86 ended. Search finished for the next optimal point.
Time taken: 1.4593
Function value obtained: -1.3204
Current minimum: -1.6533
Iteration No: 87 started. Searching for the next optimal point.
Iteration No: 87 ended. Search finished for the next optimal point.
Time taken: 1.4009
Function value obtained: -1.2663
Current minimum: -1.6533
Iteration No: 88 started. Searching for the next optimal point.
Iteration No: 88 ended. Search finished for the next optimal point.
Time taken: 1.5073
Function value obtained: -0.4796
Current minimum: -1.6533
Iteration No: 89 started. Searching for the next optimal point.
Iteration No: 89 ended. Search finished for the next optimal point.
Time taken: 1.4333
Function value obtained: -0.2405
Current minimum: -1.6533
Iteration No: 90 started. Searching for the next optimal point.
Iteration No: 90 ended. Search finished for the next optimal point.
Time taken: 1.5209
Function value obtained: -1.1396
Current minimum: -1.6533
Iteration No: 91 started. Searching for the next optimal point.
Iteration No: 91 ended. Search finished for the next optimal point.
Time taken: 1.4143
Function value obtained: -1.1935
Current minimum: -1.6533
Iteration No: 92 started. Searching for the next optimal point.
Iteration No: 92 ended. Search finished for the next optimal point.
Time taken: 1.4269
Function value obtained: -1.2097
Current minimum: -1.6533
Iteration No: 93 started. Searching for the next optimal point.
Iteration No: 93 ended. Search finished for the next optimal point.
Time taken: 1.5254
Function value obtained: -1.1508
Current minimum: -1.6533
Iteration No: 94 started. Searching for the next optimal point.
Iteration No: 94 ended. Search finished for the next optimal point.
Time taken: 1.5658
Function value obtained: -0.7128
Current minimum: -1.6533
Iteration No: 95 started. Searching for the next optimal point.
Iteration No: 95 ended. Search finished for the next optimal point.
Time taken: 1.6393
Function value obtained: -0.3034
Current minimum: -1.6533
Iteration No: 96 started. Searching for the next optimal point.
Iteration No: 96 ended. Search finished for the next optimal point.
Time taken: 1.5807
Function value obtained: -0.2045
Current minimum: -1.6533
Iteration No: 97 started. Searching for the next optimal point.
Iteration No: 97 ended. Search finished for the next optimal point.
Time taken: 1.6780
Function value obtained: -1.0611
Current minimum: -1.6533
Iteration No: 98 started. Searching for the next optimal point.
Iteration No: 98 ended. Search finished for the next optimal point.
Time taken: 1.5847
Function value obtained: -0.1525
Current minimum: -1.6533
Iteration No: 99 started. Searching for the next optimal point.
Iteration No: 99 ended. Search finished for the next optimal point.
Time taken: 1.5951
Function value obtained: -1.0377
Current minimum: -1.6533
Iteration No: 100 started. Searching for the next optimal point.
Iteration No: 100 ended. Search finished for the next optimal point.
Time taken: 1.6946
Function value obtained: -0.6358
Current minimum: -1.6533
Iteration No: 101 started. Searching for the next optimal point.
Iteration No: 101 ended. Search finished for the next optimal point.
Time taken: 1.5894
Function value obtained: -1.0265
Current minimum: -1.6533
Iteration No: 102 started. Searching for the next optimal point.
Iteration No: 102 ended. Search finished for the next optimal point.
Time taken: 1.6844
Function value obtained: -0.4785
Current minimum: -1.6533
Iteration No: 103 started. Searching for the next optimal point.
Iteration No: 103 ended. Search finished for the next optimal point.
Time taken: 1.6888
Function value obtained: -0.3213
Current minimum: -1.6533
Iteration No: 104 started. Searching for the next optimal point.
Iteration No: 104 ended. Search finished for the next optimal point.
Time taken: 1.7846
Function value obtained: -0.2814
Current minimum: -1.6533
Iteration No: 105 started. Searching for the next optimal point.
Iteration No: 105 ended. Search finished for the next optimal point.
Time taken: 1.6198
Function value obtained: -1.1431
Current minimum: -1.6533
Iteration No: 106 started. Searching for the next optimal point.
Iteration No: 106 ended. Search finished for the next optimal point.
Time taken: 1.7322
Function value obtained: -1.2408
Current minimum: -1.6533
Iteration No: 107 started. Searching for the next optimal point.
Iteration No: 107 ended. Search finished for the next optimal point.
Time taken: 1.7285
Function value obtained: -0.8831
Current minimum: -1.6533
Iteration No: 108 started. Searching for the next optimal point.
Iteration No: 108 ended. Search finished for the next optimal point.
Time taken: 1.5097
Function value obtained: -0.8263
Current minimum: -1.6533
Iteration No: 109 started. Searching for the next optimal point.
Iteration No: 109 ended. Search finished for the next optimal point.
Time taken: 1.7306
Function value obtained: -1.0830
Current minimum: -1.6533
Iteration No: 110 started. Searching for the next optimal point.
Iteration No: 110 ended. Search finished for the next optimal point.
Time taken: 1.7384
Function value obtained: -1.5610
Current minimum: -1.6533
Iteration No: 111 started. Searching for the next optimal point.
Iteration No: 111 ended. Search finished for the next optimal point.
Time taken: 1.5136
Function value obtained: -0.7076
Current minimum: -1.6533
Iteration No: 112 started. Searching for the next optimal point.
Iteration No: 112 ended. Search finished for the next optimal point.
Time taken: 1.7433
Function value obtained: -0.5596
Current minimum: -1.6533
Iteration No: 113 started. Searching for the next optimal point.
Iteration No: 113 ended. Search finished for the next optimal point.
Time taken: 1.8242
Function value obtained: -0.9910
Current minimum: -1.6533
Iteration No: 114 started. Searching for the next optimal point.
Iteration No: 114 ended. Search finished for the next optimal point.
Time taken: 1.7532
Function value obtained: -0.6198
Current minimum: -1.6533
Iteration No: 115 started. Searching for the next optimal point.
Iteration No: 115 ended. Search finished for the next optimal point.
Time taken: 1.7494
Function value obtained: -0.7737
Current minimum: -1.6533
Iteration No: 116 started. Searching for the next optimal point.
Iteration No: 116 ended. Search finished for the next optimal point.
Time taken: 1.7420
Function value obtained: -1.0556
Current minimum: -1.6533
Iteration No: 117 started. Searching for the next optimal point.
Iteration No: 117 ended. Search finished for the next optimal point.
Time taken: 1.5837
Function value obtained: -1.0809
Current minimum: -1.6533
Iteration No: 118 started. Searching for the next optimal point.
Iteration No: 118 ended. Search finished for the next optimal point.
Time taken: 1.6445
Function value obtained: -0.7251
Current minimum: -1.6533
Iteration No: 119 started. Searching for the next optimal point.
Iteration No: 119 ended. Search finished for the next optimal point.
Time taken: 1.6699
Function value obtained: -0.8614
Current minimum: -1.6533
Iteration No: 120 started. Searching for the next optimal point.
Iteration No: 120 ended. Search finished for the next optimal point.
Time taken: 1.6301
Function value obtained: -1.2317
Current minimum: -1.6533
Iteration No: 121 started. Searching for the next optimal point.
Iteration No: 121 ended. Search finished for the next optimal point.
Time taken: 1.7135
Function value obtained: -1.5386
Current minimum: -1.6533
Iteration No: 122 started. Searching for the next optimal point.
Iteration No: 122 ended. Search finished for the next optimal point.
Time taken: 1.7221
Function value obtained: -1.1135
Current minimum: -1.6533
Iteration No: 123 started. Searching for the next optimal point.
Iteration No: 123 ended. Search finished for the next optimal point.
Time taken: 1.6772
Function value obtained: -1.5426
Current minimum: -1.6533
Iteration No: 124 started. Searching for the next optimal point.
Iteration No: 124 ended. Search finished for the next optimal point.
Time taken: 1.6829
Function value obtained: -0.2487
Current minimum: -1.6533
Iteration No: 125 started. Searching for the next optimal point.
Iteration No: 125 ended. Search finished for the next optimal point.
Time taken: 1.5931
Function value obtained: -0.3137
Current minimum: -1.6533
Iteration No: 126 started. Searching for the next optimal point.
Iteration No: 126 ended. Search finished for the next optimal point.
Time taken: 1.7075
Function value obtained: -0.6687
Current minimum: -1.6533
Iteration No: 127 started. Searching for the next optimal point.
Iteration No: 127 ended. Search finished for the next optimal point.
Time taken: 1.7174
Function value obtained: -1.5663
Current minimum: -1.6533
Iteration No: 128 started. Searching for the next optimal point.
Iteration No: 128 ended. Search finished for the next optimal point.
Time taken: 1.7077
Function value obtained: -0.3473
Current minimum: -1.6533
Iteration No: 129 started. Searching for the next optimal point.
Iteration No: 129 ended. Search finished for the next optimal point.
Time taken: 1.5744
Function value obtained: -0.6327
Current minimum: -1.6533
Iteration No: 130 started. Searching for the next optimal point.
Iteration No: 130 ended. Search finished for the next optimal point.
Time taken: 1.7819
Function value obtained: -0.1575
Current minimum: -1.6533
Iteration No: 131 started. Searching for the next optimal point.
Iteration No: 131 ended. Search finished for the next optimal point.
Time taken: 1.7126
Function value obtained: -1.2646
Current minimum: -1.6533
Iteration No: 132 started. Searching for the next optimal point.
Iteration No: 132 ended. Search finished for the next optimal point.
Time taken: 1.7569
Function value obtained: -1.6477
Current minimum: -1.6533
Iteration No: 133 started. Searching for the next optimal point.
Iteration No: 133 ended. Search finished for the next optimal point.
Time taken: 1.6262
Function value obtained: -0.4861
Current minimum: -1.6533
Iteration No: 134 started. Searching for the next optimal point.
Iteration No: 134 ended. Search finished for the next optimal point.
Time taken: 1.6255
Function value obtained: -1.6464
Current minimum: -1.6533
Iteration No: 135 started. Searching for the next optimal point.
Iteration No: 135 ended. Search finished for the next optimal point.
Time taken: 1.7181
Function value obtained: -1.6231
Current minimum: -1.6533
Iteration No: 136 started. Searching for the next optimal point.
Iteration No: 136 ended. Search finished for the next optimal point.
Time taken: 1.6122
Function value obtained: -1.6401
Current minimum: -1.6533
Iteration No: 137 started. Searching for the next optimal point.
Iteration No: 137 ended. Search finished for the next optimal point.
Time taken: 1.7521
Function value obtained: -0.9583
Current minimum: -1.6533
Iteration No: 138 started. Searching for the next optimal point.
Iteration No: 138 ended. Search finished for the next optimal point.
Time taken: 1.6883
Function value obtained: -0.7005
Current minimum: -1.6533
Iteration No: 139 started. Searching for the next optimal point.
Iteration No: 139 ended. Search finished for the next optimal point.
Time taken: 1.8776
Function value obtained: -1.2380
Current minimum: -1.6533
Iteration No: 140 started. Searching for the next optimal point.
Iteration No: 140 ended. Search finished for the next optimal point.
Time taken: 1.6718
Function value obtained: -0.3181
Current minimum: -1.6533
Iteration No: 141 started. Searching for the next optimal point.
Iteration No: 141 ended. Search finished for the next optimal point.
Time taken: 1.7698
Function value obtained: -1.2978
Current minimum: -1.6533
Iteration No: 142 started. Searching for the next optimal point.
Iteration No: 142 ended. Search finished for the next optimal point.
Time taken: 1.7256
Function value obtained: -1.6843
Current minimum: -1.6843
Iteration No: 143 started. Searching for the next optimal point.
Iteration No: 143 ended. Search finished for the next optimal point.
Time taken: 1.6885
Function value obtained: -0.7780
Current minimum: -1.6843
Iteration No: 144 started. Searching for the next optimal point.
Iteration No: 144 ended. Search finished for the next optimal point.
Time taken: 1.7210
Function value obtained: -1.0255
Current minimum: -1.6843
Iteration No: 145 started. Searching for the next optimal point.
Iteration No: 145 ended. Search finished for the next optimal point.
Time taken: 1.6582
Function value obtained: -0.6620
Current minimum: -1.6843
Iteration No: 146 started. Searching for the next optimal point.
Iteration No: 146 ended. Search finished for the next optimal point.
Time taken: 1.7268
Function value obtained: -0.9537
Current minimum: -1.6843
Iteration No: 147 started. Searching for the next optimal point.
Iteration No: 147 ended. Search finished for the next optimal point.
Time taken: 1.7652
Function value obtained: -1.2921
Current minimum: -1.6843
Iteration No: 148 started. Searching for the next optimal point.
Iteration No: 148 ended. Search finished for the next optimal point.
Time taken: 1.9368
Function value obtained: -1.5254
Current minimum: -1.6843
Iteration No: 149 started. Searching for the next optimal point.
Iteration No: 149 ended. Search finished for the next optimal point.
Time taken: 1.6841
Function value obtained: -1.2536
Current minimum: -1.6843
Iteration No: 150 started. Searching for the next optimal point.
Iteration No: 150 ended. Search finished for the next optimal point.
Time taken: 1.7396
Function value obtained: -0.2424
Current minimum: -1.6843
Iteration No: 151 started. Searching for the next optimal point.
Iteration No: 151 ended. Search finished for the next optimal point.
Time taken: 1.8393
Function value obtained: -0.3599
Current minimum: -1.6843
Iteration No: 152 started. Searching for the next optimal point.
Iteration No: 152 ended. Search finished for the next optimal point.
Time taken: 1.8224
Function value obtained: -0.5132
Current minimum: -1.6843
Iteration No: 153 started. Searching for the next optimal point.
Iteration No: 153 ended. Search finished for the next optimal point.
Time taken: 1.7085
Function value obtained: -1.2677
Current minimum: -1.6843
Iteration No: 154 started. Searching for the next optimal point.
Iteration No: 154 ended. Search finished for the next optimal point.
Time taken: 1.7298
Function value obtained: -1.1058
Current minimum: -1.6843
Iteration No: 155 started. Searching for the next optimal point.
Iteration No: 155 ended. Search finished for the next optimal point.
Time taken: 1.7194
Function value obtained: -1.2150
Current minimum: -1.6843
Iteration No: 156 started. Searching for the next optimal point.
Iteration No: 156 ended. Search finished for the next optimal point.
Time taken: 1.6052
Function value obtained: -0.8481
Current minimum: -1.6843
Iteration No: 157 started. Searching for the next optimal point.
Iteration No: 157 ended. Search finished for the next optimal point.
Time taken: 1.7785
Function value obtained: -0.2522
Current minimum: -1.6843
Iteration No: 158 started. Searching for the next optimal point.
Iteration No: 158 ended. Search finished for the next optimal point.
Time taken: 1.8267
Function value obtained: -0.5556
Current minimum: -1.6843
Iteration No: 159 started. Searching for the next optimal point.
Iteration No: 159 ended. Search finished for the next optimal point.
Time taken: 1.8633
Function value obtained: -1.1772
Current minimum: -1.6843
Iteration No: 160 started. Searching for the next optimal point.
Iteration No: 160 ended. Search finished for the next optimal point.
Time taken: 1.8393
Function value obtained: -1.0478
Current minimum: -1.6843
Iteration No: 161 started. Searching for the next optimal point.
Iteration No: 161 ended. Search finished for the next optimal point.
Time taken: 1.8288
Function value obtained: -0.4101
Current minimum: -1.6843
Iteration No: 162 started. Searching for the next optimal point.
Iteration No: 162 ended. Search finished for the next optimal point.
Time taken: 1.8479
Function value obtained: -1.6448
Current minimum: -1.6843
Iteration No: 163 started. Searching for the next optimal point.
Iteration No: 163 ended. Search finished for the next optimal point.
Time taken: 1.8519
Function value obtained: -0.6035
Current minimum: -1.6843
Iteration No: 164 started. Searching for the next optimal point.
Iteration No: 164 ended. Search finished for the next optimal point.
Time taken: 1.7363
Function value obtained: -1.2804
Current minimum: -1.6843
Iteration No: 165 started. Searching for the next optimal point.
Iteration No: 165 ended. Search finished for the next optimal point.
Time taken: 1.7888
Function value obtained: -0.9202
Current minimum: -1.6843
Iteration No: 166 started. Searching for the next optimal point.
Iteration No: 166 ended. Search finished for the next optimal point.
Time taken: 1.7863
Function value obtained: -1.3259
Current minimum: -1.6843
Iteration No: 167 started. Searching for the next optimal point.
Iteration No: 167 ended. Search finished for the next optimal point.
Time taken: 1.7076
Function value obtained: -1.1283
Current minimum: -1.6843
Iteration No: 168 started. Searching for the next optimal point.
Iteration No: 168 ended. Search finished for the next optimal point.
Time taken: 1.8028
Function value obtained: -0.7863
Current minimum: -1.6843
Iteration No: 169 started. Searching for the next optimal point.
Iteration No: 169 ended. Search finished for the next optimal point.
Time taken: 1.7456
Function value obtained: -0.5784
Current minimum: -1.6843
Iteration No: 170 started. Searching for the next optimal point.
Iteration No: 170 ended. Search finished for the next optimal point.
Time taken: 1.8006
Function value obtained: -0.5683
Current minimum: -1.6843
Iteration No: 171 started. Searching for the next optimal point.
Iteration No: 171 ended. Search finished for the next optimal point.
Time taken: 1.8228
Function value obtained: -1.3717
Current minimum: -1.6843
Iteration No: 172 started. Searching for the next optimal point.
Iteration No: 172 ended. Search finished for the next optimal point.
Time taken: 1.7086
Function value obtained: -1.2707
Current minimum: -1.6843
Iteration No: 173 started. Searching for the next optimal point.
Iteration No: 173 ended. Search finished for the next optimal point.
Time taken: 1.9280
Function value obtained: -0.7453
Current minimum: -1.6843
Iteration No: 174 started. Searching for the next optimal point.
Iteration No: 174 ended. Search finished for the next optimal point.
Time taken: 1.9599
Function value obtained: -0.5960
Current minimum: -1.6843
Iteration No: 175 started. Searching for the next optimal point.
Iteration No: 175 ended. Search finished for the next optimal point.
Time taken: 1.8114
Function value obtained: -0.2744
Current minimum: -1.6843
Iteration No: 176 started. Searching for the next optimal point.
Iteration No: 176 ended. Search finished for the next optimal point.
Time taken: 1.9012
Function value obtained: -0.8892
Current minimum: -1.6843
Iteration No: 177 started. Searching for the next optimal point.
Iteration No: 177 ended. Search finished for the next optimal point.
Time taken: 1.7986
Function value obtained: -0.5976
Current minimum: -1.6843
Iteration No: 178 started. Searching for the next optimal point.
Iteration No: 178 ended. Search finished for the next optimal point.
Time taken: 1.8245
Function value obtained: -0.3016
Current minimum: -1.6843
Iteration No: 179 started. Searching for the next optimal point.
Iteration No: 179 ended. Search finished for the next optimal point.
Time taken: 1.8182
Function value obtained: -0.2835
Current minimum: -1.6843
Iteration No: 180 started. Searching for the next optimal point.
Iteration No: 180 ended. Search finished for the next optimal point.
Time taken: 1.9420
Function value obtained: -0.3354
Current minimum: -1.6843
Iteration No: 181 started. Searching for the next optimal point.
Iteration No: 181 ended. Search finished for the next optimal point.
Time taken: 1.9225
Function value obtained: -0.8471
Current minimum: -1.6843
Iteration No: 182 started. Searching for the next optimal point.
Iteration No: 182 ended. Search finished for the next optimal point.
Time taken: 1.7940
Function value obtained: -1.3808
Current minimum: -1.6843
Iteration No: 183 started. Searching for the next optimal point.
Iteration No: 183 ended. Search finished for the next optimal point.
Time taken: 2.0099
Function value obtained: -0.2762
Current minimum: -1.6843
Iteration No: 184 started. Searching for the next optimal point.
Iteration No: 184 ended. Search finished for the next optimal point.
Time taken: 1.7499
Function value obtained: -0.8845
Current minimum: -1.6843
Iteration No: 185 started. Searching for the next optimal point.
Iteration No: 185 ended. Search finished for the next optimal point.
Time taken: 1.9217
Function value obtained: -1.3741
Current minimum: -1.6843
Iteration No: 186 started. Searching for the next optimal point.
Iteration No: 186 ended. Search finished for the next optimal point.
Time taken: 1.8008
Function value obtained: -0.8041
Current minimum: -1.6843
Iteration No: 187 started. Searching for the next optimal point.
Iteration No: 187 ended. Search finished for the next optimal point.
Time taken: 1.9288
Function value obtained: -0.7722
Current minimum: -1.6843
Iteration No: 188 started. Searching for the next optimal point.
Iteration No: 188 ended. Search finished for the next optimal point.
Time taken: 1.9888
Function value obtained: -1.1958
Current minimum: -1.6843
Iteration No: 189 started. Searching for the next optimal point.
Iteration No: 189 ended. Search finished for the next optimal point.
Time taken: 1.8197
Function value obtained: -1.4566
Current minimum: -1.6843
Iteration No: 190 started. Searching for the next optimal point.
Iteration No: 190 ended. Search finished for the next optimal point.
Time taken: 1.9297
Function value obtained: -0.4901
Current minimum: -1.6843
Iteration No: 191 started. Searching for the next optimal point.
Iteration No: 191 ended. Search finished for the next optimal point.
Time taken: 1.8360
Function value obtained: -0.8818
Current minimum: -1.6843
Iteration No: 192 started. Searching for the next optimal point.
Iteration No: 192 ended. Search finished for the next optimal point.
Time taken: 1.9393
Function value obtained: -0.9274
Current minimum: -1.6843
Iteration No: 193 started. Searching for the next optimal point.
Iteration No: 193 ended. Search finished for the next optimal point.
Time taken: 2.0269
Function value obtained: -1.2284
Current minimum: -1.6843
Iteration No: 194 started. Searching for the next optimal point.
Iteration No: 194 ended. Search finished for the next optimal point.
Time taken: 1.8796
Function value obtained: -0.7016
Current minimum: -1.6843
Iteration No: 195 started. Searching for the next optimal point.
Iteration No: 195 ended. Search finished for the next optimal point.
Time taken: 1.8187
Function value obtained: -1.4800
Current minimum: -1.6843
Iteration No: 196 started. Searching for the next optimal point.
Iteration No: 196 ended. Search finished for the next optimal point.
Time taken: 1.9988
Function value obtained: -0.5783
Current minimum: -1.6843
Iteration No: 197 started. Searching for the next optimal point.
Iteration No: 197 ended. Search finished for the next optimal point.
Time taken: 2.0304
Function value obtained: -1.6439
Current minimum: -1.6843
Iteration No: 198 started. Searching for the next optimal point.
Iteration No: 198 ended. Search finished for the next optimal point.
Time taken: 2.0540
Function value obtained: -1.2796
Current minimum: -1.6843
Iteration No: 199 started. Searching for the next optimal point.
Iteration No: 199 ended. Search finished for the next optimal point.
Time taken: 1.9356
Function value obtained: -1.2481
Current minimum: -1.6843
Iteration No: 200 started. Searching for the next optimal point.
Iteration No: 200 ended. Search finished for the next optimal point.
Time taken: 1.8568
Function value obtained: -1.3188
Current minimum: -1.6843
Iteration No: 201 started. Searching for the next optimal point.
Iteration No: 201 ended. Search finished for the next optimal point.
Time taken: 1.9032
Function value obtained: -0.4450
Current minimum: -1.6843
Iteration No: 202 started. Searching for the next optimal point.
Iteration No: 202 ended. Search finished for the next optimal point.
Time taken: 2.0741
Function value obtained: -1.5269
Current minimum: -1.6843
Iteration No: 203 started. Searching for the next optimal point.
Iteration No: 203 ended. Search finished for the next optimal point.
Time taken: 1.9247
Function value obtained: -0.1797
Current minimum: -1.6843
Iteration No: 204 started. Searching for the next optimal point.
Iteration No: 204 ended. Search finished for the next optimal point.
Time taken: 2.0103
Function value obtained: -0.2563
Current minimum: -1.6843
Iteration No: 205 started. Searching for the next optimal point.
Iteration No: 205 ended. Search finished for the next optimal point.
Time taken: 1.9892
Function value obtained: -1.5407
Current minimum: -1.6843
Iteration No: 206 started. Searching for the next optimal point.
Iteration No: 206 ended. Search finished for the next optimal point.
Time taken: 1.9316
Function value obtained: -1.1559
Current minimum: -1.6843
Iteration No: 207 started. Searching for the next optimal point.
Iteration No: 207 ended. Search finished for the next optimal point.
Time taken: 1.9844
Function value obtained: -0.8694
Current minimum: -1.6843
Iteration No: 208 started. Searching for the next optimal point.
Iteration No: 208 ended. Search finished for the next optimal point.
Time taken: 1.9928
Function value obtained: -0.6099
Current minimum: -1.6843
Iteration No: 209 started. Searching for the next optimal point.
Iteration No: 209 ended. Search finished for the next optimal point.
Time taken: 1.9868
Function value obtained: -0.7559
Current minimum: -1.6843
Iteration No: 210 started. Searching for the next optimal point.
Iteration No: 210 ended. Search finished for the next optimal point.
Time taken: 1.8957
Function value obtained: -1.6035
Current minimum: -1.6843
Iteration No: 211 started. Searching for the next optimal point.
Iteration No: 211 ended. Search finished for the next optimal point.
Time taken: 1.9136
Function value obtained: -1.2053
Current minimum: -1.6843
Iteration No: 212 started. Searching for the next optimal point.
Iteration No: 212 ended. Search finished for the next optimal point.
Time taken: 1.9998
Function value obtained: -0.2487
Current minimum: -1.6843
Iteration No: 213 started. Searching for the next optimal point.
Iteration No: 213 ended. Search finished for the next optimal point.
Time taken: 1.8792
Function value obtained: -1.5472
Current minimum: -1.6843
Iteration No: 214 started. Searching for the next optimal point.
Iteration No: 214 ended. Search finished for the next optimal point.
Time taken: 1.9379
Function value obtained: -0.4974
Current minimum: -1.6843
Iteration No: 215 started. Searching for the next optimal point.
Iteration No: 215 ended. Search finished for the next optimal point.
Time taken: 1.9546
Function value obtained: -0.1816
Current minimum: -1.6843
Iteration No: 216 started. Searching for the next optimal point.
Iteration No: 216 ended. Search finished for the next optimal point.
Time taken: 1.9515
Function value obtained: -1.2115
Current minimum: -1.6843
Iteration No: 217 started. Searching for the next optimal point.
Iteration No: 217 ended. Search finished for the next optimal point.
Time taken: 2.2255
Function value obtained: -1.1268
Current minimum: -1.6843
Iteration No: 218 started. Searching for the next optimal point.
Iteration No: 218 ended. Search finished for the next optimal point.
Time taken: 1.9495
Function value obtained: -0.8316
Current minimum: -1.6843
Iteration No: 219 started. Searching for the next optimal point.
Iteration No: 219 ended. Search finished for the next optimal point.
Time taken: 2.0719
Function value obtained: -1.2700
Current minimum: -1.6843
Iteration No: 220 started. Searching for the next optimal point.
Iteration No: 220 ended. Search finished for the next optimal point.
Time taken: 1.9733
Function value obtained: -0.6312
Current minimum: -1.6843
Iteration No: 221 started. Searching for the next optimal point.
Iteration No: 221 ended. Search finished for the next optimal point.
Time taken: 1.9804
Function value obtained: -1.2322
Current minimum: -1.6843
Iteration No: 222 started. Searching for the next optimal point.
Iteration No: 222 ended. Search finished for the next optimal point.
Time taken: 1.9854
Function value obtained: -1.2544
Current minimum: -1.6843
Iteration No: 223 started. Searching for the next optimal point.
Iteration No: 223 ended. Search finished for the next optimal point.
Time taken: 1.8840
Function value obtained: -1.4262
Current minimum: -1.6843
Iteration No: 224 started. Searching for the next optimal point.
Iteration No: 224 ended. Search finished for the next optimal point.
Time taken: 1.9572
Function value obtained: -1.5020
Current minimum: -1.6843
Iteration No: 225 started. Searching for the next optimal point.
Iteration No: 225 ended. Search finished for the next optimal point.
Time taken: 2.0389
Function value obtained: -1.1237
Current minimum: -1.6843
Iteration No: 226 started. Searching for the next optimal point.
Iteration No: 226 ended. Search finished for the next optimal point.
Time taken: 1.9423
Function value obtained: -0.7514
Current minimum: -1.6843
Iteration No: 227 started. Searching for the next optimal point.
Iteration No: 227 ended. Search finished for the next optimal point.
Time taken: 2.0146
Function value obtained: -1.3544
Current minimum: -1.6843
Iteration No: 228 started. Searching for the next optimal point.
Iteration No: 228 ended. Search finished for the next optimal point.
Time taken: 1.9639
Function value obtained: -0.6648
Current minimum: -1.6843
Iteration No: 229 started. Searching for the next optimal point.
Iteration No: 229 ended. Search finished for the next optimal point.
Time taken: 2.0031
Function value obtained: -1.5780
Current minimum: -1.6843
Iteration No: 230 started. Searching for the next optimal point.
Iteration No: 230 ended. Search finished for the next optimal point.
Time taken: 2.1775
Function value obtained: -1.3460
Current minimum: -1.6843
Iteration No: 231 started. Searching for the next optimal point.
Iteration No: 231 ended. Search finished for the next optimal point.
Time taken: 2.1843
Function value obtained: -0.8827
Current minimum: -1.6843
Iteration No: 232 started. Searching for the next optimal point.
Iteration No: 232 ended. Search finished for the next optimal point.
Time taken: 1.9746
Function value obtained: -0.5278
Current minimum: -1.6843
Iteration No: 233 started. Searching for the next optimal point.
Iteration No: 233 ended. Search finished for the next optimal point.
Time taken: 1.9773
Function value obtained: -0.3101
Current minimum: -1.6843
Iteration No: 234 started. Searching for the next optimal point.
Iteration No: 234 ended. Search finished for the next optimal point.
Time taken: 1.9896
Function value obtained: -1.2086
Current minimum: -1.6843
Iteration No: 235 started. Searching for the next optimal point.
Iteration No: 235 ended. Search finished for the next optimal point.
Time taken: 2.0932
Function value obtained: -1.5296
Current minimum: -1.6843
Iteration No: 236 started. Searching for the next optimal point.
Iteration No: 236 ended. Search finished for the next optimal point.
Time taken: 1.9486
Function value obtained: -0.3033
Current minimum: -1.6843
Iteration No: 237 started. Searching for the next optimal point.
Iteration No: 237 ended. Search finished for the next optimal point.
Time taken: 1.9235
Function value obtained: -1.5147
Current minimum: -1.6843
Iteration No: 238 started. Searching for the next optimal point.
Iteration No: 238 ended. Search finished for the next optimal point.
Time taken: 2.0935
Function value obtained: -1.1041
Current minimum: -1.6843
Iteration No: 239 started. Searching for the next optimal point.
Iteration No: 239 ended. Search finished for the next optimal point.
Time taken: 1.9340
Function value obtained: -0.3968
Current minimum: -1.6843
Iteration No: 240 started. Searching for the next optimal point.
Iteration No: 240 ended. Search finished for the next optimal point.
Time taken: 2.1179
Function value obtained: -1.5864
Current minimum: -1.6843
Iteration No: 241 started. Searching for the next optimal point.
Iteration No: 241 ended. Search finished for the next optimal point.
Time taken: 2.2127
Function value obtained: -1.3107
Current minimum: -1.6843
Iteration No: 242 started. Searching for the next optimal point.
Iteration No: 242 ended. Search finished for the next optimal point.
Time taken: 1.9663
Function value obtained: -0.3821
Current minimum: -1.6843
Iteration No: 243 started. Searching for the next optimal point.
Iteration No: 243 ended. Search finished for the next optimal point.
Time taken: 2.0237
Function value obtained: -1.5840
Current minimum: -1.6843
Iteration No: 244 started. Searching for the next optimal point.
Iteration No: 244 ended. Search finished for the next optimal point.
Time taken: 1.9905
Function value obtained: 0.2157
Current minimum: -1.6843
Iteration No: 245 started. Searching for the next optimal point.
Iteration No: 245 ended. Search finished for the next optimal point.
Time taken: 2.1058
Function value obtained: -1.6528
Current minimum: -1.6843
Iteration No: 246 started. Searching for the next optimal point.
Iteration No: 246 ended. Search finished for the next optimal point.
Time taken: 2.1600
Function value obtained: -0.9801
Current minimum: -1.6843
Iteration No: 247 started. Searching for the next optimal point.
Iteration No: 247 ended. Search finished for the next optimal point.
Time taken: 2.1431
Function value obtained: -1.5436
Current minimum: -1.6843
Iteration No: 248 started. Searching for the next optimal point.
Iteration No: 248 ended. Search finished for the next optimal point.
Time taken: 2.0488
Function value obtained: -0.5629
Current minimum: -1.6843
Iteration No: 249 started. Searching for the next optimal point.
Iteration No: 249 ended. Search finished for the next optimal point.
Time taken: 2.1159
Function value obtained: -0.1949
Current minimum: -1.6843
Iteration No: 250 started. Searching for the next optimal point.
Iteration No: 250 ended. Search finished for the next optimal point.
Time taken: 2.1115
Function value obtained: -0.1387
Current minimum: -1.6843
In [6]:
x = opt_res.x_iters
y = opt_res.func_vals
x_random_start = x[:n_random_start]
y_random_start = y[:n_random_start]
In [7]:
fig, ax = plt.subplots(figsize=(8, 5))
plot_func(func, xmin, xmax, ax=ax)
ax2 = ax.twinx()
ax2.set_ylabel("$\mathbb{E}I(x)$")
ax.plot(x_random_start, y_random_start, 'b.', label='Random-start')
def init():
line_acq, = ax2.plot([], [], "y", label="$\mathbb{E}I(x)$")
line_iter, = ax.plot([], [], 'r.', label='Iterations')
line_quant, = ax.plot([], [], 'r-', label='Estimated quantile')
line_min, = ax.plot([], [], 'mo', markersize=13, label='Minimum')
return (line_acq, line_iter, line_quant, line_min, )
line_acq, line_iter, line_quant, line_min = init()
ax.legend(loc=0)
fig.tight_layout()
In [8]:
x_plot = np.linspace(xmin, xmax, 100)
def animate(i):
model_i = opt_res.models[i]
q_i = model_i.predict(x_plot[:, np.newaxis])
acq = gaussian_ei(x_plot[:, np.newaxis], model_i, y_opt=np.min(q_i))
x_iter = x[n_random_start:n_random_start+i+1]
y_iter = y[n_random_start:n_random_start+i+1]
id_min = q_i.argmin()
x_min = x_plot[id_min]
q_min = q_i[id_min]
line_acq.set_data(x_plot, acq)
line_iter.set_data(x_iter, y_iter)
line_quant.set_data(x_plot, q_i)
line_min.set_data(x_min, q_min)
ax.title.set_text('n_start = %d - iteration %d' % (n_random_start, i+1))
print(i)
return (line_acq, line_iter, line_min, )
In [9]:
from matplotlib import animation
# call the animator. blit=True means only re-draw the parts that
# have changed.
anim = animation.FuncAnimation(fig, animate, init_func=init,
frames=n_iter, interval=1, blit=True)
In [10]:
filename = 'bayesian_optim_ns_%d_niter_%d_%s.gif' % (n_random_start, n_iter, acq_func)
anim.save(filename, writer='imagemagick', fps=2)
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In [ ]:
Content source: NazBen/impact-of-dependence
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