相関係数が0.63の散布図が話題になっているようなので、相関係数が0.63の散布図を作成するPythonスクリプトを作ってみました。

以下のコードは Google Colaboratory 上での動作を確認しています。

乱数の散布図

まずは乱数を使った散布図の描きかたと、相関係数の計算の仕方です。

import numpy as np

n_data = 20
X = np.random.rand(n_data)
Y = np.random.rand(n_data)

import matplotlib.pyplot as plt

coeff = np.corrcoef(X, Y)[0, 1]
plt.figure(figsize=(5,5))
plt.title("correlation coefficient = {0:.3f}".format(coeff))
plt.scatter(X, Y)
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.grid()
plt.show()

Optuna のインストール

今回は最適化ツールとしてOptunaを使いたいと思います。

!pip install optuna

Collecting optuna
  Downloading optuna-2.10.0-py3-none-any.whl (308 kB)
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Requirement already satisfied: scipy!=1.4.0 in /usr/local/lib/python3.7/dist-packages (from optuna) (1.4.1)
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Building wheels for collected packages: pyperclip
  Building wheel for pyperclip (setup.py) ... [?25l[?25hdone
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Successfully built pyperclip
Installing collected packages: pyperclip, pbr, stevedore, Mako, cmd2, autopage, colorlog, cmaes, cliff, alembic, optuna
Successfully installed Mako-1.1.6 alembic-1.7.5 autopage-0.4.0 cliff-3.10.0 cmaes-0.8.2 cmd2-2.3.3 colorlog-6.6.0 optuna-2.10.0 pbr-5.8.0 pyperclip-1.8.2 stevedore-3.5.0

目的関数

２０組の変数X, Yを用意して、その相関係数が0.63になるように目的関数を設定します。

class Objective:
    def __init__(self, n_data = 20, target_coeff = 0.63):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None
        self.target_coeff = target_coeff

    def __call__(self, trial):
        self.X = []
        self.Y = []
        for i in range(n_data):
            self.X.append(trial.suggest_uniform("x{}".format(i), 0, 1))
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        coeff = np.corrcoef(self.X, self.Y)[0, 1]
        score = abs(coeff - self.target_coeff)
        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

最適化計算の実行

以下のようにして最適化計算を実行します。

import optuna

objective = Objective()
study = optuna.create_study()
study.optimize(objective, n_trials=100)

[32m[I 2022-01-18 06:52:22,159][0m A new study created in memory with name: no-name-39f290fa-59cb-4ac2-b3eb-0481b17f3b1d[0m
[32m[I 2022-01-18 06:52:22,175][0m Trial 0 finished with value: 0.9524452430812576 and parameters: {'x0': 0.049064883853020214, 'y0': 0.9103176992059397, 'x1': 0.535479097992503, 'y1': 0.7302769130029191, 'x2': 0.2435776257071065, 'y2': 0.637297009855205, 'x3': 0.3085009702675596, 'y3': 0.22867377506203157, 'x4': 0.6834774037557331, 'y4': 0.6462665433359349, 'x5': 0.2243850540375657, 'y5': 0.902525070787008, 'x6': 0.7986299093784387, 'y6': 0.9974043881279312, 'x7': 0.20580617120137368, 'y7': 0.5105672286880534, 'x8': 0.3008403170440196, 'y8': 0.6443052304553223, 'x9': 0.9822404171037408, 'y9': 0.13912513861307652, 'x10': 0.12633664264033717, 'y10': 0.9165142767630589, 'x11': 0.6760967896893568, 'y11': 0.7684312089454229, 'x12': 0.31421462234809383, 'y12': 0.9339325667155108, 'x13': 0.8550983410948428, 'y13': 0.2746002737345232, 'x14': 0.012681954610688217, 'y14': 0.7395717835378682, 'x15': 0.36657664195459316, 'y15': 0.08195540504986998, 'x16': 0.47460165321203895, 'y16': 0.48824033482837204, 'x17': 0.3816413573031281, 'y17': 0.8924522361676958, 'x18': 0.07237246931703334, 'y18': 0.6255247007556458, 'x19': 0.40823328128746583, 'y19': 0.3651315860129464}. Best is trial 0 with value: 0.9524452430812576.[0m
[32m[I 2022-01-18 06:52:22,189][0m Trial 1 finished with value: 0.7582547150412606 and parameters: {'x0': 0.005375515402640252, 'y0': 0.6641742199583752, 'x1': 0.7705839250882497, 'y1': 0.8482395645092604, 'x2': 0.7351957492482576, 'y2': 0.05719488130786987, 'x3': 0.9373389919949929, 'y3': 0.8518960631609683, 'x4': 0.8939391723698678, 'y4': 0.6892918246320512, 'x5': 0.9462376035622662, 'y5': 0.13816730288996815, 'x6': 0.7772012271005223, 'y6': 0.7788334140187778, 'x7': 0.7998832484560089, 'y7': 0.1624823797888134, 'x8': 0.6531941257722433, 'y8': 0.07434417481981337, 'x9': 0.6628583075976205, 'y9': 0.9807609227470127, 'x10': 0.8031442842921543, 'y10': 0.11390425499607215, 'x11': 0.5281687209330447, 'y11': 0.12937399570461017, 'x12': 0.9543118265790466, 'y12': 0.4083090575374273, 'x13': 0.02142786358430271, 'y13': 0.8444398640087899, 'x14': 0.1791969829530219, 'y14': 0.5740438547736052, 'x15': 0.8986617875892967, 'y15': 0.5432044440124053, 'x16': 0.22745526260072524, 'y16': 0.44087765823139524, 'x17': 0.6196611650447298, 'y17': 0.24504355530151234, 'x18': 0.10084104456740484, 'y18': 0.3206772210371246, 'x19': 0.6931800663111516, 'y19': 0.6154669828275484}. Best is trial 1 with value: 0.7582547150412606.[0m
[32m[I 2022-01-18 06:52:22,201][0m Trial 2 finished with value: 0.3973827054764325 and parameters: {'x0': 0.672104463936861, 'y0': 0.073825766130864, 'x1': 0.534601740361486, 'y1': 0.866388257648174, 'x2': 0.5440358110982255, 'y2': 0.13660201098216485, 'x3': 0.3613121444986028, 'y3': 0.08847677692602274, 'x4': 0.9826408701298279, 'y4': 0.5356171546352821, 'x5': 0.501455006577748, 'y5': 0.6096152327743308, 'x6': 0.09184010063918813, 'y6': 0.15057474713382302, 'x7': 0.6560840483295193, 'y7': 0.16493408690486, 'x8': 0.4549263960353618, 'y8': 0.4107541809051122, 'x9': 0.2863046859142431, 'y9': 0.41726631132849124, 'x10': 0.005747765698591922, 'y10': 0.45032076487482564, 'x11': 0.9986402953759149, 'y11': 0.4036790110156794, 'x12': 0.5465489172870974, 'y12': 0.46954611225644616, 'x13': 0.7170086079354948, 'y13': 0.2194398537867005, 'x14': 0.8109660505846924, 'y14': 0.5150671976426966, 'x15': 0.12392472729075621, 'y15': 0.31238908376144525, 'x16': 0.013685397140668853, 'y16': 0.42696735092480476, 'x17': 0.8274923807351036, 'y17': 0.33672421418888976, 'x18': 0.34725814767239505, 'y18': 0.14921156707665428, 'x19': 0.8896669347336637, 'y19': 0.8364979282454862}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,219][0m Trial 3 finished with value: 0.7792140884977898 and parameters: {'x0': 0.696733905100572, 'y0': 0.9838970714535153, 'x1': 0.12342518477230069, 'y1': 0.05532726171143809, 'x2': 0.6851122000755443, 'y2': 0.091232766584461, 'x3': 0.8138590477841956, 'y3': 0.2891029423911109, 'x4': 0.4365817599783486, 'y4': 0.9113775342868551, 'x5': 0.5537594547959809, 'y5': 0.3990504539816544, 'x6': 0.5934502689717518, 'y6': 0.10225634874690226, 'x7': 0.6730599483827036, 'y7': 0.7676002045909533, 'x8': 0.3129654430728205, 'y8': 0.8374084556891036, 'x9': 0.48132664847773043, 'y9': 0.08040484455841401, 'x10': 0.9682996448139835, 'y10': 0.2429112125493762, 'x11': 0.6700320302488939, 'y11': 0.4036845343242379, 'x12': 0.8243999764433323, 'y12': 0.1456625687573877, 'x13': 0.3016395690232321, 'y13': 0.05544479755225107, 'x14': 0.9062683240260004, 'y14': 0.044946086909838034, 'x15': 0.16086943432960965, 'y15': 0.4922094742153501, 'x16': 0.01933857954522633, 'y16': 0.48961675099420643, 'x17': 0.4593608008431357, 'y17': 0.7617077916360556, 'x18': 0.7016505030025091, 'y18': 0.4904465421750809, 'x19': 0.5983106465985567, 'y19': 0.2326586465588849}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,234][0m Trial 4 finished with value: 1.0582673971241991 and parameters: {'x0': 0.8254639602030226, 'y0': 0.21946134272526296, 'x1': 0.7654468174911365, 'y1': 0.23166762365399263, 'x2': 0.602326639443575, 'y2': 0.10237832530325519, 'x3': 0.33657876230971384, 'y3': 0.8407906306131034, 'x4': 0.9929828729437794, 'y4': 0.6068388723894697, 'x5': 0.24563220302051458, 'y5': 0.5955779441536074, 'x6': 0.2690020510210316, 'y6': 0.9403534027788442, 'x7': 0.2020787824197775, 'y7': 0.41285790301770586, 'x8': 0.3308376486395481, 'y8': 0.9197856563159879, 'x9': 0.7208677626908275, 'y9': 0.24551038362925615, 'x10': 0.7972767793195811, 'y10': 0.9314022655192427, 'x11': 0.9281596169035699, 'y11': 0.3421791669066876, 'x12': 0.5811915736093594, 'y12': 0.6814099583092188, 'x13': 0.9546496225880567, 'y13': 0.2660600023873423, 'x14': 0.16105034603025636, 'y14': 0.5563466276011122, 'x15': 0.5670913812360525, 'y15': 0.47177926937463144, 'x16': 0.3165454954424095, 'y16': 0.9952098776213242, 'x17': 0.6521703863067173, 'y17': 0.04426116963016369, 'x18': 0.9676429237181149, 'y18': 0.46595152231768877, 'x19': 0.4178548537207216, 'y19': 0.3865178683116697}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,251][0m Trial 5 finished with value: 0.6114851854176266 and parameters: {'x0': 0.4961671837886219, 'y0': 0.6122669617184184, 'x1': 0.17592851342471838, 'y1': 0.2618252718936601, 'x2': 0.48543596633407804, 'y2': 0.18688790934140764, 'x3': 0.5303053550424436, 'y3': 0.4535717123798664, 'x4': 0.5630794579802378, 'y4': 0.4623310909325232, 'x5': 0.03006336720091851, 'y5': 0.5604010207083647, 'x6': 0.7928444924237329, 'y6': 0.15884294227539741, 'x7': 0.0718034119058153, 'y7': 0.3076677413261809, 'x8': 0.44602330389931977, 'y8': 0.07327660578070372, 'x9': 0.33981099808389836, 'y9': 0.8575331098419425, 'x10': 0.9736735927554085, 'y10': 0.9849644176545186, 'x11': 0.1021748746244786, 'y11': 0.992361195439134, 'x12': 0.7101951684255589, 'y12': 0.32897566715262005, 'x13': 0.11629016963844485, 'y13': 0.6123857875048704, 'x14': 0.1151033345597533, 'y14': 0.7190635400906739, 'x15': 0.5122433241095159, 'y15': 0.5699567476918104, 'x16': 0.5617599973343447, 'y16': 0.7331502499318511, 'x17': 0.0974645605924368, 'y17': 0.036835827755289485, 'x18': 0.01558073180205688, 'y18': 0.7024886477988875, 'x19': 0.2505031032720979, 'y19': 0.14322202818949903}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,262][0m Trial 6 finished with value: 0.9000266587296823 and parameters: {'x0': 0.25128805689442535, 'y0': 0.2124065849191099, 'x1': 0.17477872869309186, 'y1': 0.13644596971469447, 'x2': 0.09097373296170375, 'y2': 0.5683077018996302, 'x3': 0.5901490202326255, 'y3': 0.7953553997665256, 'x4': 0.653319265124721, 'y4': 0.240096726101641, 'x5': 0.20382921721108638, 'y5': 0.5370881131448513, 'x6': 0.2845032260511241, 'y6': 0.8742749631172029, 'x7': 0.8735245595473571, 'y7': 0.5765474760681525, 'x8': 0.1278235187997684, 'y8': 0.5896796204532035, 'x9': 0.16368164836794508, 'y9': 0.31398145384237475, 'x10': 0.17963184636698604, 'y10': 0.2802427427033428, 'x11': 0.735243978769563, 'y11': 0.2946103535036979, 'x12': 0.30490310605654125, 'y12': 0.8652495964747674, 'x13': 0.29262184796389656, 'y13': 0.6139328024901965, 'x14': 0.6081547743514699, 'y14': 0.08916106177185923, 'x15': 0.37617318828768953, 'y15': 0.4326365898179284, 'x16': 0.704937233458455, 'y16': 0.4302226547899082, 'x17': 0.12420365164725744, 'y17': 0.9973373697894161, 'x18': 0.011622045069673348, 'y18': 0.7348409858132819, 'x19': 0.5091480335806983, 'y19': 0.13584271602483766}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,280][0m Trial 7 finished with value: 0.6629874385990133 and parameters: {'x0': 0.36970147800118924, 'y0': 0.18177430064490485, 'x1': 0.6125013650491533, 'y1': 0.676645216373579, 'x2': 0.05258730786630583, 'y2': 0.9363570873680118, 'x3': 0.5043112276080248, 'y3': 0.40032142965687245, 'x4': 0.36761075421973366, 'y4': 0.10348831426543115, 'x5': 0.9742922088672088, 'y5': 0.3570444193697905, 'x6': 0.308676648888742, 'y6': 0.21334818513689913, 'x7': 0.5013838986985332, 'y7': 0.3632508512389847, 'x8': 0.22922171385450218, 'y8': 0.5667776474759543, 'x9': 0.9071321160757363, 'y9': 0.9100348200575245, 'x10': 0.4548882894218007, 'y10': 0.995598578525686, 'x11': 0.1082905887222525, 'y11': 0.6637554881377632, 'x12': 0.5328575468444964, 'y12': 0.049498262768756685, 'x13': 0.34927359295744964, 'y13': 0.2337042422377822, 'x14': 0.824734382265034, 'y14': 0.027115366874090663, 'x15': 0.8149219172889522, 'y15': 0.41772761222308497, 'x16': 0.1865852774828517, 'y16': 0.41253758609942637, 'x17': 0.6458688331421808, 'y17': 0.3227562466292242, 'x18': 0.8149595023785106, 'y18': 0.7708571034425503, 'x19': 0.5889443259559991, 'y19': 0.992480608519001}. Best is trial 2 with value: 0.3973827054764325.[0m
[32m[I 2022-01-18 06:52:22,290][0m Trial 8 finished with value: 0.26292937262980326 and parameters: {'x0': 0.18277472290711638, 'y0': 0.8521997252309496, 'x1': 0.8949743298381749, 'y1': 0.12317984240007707, 'x2': 0.7876409614012722, 'y2': 0.8836404656903423, 'x3': 0.302130485681399, 'y3': 0.8432515511865611, 'x4': 0.435160513441771, 'y4': 0.04296781510665848, 'x5': 0.636691441576373, 'y5': 0.8960624434664114, 'x6': 0.957092233233469, 'y6': 0.712380055367593, 'x7': 0.1839667641058883, 'y7': 0.2910622123938279, 'x8': 0.8527400030281962, 'y8': 0.5670047221239161, 'x9': 0.2650724046077446, 'y9': 0.12198559209527327, 'x10': 0.4009291624367005, 'y10': 0.5229276612397417, 'x11': 0.5999438784883662, 'y11': 0.6550543695140976, 'x12': 0.4185511787985382, 'y12': 0.22628379732777393, 'x13': 0.9192460160282634, 'y13': 0.9995798510932175, 'x14': 0.07706076031085463, 'y14': 0.29234691092770815, 'x15': 0.25890002487391073, 'y15': 0.061825576704477525, 'x16': 0.34004176935725605, 'y16': 0.6636094184704852, 'x17': 0.16424698458802156, 'y17': 0.30408096162755494, 'x18': 0.07044092106474675, 'y18': 0.49626211119720853, 'x19': 0.5024552346142779, 'y19': 0.7025816125409214}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,307][0m Trial 9 finished with value: 0.7397518112994116 and parameters: {'x0': 0.04297986569994283, 'y0': 0.3190936549467892, 'x1': 0.25296416995669313, 'y1': 0.821520145428977, 'x2': 0.8785070593757188, 'y2': 0.5466387077504077, 'x3': 0.35454386372848856, 'y3': 0.8830130291296626, 'x4': 0.6468624005697564, 'y4': 0.5271943609176284, 'x5': 0.39768159539028847, 'y5': 0.10387435465276607, 'x6': 0.24718449891394545, 'y6': 0.9083554964205247, 'x7': 0.9516522644274888, 'y7': 0.7162709433404121, 'x8': 0.8897470996309339, 'y8': 0.7488525127645492, 'x9': 0.33610934239493695, 'y9': 0.25893783001536574, 'x10': 0.21129813478004744, 'y10': 0.4475979674984968, 'x11': 0.6276158677912774, 'y11': 0.30716352845225126, 'x12': 0.5362957947950713, 'y12': 0.5015926834046467, 'x13': 0.6816845004791405, 'y13': 0.4678355717833398, 'x14': 0.037189677445661595, 'y14': 0.9940073355537395, 'x15': 0.218996496576629, 'y15': 0.487480979223483, 'x16': 0.514257423477219, 'y16': 0.10320015121433801, 'x17': 0.8323740916946778, 'y17': 0.5780716442671952, 'x18': 0.9872477986334385, 'y18': 0.6045818697466709, 'x19': 0.8788258511316168, 'y19': 0.15578433289664528}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,359][0m Trial 10 finished with value: 0.42845194292923994 and parameters: {'x0': 0.9833738222445754, 'y0': 0.8030697355259837, 'x1': 0.9448665687144864, 'y1': 0.41832334531247223, 'x2': 0.9794931693591274, 'y2': 0.9656180488925075, 'x3': 0.12967058102231677, 'y3': 0.6384204606173856, 'x4': 0.08826107127184729, 'y4': 0.004842556620104334, 'x5': 0.7418697058434178, 'y5': 0.9839199219146579, 'x6': 0.9446451193127109, 'y6': 0.5438913130657792, 'x7': 0.3781866560388155, 'y7': 0.014768175998526367, 'x8': 0.9827814423204022, 'y8': 0.34131404733889936, 'x9': 0.019753727107825858, 'y9': 0.6290264420936679, 'x10': 0.44291385831079366, 'y10': 0.6858557229345172, 'x11': 0.3328254612192718, 'y11': 0.6439761062794305, 'x12': 0.05899420628106006, 'y12': 0.23636666607070878, 'x13': 0.549099923639225, 'y13': 0.9334078034434465, 'x14': 0.3497162583694583, 'y14': 0.2709934812765241, 'x15': 0.0053561298941649516, 'y15': 0.9811197438330687, 'x16': 0.9832233876115752, 'y16': 0.740646335757707, 'x17': 0.24715179542344856, 'y17': 0.5714690774451742, 'x18': 0.33123823736841834, 'y18': 0.9594713572647943, 'x19': 0.11243471385204756, 'y19': 0.6637400553642284}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,418][0m Trial 11 finished with value: 0.31750163547332105 and parameters: {'x0': 0.634142126791976, 'y0': 0.009726209100246921, 'x1': 0.35537735952906624, 'y1': 0.49464830954170724, 'x2': 0.4186863062264051, 'y2': 0.3409725744996155, 'x3': 0.029318816573017215, 'y3': 0.03632949597139777, 'x4': 0.2043167680407847, 'y4': 0.31320917081285254, 'x5': 0.6290716397137686, 'y5': 0.7791693234981274, 'x6': 0.06942505018169111, 'y6': 0.4429046196378725, 'x7': 0.6393059630925195, 'y7': 0.9853613226595812, 'x8': 0.6408060719988324, 'y8': 0.3550065962629084, 'x9': 0.25730271906493124, 'y9': 0.4673402164272409, 'x10': 0.0254517955438906, 'y10': 0.5796378992290342, 'x11': 0.9970557364709991, 'y11': 0.5478414193865849, 'x12': 0.28886596813438475, 'y12': 0.5443351332329317, 'x13': 0.7379347499183674, 'y13': 0.032932755465314184, 'x14': 0.6787750232528421, 'y14': 0.31545552062968857, 'x15': 0.016187465554627162, 'y15': 0.03407358876173689, 'x16': 0.02140862819328854, 'y16': 0.18788562572176315, 'x17': 0.9973078552254457, 'y17': 0.3550253953368342, 'x18': 0.354786130436424, 'y18': 0.01393572645232835, 'x19': 0.9180944816816904, 'y19': 0.8502756985017526}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,484][0m Trial 12 finished with value: 0.4104791414527484 and parameters: {'x0': 0.3315724550850484, 'y0': 0.45401665735812685, 'x1': 0.39362576715495745, 'y1': 0.5118255440808904, 'x2': 0.35701401437304564, 'y2': 0.3680321431111638, 'x3': 0.019282445230003855, 'y3': 0.004780503330200601, 'x4': 0.18447191608444186, 'y4': 0.28544463462990954, 'x5': 0.7042261048094364, 'y5': 0.800493633698081, 'x6': 0.5322379573940831, 'y6': 0.5363836469085229, 'x7': 0.46562310096903115, 'y7': 0.9943672903393017, 'x8': 0.711763887403418, 'y8': 0.28133811227823907, 'x9': 0.08186182615125664, 'y9': 0.621339518968921, 'x10': 0.324765098584097, 'y10': 0.6227635905739958, 'x11': 0.2952563204285308, 'y11': 0.5730811288341552, 'x12': 0.2863491265822117, 'y12': 0.6412940458847386, 'x13': 0.9731115770434123, 'y13': 0.0021771110669198124, 'x14': 0.5547343483629031, 'y14': 0.30185961041403697, 'x15': 0.06776285320263348, 'y15': 0.02015317365084429, 'x16': 0.3380221660857682, 'y16': 0.012886426162929565, 'x17': 0.9842190985390916, 'y17': 0.4491777610462277, 'x18': 0.3044811378748261, 'y18': 0.011847365519458478, 'x19': 0.9903645781182832, 'y19': 0.7810123280748672}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,555][0m Trial 13 finished with value: 0.45441169504274215 and parameters: {'x0': 0.48895271830512566, 'y0': 0.4276813648108094, 'x1': 0.998274057590417, 'y1': 0.46782852101128386, 'x2': 0.38116750148397194, 'y2': 0.358517356400743, 'x3': 0.1527488540242766, 'y3': 0.6301905109958585, 'x4': 0.26880089324547646, 'y4': 0.28233141193433353, 'x5': 0.6868777492493953, 'y5': 0.765294357197654, 'x6': 0.08389491628060151, 'y6': 0.3756666399142119, 'x7': 0.0014238662616931075, 'y7': 0.8878071848330972, 'x8': 0.7230504973756956, 'y8': 0.20763042604286785, 'x9': 0.2072347152065056, 'y9': 0.4906112284323037, 'x10': 0.6620456031827576, 'y10': 0.692823126840496, 'x11': 0.8322146581019094, 'y11': 0.8547920457579271, 'x12': 0.1363741860313791, 'y12': 0.62754787483453, 'x13': 0.7726083670002819, 'y13': 0.7663674708926606, 'x14': 0.3723276133699177, 'y14': 0.2879859220258796, 'x15': 0.2915290679088955, 'y15': 0.21892611472842272, 'x16': 0.1432037426708398, 'y16': 0.6925990803420019, 'x17': 0.30062231406212137, 'y17': 0.24321541652391343, 'x18': 0.5327491144065384, 'y18': 0.2785119023876995, 'x19': 0.7564727931967953, 'y19': 0.9542813617122367}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,610][0m Trial 14 finished with value: 0.35265226559532586 and parameters: {'x0': 0.18818357058024426, 'y0': 0.7311046555571981, 'x1': 0.38108654841570966, 'y1': 0.3511662280134601, 'x2': 0.7893445926389259, 'y2': 0.7761117785499849, 'x3': 0.05696386158336825, 'y3': 0.6375219507257436, 'x4': 0.03280633712518444, 'y4': 0.14018511287049326, 'x5': 0.8175540270143772, 'y5': 0.7633719160643091, 'x6': 0.9963590109485984, 'y6': 0.7037029287998326, 'x7': 0.3305343202785428, 'y7': 0.642550566682877, 'x8': 0.8419009377436703, 'y8': 0.42391361731014804, 'x9': 0.4868176591614106, 'y9': 0.640327518102656, 'x10': 0.5929978986487907, 'y10': 0.5691955379693542, 'x11': 0.3964404867812149, 'y11': 0.5106914079774663, 'x12': 0.37066283999131727, 'y12': 0.004337820700335837, 'x13': 0.577212760697252, 'y13': 0.9982924541741311, 'x14': 0.7013886761532855, 'y14': 0.3693767727821171, 'x15': 0.2634993674304298, 'y15': 0.16752761089031332, 'x16': 0.7470875708859359, 'y16': 0.2754521909841102, 'x17': 0.002283952109407572, 'y17': 0.1503672776163402, 'x18': 0.2621809717877349, 'y18': 0.9847545506671838, 'x19': 0.305199215329943, 'y19': 0.5937397591489793}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,677][0m Trial 15 finished with value: 0.8058618423775084 and parameters: {'x0': 0.6541168388843799, 'y0': 0.8421011210696326, 'x1': 0.02681316941932127, 'y1': 0.6130740488478497, 'x2': 0.2430629355868028, 'y2': 0.35047724408992015, 'x3': 0.19946932777200713, 'y3': 0.9677302659874795, 'x4': 0.3198100490081262, 'y4': 0.35713600176393995, 'x5': 0.6115079428717731, 'y5': 0.9894051052272608, 'x6': 0.41965634339827645, 'y6': 0.3806726144775832, 'x7': 0.6298832919387232, 'y7': 0.2556065768126041, 'x8': 0.5851871499835983, 'y8': 0.7197228369043983, 'x9': 0.38855681635130146, 'y9': 0.008912955113080545, 'x10': 0.04408584972897761, 'y10': 0.7552310689282291, 'x11': 0.8428853572337814, 'y11': 0.006265432950823213, 'x12': 0.17815667300585747, 'y12': 0.2789113095430484, 'x13': 0.8464887284301833, 'y13': 0.4315848565388368, 'x14': 0.38633581149559276, 'y14': 0.18268716738414353, 'x15': 0.6670202333608153, 'y15': 0.7322090890526226, 'x16': 0.3709919913250232, 'y16': 0.21600276929358497, 'x17': 0.9782125641521561, 'y17': 0.4607402205250027, 'x18': 0.5280011478458517, 'y18': 0.0021160979003717224, 'x19': 0.03871659430734087, 'y19': 0.7816293913397825}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,733][0m Trial 16 finished with value: 0.7132190762816455 and parameters: {'x0': 0.834674671448585, 'y0': 0.0028666029825253694, 'x1': 0.7089769235006637, 'y1': 0.04537793796631673, 'x2': 0.45305435731081417, 'y2': 0.7168264819927674, 'x3': 0.6949840731088226, 'y3': 0.2034738985365966, 'x4': 0.2455782104803856, 'y4': 0.03700784632967158, 'x5': 0.3912581990147513, 'y5': 0.7063030301445961, 'x6': 0.013818250996094697, 'y6': 0.6513766014429404, 'x7': 0.5518138091957596, 'y7': 0.4499450186833124, 'x8': 0.7991165863313403, 'y8': 0.49069671765861667, 'x9': 0.6347105431288247, 'y9': 0.7793484248498206, 'x10': 0.31963383582561733, 'y10': 0.3291795597064713, 'x11': 0.4680690944024194, 'y11': 0.7588191078444445, 'x12': 0.388333114066799, 'y12': 0.5489204587550922, 'x13': 0.6367023416142993, 'y13': 0.6710339706248992, 'x14': 0.9979540114546535, 'y14': 0.4024067511514598, 'x15': 0.05874574936244912, 'y15': 0.148501050914087, 'x16': 0.1079281978982597, 'y16': 0.6290540618465041, 'x17': 0.5164549165021923, 'y17': 0.6809325036168516, 'x18': 0.14950419208437157, 'y18': 0.2792531729583533, 'x19': 0.7593615110478377, 'y19': 0.4945391167537493}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,790][0m Trial 17 finished with value: 0.3871100929693111 and parameters: {'x0': 0.5903839265930273, 'y0': 0.6140937207567, 'x1': 0.8785059826476828, 'y1': 0.5613858248409574, 'x2': 0.6213875277870202, 'y2': 0.8104351745391984, 'x3': 0.2272731182767151, 'y3': 0.3495399416043758, 'x4': 0.49171441309349323, 'y4': 0.18472315973774012, 'x5': 0.796364523058267, 'y5': 0.8632256296762671, 'x6': 0.6582096116592873, 'y6': 0.35015158221415643, 'x7': 0.7688580390944131, 'y7': 0.807867457667385, 'x8': 0.5635387416456688, 'y8': 0.1814649450426929, 'x9': 0.20573152820413113, 'y9': 0.3594292960719806, 'x10': 0.3038287427023504, 'y10': 0.49375234345260083, 'x11': 0.5431520976137547, 'y11': 0.942420607251013, 'x12': 0.01232921257227465, 'y12': 0.8184349890393627, 'x13': 0.447553849629765, 'y13': 0.3601475320239338, 'x14': 0.4595026036264479, 'y14': 0.1623954598576186, 'x15': 0.40224862763641617, 'y15': 0.006303856638857498, 'x16': 0.697290946673766, 'y16': 0.8772176311723101, 'x17': 0.8018074891558027, 'y17': 0.3699533507997051, 'x18': 0.18746518026358944, 'y18': 0.1374756606209966, 'x19': 0.20876855693239393, 'y19': 0.7020572153752908}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,841][0m Trial 18 finished with value: 0.4035234280629654 and parameters: {'x0': 0.35706787413355445, 'y0': 0.33190908932315516, 'x1': 0.3599552365191307, 'y1': 0.2940047426067809, 'x2': 0.8623010347095202, 'y2': 0.44677115239273724, 'x3': 0.009237460795453577, 'y3': 0.5468727759927128, 'x4': 0.10433340686119336, 'y4': 0.3989255740752212, 'x5': 0.375876884932863, 'y5': 0.6726885017553766, 'x6': 0.4543712283891045, 'y6': 0.619689568698104, 'x7': 0.24372643505989394, 'y7': 0.011125143534436388, 'x8': 0.9945375449664393, 'y8': 0.48957577287340537, 'x9': 0.14699454040073928, 'y9': 0.1679748472464262, 'x10': 0.6474725346652924, 'y10': 0.8066048074968003, 'x11': 0.01074872285339673, 'y11': 0.5814295165637123, 'x12': 0.21435322325707967, 'y12': 0.1899074993651953, 'x13': 0.8230380810733693, 'y13': 0.12095911184092567, 'x14': 0.6807919299525964, 'y14': 0.4293285152808092, 'x15': 0.17926772918752815, 'y15': 0.704828965344055, 'x16': 0.41485080518904055, 'y16': 0.28063407658461703, 'x17': 0.23382656821562822, 'y17': 0.14562092519355768, 'x18': 0.4227008993465427, 'y18': 0.8467639457729308, 'x19': 0.9546771902297939, 'y19': 0.887641912712992}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,898][0m Trial 19 finished with value: 0.5606652700069975 and parameters: {'x0': 0.12355322720615483, 'y0': 0.52008667312515, 'x1': 0.6386361369191412, 'y1': 0.21218421766287227, 'x2': 0.23235254414794926, 'y2': 0.2470431723940928, 'x3': 0.45089801146083497, 'y3': 0.10565810429155259, 'x4': 0.40540245282898846, 'y4': 0.8599504173256936, 'x5': 0.8849032230943051, 'y5': 0.4091359287052234, 'x6': 0.7032490506886593, 'y6': 0.4439960895186049, 'x7': 0.3922662585210004, 'y7': 0.9732418650178774, 'x8': 0.7676104942692306, 'y8': 0.31824114802162085, 'x9': 0.4325483662849404, 'y9': 0.5304645451883128, 'x10': 0.5478211085029434, 'y10': 0.011344322218340697, 'x11': 0.7973981530457785, 'y11': 0.7420717561245178, 'x12': 0.44464491166388265, 'y12': 0.36206478700717504, 'x13': 0.9916408192323465, 'y13': 0.5387823294037574, 'x14': 0.2847269394486984, 'y14': 0.19204545000838258, 'x15': 0.006819505418219395, 'y15': 0.2634964209914922, 'x16': 0.2558207886732677, 'y16': 0.5846733525053112, 'x17': 0.5005600328265695, 'y17': 0.5696981144459342, 'x18': 0.6580088469517595, 'y18': 0.39706615106106524, 'x19': 0.6628941580685483, 'y19': 0.44855220127472434}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:22,964][0m Trial 20 finished with value: 0.26657309524960926 and parameters: {'x0': 0.4466169531085213, 'y0': 0.5524548849307886, 'x1': 0.45468374635930675, 'y1': 0.38927306489714936, 'x2': 0.9564973046454222, 'y2': 0.4695262965012544, 'x3': 0.2607585564271033, 'y3': 0.7051104005425359, 'x4': 0.7803220244075337, 'y4': 0.08921007947439294, 'x5': 0.6025205031868178, 'y5': 0.8879747918940247, 'x6': 0.3863498213741728, 'y6': 0.017369613203327916, 'x7': 0.11841283576808392, 'y7': 0.17879538933294692, 'x8': 0.891180791882717, 'y8': 0.6836874136363589, 'x9': 0.5699644309959752, 'y9': 0.7492397492976821, 'x10': 0.10171176551399308, 'y10': 0.3654642103081894, 'x11': 0.9907471910054579, 'y11': 0.45975902749624864, 'x12': 0.6673243511632022, 'y12': 0.7416113867251732, 'x13': 0.8952568978194948, 'y13': 0.7669449010159128, 'x14': 0.4735820108894928, 'y14': 0.7080527311803564, 'x15': 0.6812534853932495, 'y15': 0.3263381535136364, 'x16': 0.5903482300401585, 'y16': 0.8223451518891259, 'x17': 0.3844318168451988, 'y17': 0.1999794693306834, 'x18': 0.20351418485241873, 'y18': 0.15407167062024069, 'x19': 0.8189597381713647, 'y19': 0.7268995257165689}. Best is trial 8 with value: 0.26292937262980326.[0m
[32m[I 2022-01-18 06:52:23,024][0m Trial 21 finished with value: 0.20791297194922942 and parameters: {'x0': 0.43577410518779663, 'y0': 0.5224299895948419, 'x1': 0.4724431838807994, 'y1': 0.3827489597924426, 'x2': 0.9348583896077536, 'y2': 0.45602954684518293, 'x3': 0.2515439804006244, 'y3': 0.7240552854409734, 'x4': 0.7570489142305006, 'y4': 0.07720202841803792, 'x5': 0.6167517685083169, 'y5': 0.8837973355491523, 'x6': 0.15571557795151492, 'y6': 0.23362960630104807, 'x7': 0.10172736856024746, 'y7': 0.17108605914572916, 'x8': 0.8600282736507207, 'y8': 0.6990777549841053, 'x9': 0.5774304499873033, 'y9': 0.7575090046321568, 'x10': 0.11193376514712339, 'y10': 0.3847998476779344, 'x11': 0.9992825526975955, 'y11': 0.48646201943513934, 'x12': 0.6783290232584686, 'y12': 0.7466657702067777, 'x13': 0.8846340301224458, 'y13': 0.8134719863905171, 'x14': 0.48381193566785224, 'y14': 0.6814779024428216, 'x15': 0.693545605517007, 'y15': 0.33017821321417673, 'x16': 0.6470072247790435, 'y16': 0.8099453720696685, 'x17': 0.35386829584638496, 'y17': 0.21017109379655494, 'x18': 0.23651923867081753, 'y18': 0.13462072484825133, 'x19': 0.817652843194364, 'y19': 0.725305018944864}. Best is trial 21 with value: 0.20791297194922942.[0m
[32m[I 2022-01-18 06:52:23,089][0m Trial 22 finished with value: 0.2331333126123165 and parameters: {'x0': 0.4648596093700004, 'y0': 0.5244204528419077, 'x1': 0.4731658641622481, 'y1': 0.3698798972623248, 'x2': 0.9977062612817265, 'y2': 0.48670627262389793, 'x3': 0.25224798149388794, 'y3': 0.7374162373253759, 'x4': 0.7919553467626397, 'y4': 0.10269927413068475, 'x5': 0.4916945209834363, 'y5': 0.8702842636166374, 'x6': 0.1913795787465732, 'y6': 0.004164688203321986, 'x7': 0.11172647800882102, 'y7': 0.1770525926107356, 'x8': 0.9139510312667619, 'y8': 0.7182361944807669, 'x9': 0.5761603972049565, 'y9': 0.7767309819682797, 'x10': 0.12836403323328138, 'y10': 0.39622571359745173, 'x11': 0.9009209984891288, 'y11': 0.46472927964929056, 'x12': 0.6761491089203697, 'y12': 0.7568690566910722, 'x13': 0.8777877655267798, 'y13': 0.8003373399994013, 'x14': 0.4676599173715977, 'y14': 0.7114802200092271, 'x15': 0.7034152049622222, 'y15': 0.35001844978496627, 'x16': 0.6066621011444648, 'y16': 0.8415969616035452, 'x17': 0.3653022384471517, 'y17': 0.165981565662397, 'x18': 0.21345381384778722, 'y18': 0.17657033238695216, 'x19': 0.7933083342777465, 'y19': 0.7125695213654827}. Best is trial 21 with value: 0.20791297194922942.[0m
[32m[I 2022-01-18 06:52:23,143][0m Trial 23 finished with value: 0.287114907755382 and parameters: {'x0': 0.26985022769218436, 'y0': 0.7540835079365092, 'x1': 0.4692022468552692, 'y1': 0.1444644860796255, 'x2': 0.8652076874538897, 'y2': 0.6631290964805265, 'x3': 0.4378725708271449, 'y3': 0.996372163826974, 'x4': 0.7540999836166383, 'y4': 0.06784039183069082, 'x5': 0.47385472467673173, 'y5': 0.9161494985746671, 'x6': 0.18930457713250418, 'y6': 0.290537402436097, 'x7': 0.11502381350608634, 'y7': 0.08212231827286137, 'x8': 0.9040582935041451, 'y8': 0.8055524256596278, 'x9': 0.7920143856155398, 'y9': 0.7726958156799026, 'x10': 0.22804148715252537, 'y10': 0.39278369147194153, 'x11': 0.8941432475162824, 'y11': 0.2070850666232979, 'x12': 0.7734573044008852, 'y12': 0.7717248427981042, 'x13': 0.9087049905557547, 'y13': 0.88041821921368, 'x14': 0.24636664555764887, 'y14': 0.8598937645251237, 'x15': 0.75568035994573, 'y15': 0.34428994005536623, 'x16': 0.8244350858538305, 'y16': 0.9073993815814922, 'x17': 0.1620664946973931, 'y17': 0.11345781356521863, 'x18': 0.17969536176987194, 'y18': 0.20870853516892152, 'x19': 0.5014365426951624, 'y19': 0.5611581246954264}. Best is trial 21 with value: 0.20791297194922942.[0m
[32m[I 2022-01-18 06:52:23,203][0m Trial 24 finished with value: 0.13566437841645562 and parameters: {'x0': 0.40358399286676466, 'y0': 0.3824965861989358, 'x1': 0.612835468601004, 'y1': 0.3316269724730486, 'x2': 0.979311273462509, 'y2': 0.8566639514818808, 'x3': 0.14445323266782023, 'y3': 0.7517015963396507, 'x4': 0.850589649033521, 'y4': 0.18570146742848906, 'x5': 0.5005030192490236, 'y5': 0.8478448255614344, 'x6': 0.18827033179868113, 'y6': 0.045148329749327226, 'x7': 0.008296744320929653, 'y7': 0.2633967927464673, 'x8': 0.9483147426617651, 'y8': 0.8816370647240771, 'x9': 0.5702859123849823, 'y9': 0.6846421942659204, 'x10': 0.3975786696339249, 'y10': 0.12701929888451718, 'x11': 0.7500007836121918, 'y11': 0.4630016387964784, 'x12': 0.6490372501667299, 'y12': 0.9702603505322606, 'x13': 0.7900735484428295, 'y13': 0.9996927053530409, 'x14': 0.5623126762213543, 'y14': 0.6446498395317188, 'x15': 0.9734448691561568, 'y15': 0.6678475373780282, 'x16': 0.6001655715809975, 'y16': 0.8027073561490944, 'x17': 0.3288245875614526, 'y17': 0.2684005755468019, 'x18': 0.44181686926922364, 'y18': 0.3728332907829188, 'x19': 0.7864236207676799, 'y19': 0.6717521847693332}. Best is trial 24 with value: 0.13566437841645562.[0m
[32m[I 2022-01-18 06:52:23,257][0m Trial 25 finished with value: 0.0767860770958706 and parameters: {'x0': 0.4395925235968167, 'y0': 0.41899159155822885, 'x1': 0.602136318178007, 'y1': 0.33323122395323646, 'x2': 0.9702199741980613, 'y2': 0.589546969851732, 'x3': 0.12053565487134799, 'y3': 0.7449176994936099, 'x4': 0.8539100873052337, 'y4': 0.1874581855225559, 'x5': 0.4716360440363504, 'y5': 0.2319000871330933, 'x6': 0.17617265354368644, 'y6': 0.014963677065655712, 'x7': 0.0015886533534260304, 'y7': 0.22448762735010502, 'x8': 0.9626975342857533, 'y8': 0.9858318986796752, 'x9': 0.5590507662011073, 'y9': 0.7219587766176704, 'x10': 0.2605716416309186, 'y10': 0.1838326243341964, 'x11': 0.7507964170830314, 'y11': 0.460156638243745, 'x12': 0.8800811761098105, 'y12': 0.9947028950443753, 'x13': 0.7810488910020545, 'y13': 0.7936485476970082, 'x14': 0.541053155725587, 'y14': 0.6476670488933457, 'x15': 0.9882052184763896, 'y15': 0.6541443762793553, 'x16': 0.6253714825229915, 'y16': 0.8096815102998375, 'x17': 0.33611306272576563, 'y17': 0.0017065058323171844, 'x18': 0.4463527096251559, 'y18': 0.37249485995467474, 'x19': 0.7380147927975089, 'y19': 0.5469280944291994}. Best is trial 25 with value: 0.0767860770958706.[0m
[32m[I 2022-01-18 06:52:23,313][0m Trial 26 finished with value: 0.0366019333158234 and parameters: {'x0': 0.5612025755258196, 'y0': 0.36420570972228306, 'x1': 0.6272302022527485, 'y1': 0.3100242296484004, 'x2': 0.9029604292405757, 'y2': 0.6226236451537135, 'x3': 0.10953283633449346, 'y3': 0.55971527088372, 'x4': 0.8860683467216188, 'y4': 0.19998391766541207, 'x5': 0.33483135286417837, 'y5': 0.24880100643282232, 'x6': 0.3533669577151497, 'y6': 0.06815242446128136, 'x7': 0.015342055953088981, 'y7': 0.08470654679248632, 'x8': 0.9966261280641451, 'y8': 0.9657201684651033, 'x9': 0.7974575504559681, 'y9': 0.69486946044507, 'x10': 0.26489152312732805, 'y10': 0.1597296306770385, 'x11': 0.7496893883357877, 'y11': 0.22549136782323292, 'x12': 0.9238798991313695, 'y12': 0.974514569066904, 'x13': 0.6624097483897227, 'y13': 0.6993661631305597, 'x14': 0.5671317442433746, 'y14': 0.6168209486895255, 'x15': 0.9753666082106613, 'y15': 0.685918329891856, 'x16': 0.8600355623817113, 'y16': 0.9881796772309671, 'x17': 0.3099382876944513, 'y17': 0.020058293828134777, 'x18': 0.44256299487683465, 'y18': 0.3902801361455763, 'x19': 0.679257089360215, 'y19': 0.536144131606768}. Best is trial 26 with value: 0.0366019333158234.[0m
[32m[I 2022-01-18 06:52:23,369][0m Trial 27 finished with value: 0.022998440284408117 and parameters: {'x0': 0.544033884647938, 'y0': 0.3636721118861641, 'x1': 0.6158416429773703, 'y1': 0.2982351362148994, 'x2': 0.7998802087112614, 'y2': 0.8451212155432029, 'x3': 0.11572736582968964, 'y3': 0.5637610060211939, 'x4': 0.8947381091171613, 'y4': 0.20412795992664004, 'x5': 0.3086220465008853, 'y5': 0.004780855930402561, 'x6': 0.3524063371962796, 'y6': 0.09932828402703156, 'x7': 0.006710281816741102, 'y7': 0.08420720835465334, 'x8': 0.9725009707263436, 'y8': 0.9941800108401853, 'x9': 0.8079641545196197, 'y9': 0.6807081239236518, 'x10': 0.3743764578671397, 'y10': 0.17586967998212522, 'x11': 0.7551535506473442, 'y11': 0.20166498097814828, 'x12': 0.9923702468439163, 'y12': 0.9953408906853839, 'x13': 0.6334563782227821, 'y13': 0.6851157712809992, 'x14': 0.5729299991009034, 'y14': 0.8278274745332987, 'x15': 0.9685324048537296, 'y15': 0.6931727079912255, 'x16': 0.8601679590332063, 'y16': 0.9802623857319773, 'x17': 0.2811613333186681, 'y17': 0.008677249043666346, 'x18': 0.46849582415646845, 'y18': 0.3865400434787474, 'x19': 0.6536664580891032, 'y19': 0.28344302452584325}. Best is trial 27 with value: 0.022998440284408117.[0m
[32m[I 2022-01-18 06:52:23,427][0m Trial 28 finished with value: 0.24207702051089108 and parameters: {'x0': 0.5739918680671905, 'y0': 0.2584507901032852, 'x1': 0.6862616277714757, 'y1': 0.9594622597181997, 'x2': 0.8136436231506996, 'y2': 0.746205170293064, 'x3': 0.09987580544847435, 'y3': 0.5470005978989422, 'x4': 0.9188685999636673, 'y4': 0.4329516063196775, 'x5': 0.31325849001935224, 'y5': 0.018439067639987643, 'x6': 0.3528003104754699, 'y6': 0.12743775024114679, 'x7': 0.28267182914493566, 'y7': 0.09645183021417575, 'x8': 0.0009260882880136601, 'y8': 0.9940016740375813, 'x9': 0.7815462663142758, 'y9': 0.5782473387339495, 'x10': 0.2886350920245403, 'y10': 0.18407543721246925, 'x11': 0.7488880032392711, 'y11': 0.1850770539915516, 'x12': 0.978821447547102, 'y12': 0.9061401526674298, 'x13': 0.46979993607163073, 'y13': 0.7102983275397605, 'x14': 0.614254416532126, 'y14': 0.8261929651507516, 'x15': 0.9663058422132196, 'y15': 0.8593121342901919, 'x16': 0.905590102395213, 'y16': 0.9491291490295606, 'x17': 0.2377924403008268, 'y17': 0.012257294452572287, 'x18': 0.5966582544797919, 'y18': 0.4029982032918128, 'x19': 0.6638640050968722, 'y19': 0.30502367288560456}. Best is trial 27 with value: 0.022998440284408117.[0m
[32m[I 2022-01-18 06:52:23,490][0m Trial 29 finished with value: 0.10990816261098535 and parameters: {'x0': 0.7662975615980776, 'y0': 0.12445716535813606, 'x1': 0.8188478800839184, 'y1': 0.2013252785224633, 'x2': 0.7112251966002311, 'y2': 0.6327836751582124, 'x3': 0.17707291599036917, 'y3': 0.5161118563336327, 'x4': 0.8435973959748658, 'y4': 0.20711257810402683, 'x5': 0.13690430085377842, 'y5': 0.2582975697245245, 'x6': 0.5607974355016736, 'y6': 0.0784049619329102, 'x7': 0.042469079476243836, 'y7': 0.08206466887349037, 'x8': 0.9906286112802346, 'y8': 0.9919182724338146, 'x9': 0.9929987160175685, 'y9': 0.6898081129851668, 'x10': 0.37036256146960567, 'y10': 0.0290189956382208, 'x11': 0.6995819824612296, 'y11': 0.050879169565616084, 'x12': 0.9072230711482987, 'y12': 0.9826866848762609, 'x13': 0.6589666386834824, 'y13': 0.5523998280156931, 'x14': 0.7527130083158573, 'y14': 0.8092485593763048, 'x15': 0.8726794554836419, 'y15': 0.8377212520915723, 'x16': 0.7992480937802061, 'y16': 0.9903928838960568, 'x17': 0.41673173508586026, 'y17': 0.09429703974947651, 'x18': 0.4424976460727949, 'y18': 0.5801855255236994, 'x19': 0.5768158549218642, 'y19': 0.04190961679591318}. Best is trial 27 with value: 0.022998440284408117.[0m
[32m[I 2022-01-18 06:52:23,564][0m Trial 30 finished with value: 0.03327442045933682 and parameters: {'x0': 0.5377645804643514, 'y0': 0.3236675367987879, 'x1': 0.5674519911901562, 'y1': 0.44557269888913686, 'x2': 0.904401367654003, 'y2': 0.5828475790221744, 'x3': 0.09001362169690354, 'y3': 0.4680306326156784, 'x4': 0.5813085950976773, 'y4': 0.3537399368255484, 'x5': 0.29042692825400285, 'y5': 0.2374663224206755, 'x6': 0.45631581524299764, 'y6': 0.25820302923329363, 'x7': 0.15862231215245437, 'y7': 0.5149893101371243, 'x8': 0.7857737293647991, 'y8': 0.9236453545350634, 'x9': 0.9023878385207316, 'y9': 0.861018890359333, 'x10': 0.5022496737153347, 'y10': 0.19504211691197973, 'x11': 0.6674532208250143, 'y11': 0.23323833735875246, 'x12': 0.8681692071255661, 'y12': 0.8980617342163056, 'x13': 0.5999848016688569, 'y13': 0.7091146292965855, 'x14': 0.5601835684152608, 'y14': 0.9674649745914685, 'x15': 0.8943117990274843, 'y15': 0.637592257720612, 'x16': 0.8752440785507631, 'y16': 0.9236564959465511, 'x17': 0.046264669567140315, 'y17': 0.07111138662714034, 'x18': 0.6129775203514878, 'y18': 0.43029028769120065, 'x19': 0.6975357265556275, 'y19': 0.37829326950301567}. Best is trial 27 with value: 0.022998440284408117.[0m
[32m[I 2022-01-18 06:52:23,628][0m Trial 31 finished with value: 0.0355688312836987 and parameters: {'x0': 0.5543058928258497, 'y0': 0.31397042816790827, 'x1': 0.5772185838652177, 'y1': 0.31303895201647697, 'x2': 0.9041859506015719, 'y2': 0.619684390971774, 'x3': 0.10329881736877955, 'y3': 0.44413143786649495, 'x4': 0.5815793810209297, 'y4': 0.35910668121054345, 'x5': 0.29018678725084085, 'y5': 0.2373991644554993, 'x6': 0.46806126171548645, 'y6': 0.22585933277668716, 'x7': 0.19881989618252874, 'y7': 0.5417184645408946, 'x8': 0.7962185136861192, 'y8': 0.9130937430276193, 'x9': 0.906015542798682, 'y9': 0.8479753993321365, 'x10': 0.5235570943185488, 'y10': 0.19736077800502427, 'x11': 0.6174408905817054, 'y11': 0.22378765603641954, 'x12': 0.8549112759768082, 'y12': 0.9130226919445252, 'x13': 0.5968322215924303, 'y13': 0.7224166169628945, 'x14': 0.5519081742634603, 'y14': 0.9674120953233362, 'x15': 0.9972457167992784, 'y15': 0.6132828141524641, 'x16': 0.8937263597020513, 'y16': 0.9190426842072608, 'x17': 0.0580749778655842, 'y17': 0.07117627958149582, 'x18': 0.5959650546575742, 'y18': 0.5404229552090984, 'x19': 0.6973551631624382, 'y19': 0.37551481447679286}. Best is trial 27 with value: 0.022998440284408117.[0m
[32m[I 2022-01-18 06:52:23,690][0m Trial 32 finished with value: 0.022686100158002542 and parameters: {'x0': 0.5422685665856147, 'y0': 0.3043934563408605, 'x1': 0.5437774208294541, 'y1': 0.4581600754767161, 'x2': 0.8955810574881291, 'y2': 0.683255927752042, 'x3': 0.0817997602578783, 'y3': 0.4487670636671236, 'x4': 0.5604685647627086, 'y4': 0.3562608831408942, 'x5': 0.28627143435800667, 'y5': 0.20940118219138185, 'x6': 0.46706082045045944, 'y6': 0.24059437437112546, 'x7': 0.18325926834816791, 'y7': 0.5251214015931287, 'x8': 0.7875127769845319, 'y8': 0.927600338149722, 'x9': 0.8954830684741345, 'y9': 0.9948056396450813, 'x10': 0.5117069620357432, 'y10': 0.08419693433568999, 'x11': 0.5871621733181132, 'y11': 0.11946484682275876, 'x12': 0.8320281425298433, 'y12': 0.894648357124605, 'x13': 0.5887429983919781, 'y13': 0.6887254796597551, 'x14': 0.6253393583474472, 'y14': 0.990784199315945, 'x15': 0.8956909711335752, 'y15': 0.8081324210492998, 'x16': 0.9065801309492085, 'y16': 0.9247417744938173, 'x17': 0.01951096323861392, 'y17': 0.08226035578735519, 'x18': 0.7562983210015835, 'y18': 0.5661148426763436, 'x19': 0.6907537407135285, 'y19': 0.33343007540246583}. Best is trial 32 with value: 0.022686100158002542.[0m
[32m[I 2022-01-18 06:52:23,752][0m Trial 33 finished with value: 0.02043643807061546 and parameters: {'x0': 0.5298898149764341, 'y0': 0.27853284115949434, 'x1': 0.5382014365215544, 'y1': 0.45186720482150033, 'x2': 0.817992201807648, 'y2': 0.6945440098130247, 'x3': 0.07735237740132433, 'y3': 0.45118047224362967, 'x4': 0.5711268733492373, 'y4': 0.3583569322637998, 'x5': 0.17937301491002558, 'y5': 0.12518927616293357, 'x6': 0.44449488543335886, 'y6': 0.24514261883403046, 'x7': 0.196388017074979, 'y7': 0.5362948389944586, 'x8': 0.7857021712587633, 'y8': 0.9011456619653611, 'x9': 0.9039608972236318, 'y9': 0.9540648772272684, 'x10': 0.5139467534833951, 'y10': 0.06418169073615597, 'x11': 0.604573589188401, 'y11': 0.10870316478635511, 'x12': 0.8278623009345023, 'y12': 0.8854868353018303, 'x13': 0.5459405691419099, 'y13': 0.6259102413812596, 'x14': 0.6230456742204423, 'y14': 0.9932876118034116, 'x15': 0.8736982020919483, 'y15': 0.5801334200279729, 'x16': 0.9910769977515336, 'y16': 0.9225350696092014, 'x17': 0.0007271976958292542, 'y17': 0.06854890709545244, 'x18': 0.7804788207824083, 'y18': 0.5701753566373656, 'x19': 0.6015740936973228, 'y19': 0.3252800574616595}. Best is trial 33 with value: 0.02043643807061546.[0m
[32m[I 2022-01-18 06:52:23,816][0m Trial 34 finished with value: 0.07126440502283937 and parameters: {'x0': 0.7205983757019955, 'y0': 0.26632360749923345, 'x1': 0.6976887642561687, 'y1': 0.5858081273708639, 'x2': 0.749504224553796, 'y2': 0.683441340465361, 'x3': 0.06619547657767369, 'y3': 0.3040039093130883, 'x4': 0.5753133390448862, 'y4': 0.6062702006516523, 'x5': 0.13186027493959612, 'y5': 0.0037628561867270407, 'x6': 0.6169106546139939, 'y6': 0.29483202675809356, 'x7': 0.16594650149606513, 'y7': 0.48133395186212663, 'x8': 0.6875503182684705, 'y8': 0.8168789684276406, 'x9': 0.9158800491744314, 'y9': 0.9413511043440222, 'x10': 0.7183818098782668, 'y10': 0.06562698650361934, 'x11': 0.49112446537988763, 'y11': 0.10666172655433889, 'x12': 0.9992418207227178, 'y12': 0.8678891395853592, 'x13': 0.5223120946908862, 'y13': 0.6382698858670988, 'x14': 0.7653625423013835, 'y14': 0.9174319628215768, 'x15': 0.8970567363973684, 'y15': 0.8010486413330241, 'x16': 0.9990734430699539, 'y16': 0.9086036588607233, 'x17': 0.007106617238014697, 'y17': 0.10608335769094208, 'x18': 0.8041501907145366, 'y18': 0.65035298071274, 'x19': 0.40949341048141963, 'y19': 0.29887328141265507}. Best is trial 33 with value: 0.02043643807061546.[0m
[32m[I 2022-01-18 06:52:23,880][0m Trial 35 finished with value: 0.0034136459197382507 and parameters: {'x0': 0.529049221445093, 'y0': 0.1353538699803722, 'x1': 0.5156318088420372, 'y1': 0.45246839717163057, 'x2': 0.644028597010955, 'y2': 0.8459057442395546, 'x3': 0.19765711150694507, 'y3': 0.38607262676144133, 'x4': 0.5073717810624648, 'y4': 0.34023484807751053, 'x5': 0.17859027987922182, 'y5': 0.12723353472634924, 'x6': 0.5008758062431787, 'y6': 0.17923074710629028, 'x7': 0.2456803937197632, 'y7': 0.6333240221941105, 'x8': 0.6256370689343713, 'y8': 0.865070192960444, 'x9': 0.8461379694101644, 'y9': 0.9700427028439651, 'x10': 0.46654006898496975, 'y10': 0.09470971118516774, 'x11': 0.5616803708440128, 'y11': 0.1230698784935558, 'x12': 0.7770488123565793, 'y12': 0.8410226219401689, 'x13': 0.4058513864504114, 'y13': 0.5553658878206494, 'x14': 0.6316528294101832, 'y14': 0.9099192443596837, 'x15': 0.8582155245805269, 'y15': 0.7764711253726307, 'x16': 0.9365981636440601, 'y16': 0.8662494558153226, 'x17': 0.06655068281128504, 'y17': 0.09991378287093214, 'x18': 0.7805612471499654, 'y18': 0.5484041790873354, 'x19': 0.6184520645897706, 'y19': 0.2608190054513084}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:23,946][0m Trial 36 finished with value: 0.1356927593464779 and parameters: {'x0': 0.6202591075704982, 'y0': 0.14130152523641726, 'x1': 0.5285559838570094, 'y1': 0.6524925565259022, 'x2': 0.6403812663862903, 'y2': 0.813338091224851, 'x3': 0.9030057145735474, 'y3': 0.3841259131184733, 'x4': 0.5085051665820195, 'y4': 0.4764876227892134, 'x5': 0.018640383323469345, 'y5': 0.11401235638192248, 'x6': 0.49916767216701147, 'y6': 0.19453198290292176, 'x7': 0.2768418943441945, 'y7': 0.6299926724816068, 'x8': 0.5139074108364514, 'y8': 0.8671726551163401, 'x9': 0.8343691633071939, 'y9': 0.9967954910054951, 'x10': 0.5744172010019333, 'y10': 0.06872671063132109, 'x11': 0.5655728553901276, 'y11': 0.12112371175604633, 'x12': 0.7902492365798063, 'y12': 0.8010675659071326, 'x13': 0.4081881840657863, 'y13': 0.38684436187882243, 'x14': 0.6535737705945412, 'y14': 0.8977103965137264, 'x15': 0.8155716711098865, 'y15': 0.9170833177931069, 'x16': 0.9284567015544061, 'y16': 0.7381165260523189, 'x17': 0.09925614940066999, 'y17': 0.1769739524381974, 'x18': 0.7780619745303388, 'y18': 0.5468413426818104, 'x19': 0.6089478714197906, 'y19': 0.23990865481696463}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,007][0m Trial 37 finished with value: 0.15969942021957623 and parameters: {'x0': 0.7537059794010571, 'y0': 0.1323436164766537, 'x1': 0.28694487494590204, 'y1': 0.555503673109845, 'x2': 0.5716721721571036, 'y2': 0.8639073700661276, 'x3': 0.18777765525359885, 'y3': 0.23495083988254614, 'x4': 0.7062102876661052, 'y4': 0.2602410094298396, 'x5': 0.18590099520416353, 'y5': 0.059931858697776744, 'x6': 0.7126016409131892, 'y6': 0.14272033343849305, 'x7': 0.3357606795021039, 'y7': 0.3840594002846114, 'x8': 0.6063831921016982, 'y8': 0.7900186048319049, 'x9': 0.710876628626618, 'y9': 0.9223087419404051, 'x10': 0.6189135232295153, 'y10': 0.2527105263591586, 'x11': 0.4310729503605774, 'y11': 0.06576956630093797, 'x12': 0.7397565119725585, 'y12': 0.842563243772782, 'x13': 0.2376040828905152, 'y13': 0.5272766596005234, 'x14': 0.8391888901096414, 'y14': 0.7779384750020968, 'x15': 0.8237067404687303, 'y15': 0.7730980488400182, 'x16': 0.9472029955710161, 'y16': 0.5724889774871261, 'x17': 0.17271165296284552, 'y17': 0.11858163714272237, 'x18': 0.9006339603296756, 'y18': 0.6741949591033334, 'x19': 0.5433114621686965, 'y19': 0.3124223126044497}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,070][0m Trial 38 finished with value: 0.2638999999338144 and parameters: {'x0': 0.5220945315642723, 'y0': 0.07307591264601224, 'x1': 0.7221746327317462, 'y1': 0.5189766429865115, 'x2': 0.6587710086315718, 'y2': 0.9794438484934553, 'x3': 0.4149127830198221, 'y3': 0.4148561603443798, 'x4': 0.5118783806932543, 'y4': 0.7417112576950079, 'x5': 0.11985399817919645, 'y5': 0.1884126564013401, 'x6': 0.542666228664332, 'y6': 0.315955491205253, 'x7': 0.2527190643176297, 'y7': 0.6287493469700811, 'x8': 0.4248002091709097, 'y8': 0.6383562898225543, 'x9': 0.8398525419082044, 'y9': 0.9987224613141229, 'x10': 0.46153032391945154, 'y10': 0.0921213135143988, 'x11': 0.5529097219628403, 'y11': 0.15869037800934943, 'x12': 0.6008651010295816, 'y12': 0.685466818476391, 'x13': 0.38158349276336867, 'y13': 0.5725210759973826, 'x14': 0.7612821168637187, 'y14': 0.9164028111836309, 'x15': 0.5992846715271175, 'y15': 0.7674753217811028, 'x16': 0.7807659107112986, 'y16': 0.8697887605198273, 'x17': 0.06423469965288818, 'y17': 0.8871593081278408, 'x18': 0.735805666191208, 'y18': 0.7940504310201526, 'x19': 0.44580516060344766, 'y19': 0.44766719259323035}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,151][0m Trial 39 finished with value: 0.17993688959373688 and parameters: {'x0': 0.6885438333812286, 'y0': 0.25223982905096654, 'x1': 0.5316211714143815, 'y1': 0.7534075773106421, 'x2': 0.5260347175460285, 'y2': 0.7184189852551706, 'x3': 0.300554528822222, 'y3': 0.33690735549402373, 'x4': 0.6722605052236147, 'y4': 0.42589074945814814, 'x5': 0.07444055213814896, 'y5': 0.15956644938219217, 'x6': 0.6108595709991006, 'y6': 0.190813070470582, 'x7': 0.06007504107543238, 'y7': 0.4321692807348075, 'x8': 0.6579436043651867, 'y8': 0.9267278648648843, 'x9': 0.9518558120419813, 'y9': 0.830865596021374, 'x10': 0.7560224722436227, 'y10': 0.2981169131970327, 'x11': 0.663252966362732, 'y11': 0.35045203363484323, 'x12': 0.8074176100114356, 'y12': 0.9239031572983643, 'x13': 0.22581367769381266, 'y13': 0.598887359367086, 'x14': 0.6360547581788735, 'y14': 0.7725517236186175, 'x15': 0.7824401596991644, 'y15': 0.5322131320855116, 'x16': 0.9534371542476906, 'y16': 0.9998439137151881, 'x17': 0.13458484739942217, 'y17': 0.2490843149167002, 'x18': 0.8859667357547554, 'y18': 0.4710849918564872, 'x19': 0.6299433965674726, 'y19': 0.20283875366011997}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,214][0m Trial 40 finished with value: 0.05233474923426684 and parameters: {'x0': 0.3002340234009018, 'y0': 0.1882424292168952, 'x1': 0.8018169844908557, 'y1': 0.44147238133618283, 'x2': 0.7366901463303108, 'y2': 0.9047920417921476, 'x3': 0.6768875184406599, 'y3': 0.21860909847297, 'x4': 0.6199938833017271, 'y4': 0.5913066674317418, 'x5': 0.22460777027038298, 'y5': 0.06030027774941796, 'x6': 0.404725935499625, 'y6': 0.11728427154484108, 'x7': 0.43895772404013045, 'y7': 0.7149061696055641, 'x8': 0.7384045607332341, 'y8': 0.8536094938959327, 'x9': 0.7197516752107729, 'y9': 0.9362861553721306, 'x10': 0.4746202164810882, 'y10': 0.002265528309981363, 'x11': 0.3369301419935654, 'y11': 0.002045758007163112, 'x12': 0.9441278782877321, 'y12': 0.8458142023716924, 'x13': 0.5018949257777168, 'y13': 0.47841105085307284, 'x14': 0.41370457373575287, 'y14': 0.8701678410553924, 'x15': 0.9274640588029487, 'y15': 0.5990727394550249, 'x16': 0.8378349911154455, 'y16': 0.9429096240664613, 'x17': 0.2050424485627736, 'y17': 0.0005162799144883407, 'x18': 0.7112216293324064, 'y18': 0.547827884137701, 'x19': 0.46258507552451067, 'y19': 0.06950415339940083}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,277][0m Trial 41 finished with value: 0.039106555463766624 and parameters: {'x0': 0.5234512002489786, 'y0': 0.28583008254461434, 'x1': 0.5495880891438156, 'y1': 0.43173809622985393, 'x2': 0.8275918138866771, 'y2': 0.543252792006999, 'x3': 0.06189071812532623, 'y3': 0.4822802594428802, 'x4': 0.4652183489728974, 'y4': 0.3486088989727164, 'x5': 0.24916896318060577, 'y5': 0.31211804552066147, 'x6': 0.4676262179988299, 'y6': 0.2744264602351171, 'x7': 0.1512765507195196, 'y7': 0.5344072857769001, 'x8': 0.7922098746419288, 'y8': 0.9334434653582085, 'x9': 0.8728780009216132, 'y9': 0.8844632448982428, 'x10': 0.4956295726396645, 'y10': 0.13180299141901547, 'x11': 0.6982748231993847, 'y11': 0.2755363841550988, 'x12': 0.8495295558066878, 'y12': 0.8899477889878548, 'x13': 0.592924641888178, 'y13': 0.654311143849813, 'x14': 0.7120696292674751, 'y14': 0.9688853398660574, 'x15': 0.8877918087858698, 'y15': 0.8864466093419925, 'x16': 0.8621164163370026, 'y16': 0.8728457865428544, 'x17': 0.05231145111038159, 'y17': 0.05873145192001947, 'x18': 0.6405515426326409, 'y18': 0.4397039469845907, 'x19': 0.5438539773690264, 'y19': 0.4264246631150235}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,339][0m Trial 42 finished with value: 0.21589456493770476 and parameters: {'x0': 0.6005636000863994, 'y0': 0.2125085724659865, 'x1': 0.4214244823744752, 'y1': 0.468449287483879, 'x2': 0.7619273800863199, 'y2': 0.8123007918057337, 'x3': 0.06557084957178103, 'y3': 0.6012926839017452, 'x4': 0.5476715092118408, 'y4': 0.32185284584500257, 'x5': 0.2682190256679994, 'y5': 0.4667474213156003, 'x6': 0.3249270086815593, 'y6': 0.25243168329095556, 'x7': 0.21795507130713604, 'y7': 0.5790396727585577, 'x8': 0.5351889096962678, 'y8': 0.7693194813864966, 'x9': 0.9237093852961135, 'y9': 0.8283754311901587, 'x10': 0.41054163282934203, 'y10': 0.21926616081506228, 'x11': 0.6506079972644316, 'y11': 0.08847805707718356, 'x12': 0.7553027201892866, 'y12': 0.9425301242920266, 'x13': 0.4332524336759863, 'y13': 0.7293357782656223, 'x14': 0.5983063532311751, 'y14': 0.9967006883472007, 'x15': 0.8550436556138649, 'y15': 0.6367712518975132, 'x16': 0.7502298332372116, 'y16': 0.7761566696035238, 'x17': 0.07269807255972466, 'y17': 0.06561016058375814, 'x18': 0.8551931628684231, 'y18': 0.6031494760915107, 'x19': 0.7124351824272109, 'y19': 0.3353516352812202}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,405][0m Trial 43 finished with value: 0.019485919847105793 and parameters: {'x0': 0.39919804727522257, 'y0': 0.38466801019539304, 'x1': 0.6595878349816293, 'y1': 0.2606214080637561, 'x2': 0.6844902884250585, 'y2': 0.6868850616654618, 'x3': 0.005611315968607158, 'y3': 0.47741070599693614, 'x4': 0.3690172178591017, 'y4': 0.3991604917418155, 'x5': 0.16910824182496795, 'y5': 0.19073169126148704, 'x6': 0.4241468229077495, 'y6': 0.16644613569029826, 'x7': 0.31139942773945906, 'y7': 0.4872616406304445, 'x8': 0.6406484865730773, 'y8': 0.9176181171453579, 'x9': 0.9969197554515392, 'y9': 0.9608566996019934, 'x10': 0.5350281335332132, 'y10': 0.06579282301732112, 'x11': 0.5905458242837207, 'y11': 0.15543623544418886, 'x12': 0.9094977677644295, 'y12': 0.9406641049106765, 'x13': 0.7029349211377072, 'y13': 0.8652439666969417, 'x14': 0.6134473668770951, 'y14': 0.9601883036524874, 'x15': 0.9303881861536295, 'y15': 0.5614815108619773, 'x16': 0.8892992176643315, 'y16': 0.944641112563162, 'x17': 4.911486554589478e-05, 'y17': 0.06575023786630711, 'x18': 0.7696832298159937, 'y18': 0.31208195654781135, 'x19': 0.35076573081965734, 'y19': 0.27132852841227234}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,471][0m Trial 44 finished with value: 0.10830707301645115 and parameters: {'x0': 0.4057795657341471, 'y0': 0.38320244148337673, 'x1': 0.6485027964281449, 'y1': 0.26159585975414185, 'x2': 0.6805773029608678, 'y2': 0.012835715049718088, 'x3': 0.01800041128852134, 'y3': 0.4201518037523022, 'x4': 0.33179335951457983, 'y4': 0.5275550056274956, 'x5': 0.18081336001248952, 'y5': 0.16219182855450662, 'x6': 0.260492198139787, 'y6': 0.16992535904258604, 'x7': 0.3191773748031653, 'y7': 0.7149653930995675, 'x8': 0.4773389692112656, 'y8': 0.8532427480639766, 'x9': 0.953162271936061, 'y9': 0.96066952077197, 'x10': 0.35141531961453476, 'y10': 0.08996391353510579, 'x11': 0.5882398002644397, 'y11': 0.136383576760974, 'x12': 0.9566075163410263, 'y12': 0.7019892369403831, 'x13': 0.7201463890037328, 'y13': 0.9234827040931273, 'x14': 0.8696421763273139, 'y14': 0.9307165620431744, 'x15': 0.7465222641709832, 'y15': 0.558094863856101, 'x16': 0.9646622264785726, 'y16': 0.9584075404109301, 'x17': 0.004893600388246235, 'y17': 0.14033422859476802, 'x18': 0.9428048631283349, 'y18': 0.28782990372543665, 'x19': 0.2596514638289275, 'y19': 0.2628491526984935}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,532][0m Trial 45 finished with value: 0.38975742086619347 and parameters: {'x0': 0.49031626056384736, 'y0': 0.472740105658512, 'x1': 0.756843557477781, 'y1': 0.003385574505209432, 'x2': 0.5820682516430584, 'y2': 0.7542680217629056, 'x3': 0.16377368536567694, 'y3': 0.5063212254061052, 'x4': 0.38737870015564196, 'y4': 0.40907807337976254, 'x5': 0.06877671189674578, 'y5': 0.31167547705660803, 'x6': 0.5066774986884531, 'y6': 0.10237700755511113, 'x7': 0.37479381841941195, 'y7': 0.3453061992109848, 'x8': 0.629665885650309, 'y8': 0.004459532820069723, 'x9': 0.7573076519186317, 'y9': 0.9195655418052795, 'x10': 0.5409580747339003, 'y10': 0.036980623345601496, 'x11': 0.45340657823808983, 'y11': 0.38425887802216213, 'x12': 0.8168505998655876, 'y12': 0.8072403960765162, 'x13': 0.3320455681468022, 'y13': 0.8618306183542206, 'x14': 0.5106867047535336, 'y14': 0.8784762213545412, 'x15': 0.9301595571765325, 'y15': 0.43128483612158774, 'x16': 0.9968696503974339, 'y16': 0.8624498776077554, 'x17': 0.10992285052114087, 'y17': 0.19101537410342012, 'x18': 0.7644822003907934, 'y18': 0.32221383267018633, 'x19': 0.36961864746292317, 'y19': 0.18745494990278916}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,603][0m Trial 46 finished with value: 0.02079470900601088 and parameters: {'x0': 0.40927557761529504, 'y0': 0.07993809842842614, 'x1': 0.5104354709597796, 'y1': 0.18852524053657238, 'x2': 0.8421615047026876, 'y2': 0.9028693217516303, 'x3': 0.014578212080007936, 'y3': 0.5874840036476836, 'x4': 0.42376809655114067, 'y4': 0.2436035087265215, 'x5': 0.1660924402536699, 'y5': 0.07922862005398741, 'x6': 0.39477389742802943, 'y6': 0.33621164969698203, 'x7': 0.2118714405124626, 'y7': 0.5947757967880752, 'x8': 0.3996031255709397, 'y8': 0.8960785221210994, 'x9': 0.9989167840285024, 'y9': 0.887828096088801, 'x10': 0.4311005925758834, 'y10': 0.1379232442300728, 'x11': 0.39935835206475334, 'y11': 0.2623269601250322, 'x12': 0.8979483444555414, 'y12': 0.9557462384215893, 'x13': 0.5323741252389751, 'y13': 0.6176383770690386, 'x14': 0.6456121369421289, 'y14': 0.8321379265488634, 'x15': 0.8508203957165679, 'y15': 0.9596798379159934, 'x16': 0.9181669781201662, 'y16': 0.7745271087778663, 'x17': 0.14411520078496678, 'y17': 0.4046918925086821, 'x18': 0.830016838864813, 'y18': 0.5002239238023123, 'x19': 0.3470144687614238, 'y19': 0.10521519837062235}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,669][0m Trial 47 finished with value: 0.04402699706179847 and parameters: {'x0': 0.365475302928124, 'y0': 0.097233966353817, 'x1': 0.3108811372200009, 'y1': 0.16761381108874313, 'x2': 0.7023037080477544, 'y2': 0.9365803489299315, 'x3': 0.0008883190975830842, 'y3': 0.36461327541561017, 'x4': 0.4393266406383258, 'y4': 0.4915110641376841, 'x5': 0.07977124855065534, 'y5': 0.08573542470454648, 'x6': 0.42139462903557834, 'y6': 0.33232513767543775, 'x7': 0.2837187380767525, 'y7': 0.49124135409446795, 'x8': 0.41017840175311715, 'y8': 0.8289511220277055, 'x9': 0.9734922778069537, 'y9': 0.883078810743666, 'x10': 0.42411951436504874, 'y10': 0.13479371882781035, 'x11': 0.5191800927967287, 'y11': 0.0497275751831838, 'x12': 0.7250039161360476, 'y12': 0.9445407855832328, 'x13': 0.5304616507308089, 'y13': 0.604721285664835, 'x14': 0.7224135364160585, 'y14': 0.49821430350209395, 'x15': 0.6327357296841011, 'y15': 0.9759545052543696, 'x16': 0.9167858905311365, 'y16': 0.7780846636712758, 'x17': 0.1419404606694888, 'y17': 0.30293650790570414, 'x18': 0.8441305745120836, 'y18': 0.7130453043195125, 'x19': 0.3192214403720337, 'y19': 0.10098807603929785}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,730][0m Trial 48 finished with value: 0.09657850584934946 and parameters: {'x0': 0.41253494339875735, 'y0': 0.06096406098798486, 'x1': 0.5047634001144303, 'y1': 0.08954250812855441, 'x2': 0.847440558173478, 'y2': 0.917731379703238, 'x3': 0.049505489160889274, 'y3': 0.27156305399107955, 'x4': 0.3306640277785219, 'y4': 0.2911084121774382, 'x5': 0.1803847806595466, 'y5': 0.19084656940199984, 'x6': 0.5684063988958201, 'y6': 0.3770043394817735, 'x7': 0.20400307584321492, 'y7': 0.5958246057211842, 'x8': 0.36693316062027415, 'y8': 0.889485712514308, 'x9': 0.8590394818132758, 'y9': 0.9681862177390164, 'x10': 0.8946998721971025, 'y10': 0.2575833743666728, 'x11': 0.233059820020916, 'y11': 0.28223110993162936, 'x12': 0.8884036431887442, 'y12': 0.8605983928648011, 'x13': 0.4886468602475595, 'y13': 0.5093227841875604, 'x14': 0.6394887938476038, 'y14': 0.9424683977626629, 'x15': 0.5307092567340387, 'y15': 0.9285089205063867, 'x16': 0.69749954962618, 'y16': 0.7034224895489407, 'x17': 0.03330137880139488, 'y17': 0.40511957495769196, 'x18': 0.6913612228602728, 'y18': 0.5122696454485786, 'x19': 0.15877467789109645, 'y19': 0.011712863032029841}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,791][0m Trial 49 finished with value: 0.27750580494908433 and parameters: {'x0': 0.2191330125279095, 'y0': 0.16553130658360612, 'x1': 0.5693427660458632, 'y1': 0.23691945904045825, 'x2': 0.7709799032143124, 'y2': 0.694833035704411, 'x3': 0.20214946319653604, 'y3': 0.6633035268434949, 'x4': 0.6223423589247687, 'y4': 0.5667389817852049, 'x5': 0.14853167493586172, 'y5': 0.13056168083685799, 'x6': 0.8278126437069193, 'y6': 0.4398836887129198, 'x7': 0.422726199350259, 'y7': 0.6829214359356063, 'x8': 0.250924972010944, 'y8': 0.7633807925145751, 'x9': 0.9779432935869578, 'y9': 0.8075601272096886, 'x10': 0.6891874972962942, 'y10': 0.05761372539835254, 'x11': 0.38372456443116876, 'y11': 0.16353290324496017, 'x12': 0.9264774817634247, 'y12': 0.6380714337842313, 'x13': 0.5406739012238849, 'y13': 0.4184229276698647, 'x14': 0.7966150478921918, 'y14': 0.7526941406417743, 'x15': 0.8365391034973289, 'y15': 0.8313324816115711, 'x16': 0.7709880277083164, 'y16': 0.759492181263743, 'x17': 0.19364336746231026, 'y17': 0.8269429250685587, 'x18': 0.9427369522258606, 'y18': 0.6296308863890632, 'x19': 0.36453695636930916, 'y19': 0.1408417774482508}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,856][0m Trial 50 finished with value: 0.011758392628092862 and parameters: {'x0': 0.32599472134470175, 'y0': 0.23033500797213374, 'x1': 0.4426712442953823, 'y1': 0.702712539641166, 'x2': 0.6791961528380055, 'y2': 0.7782684764689598, 'x3': 0.3740314791216874, 'y3': 0.1522908131344719, 'x4': 0.5375445085640139, 'y4': 0.6520369419476177, 'x5': 0.21440536598299614, 'y5': 0.0552065236022283, 'x6': 0.2991152218635326, 'y6': 0.18989595991761865, 'x7': 0.509364128979388, 'y7': 0.8118326352669861, 'x8': 0.6883944862348632, 'y8': 0.6465889326339983, 'x9': 0.6509721451772847, 'y9': 0.8960928598273917, 'x10': 0.5714457431620852, 'y10': 0.08511851233123341, 'x11': 0.504512480643033, 'y11': 0.3217118015903448, 'x12': 0.8445232880533027, 'y12': 0.797045414307195, 'x13': 0.707382444326166, 'y13': 0.5771119686456749, 'x14': 0.9295131084904613, 'y14': 0.999458491205769, 'x15': 0.7714078854268582, 'y15': 0.7440701982396507, 'x16': 0.9220176090280097, 'y16': 0.4758300004189416, 'x17': 0.5601802465824938, 'y17': 0.5215143137576654, 'x18': 0.8228773129373692, 'y18': 0.48742999622638616, 'x19': 0.5523790187933099, 'y19': 0.1994551381164738}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,918][0m Trial 51 finished with value: 0.04023072031041974 and parameters: {'x0': 0.32741828469967704, 'y0': 0.22183869467273207, 'x1': 0.4324315427484251, 'y1': 0.7768834807723891, 'x2': 0.7175799098936531, 'y2': 0.7854391836601504, 'x3': 0.5642967823389761, 'y3': 0.14354250016160658, 'x4': 0.4634864248035918, 'y4': 0.6581009657073376, 'x5': 0.24106429333253426, 'y5': 0.07117707114394786, 'x6': 0.30161648818266545, 'y6': 0.16853668117440518, 'x7': 0.5168687984736353, 'y7': 0.7549801826095128, 'x8': 0.6933302489987608, 'y8': 0.6222890438055099, 'x9': 0.6659261546039384, 'y9': 0.8949393279268083, 'x10': 0.6013410884092701, 'y10': 0.11289088115157803, 'x11': 0.40866510192987565, 'y11': 0.31392685461653513, 'x12': 0.8306788848711847, 'y12': 0.7982177659279486, 'x13': 0.6947804754712215, 'y13': 0.32690423945123426, 'x14': 0.9133882799389339, 'y14': 0.9485238507312582, 'x15': 0.7810392305185153, 'y15': 0.7364136161409227, 'x16': 0.9052952354273207, 'y16': 0.5114742490718112, 'x17': 0.7309047072997649, 'y17': 0.6402961754849891, 'x18': 0.8184150148937898, 'y18': 0.5051374023541235, 'x19': 0.47003946108258876, 'y19': 0.2059311954346611}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:24,979][0m Trial 52 finished with value: 0.11183602021094108 and parameters: {'x0': 0.29907633270849704, 'y0': 0.04838485751010834, 'x1': 0.5031665245855684, 'y1': 0.6835566080647224, 'x2': 0.4889661271800773, 'y2': 0.7390966556370777, 'x3': 0.3583924027151185, 'y3': 0.5880647686196798, 'x4': 0.525591146393053, 'y4': 0.7903623525751293, 'x5': 0.20715156824360798, 'y5': 0.12246208741994669, 'x6': 0.23222432445631608, 'y6': 0.21916948010986986, 'x7': 0.705227505066867, 'y7': 0.8554504331265173, 'x8': 0.5709168980186904, 'y8': 0.9589723725929986, 'x9': 0.9963722321058476, 'y9': 0.9631952713496713, 'x10': 0.4444062277977351, 'y10': 0.08872884822645213, 'x11': 0.49799797840858473, 'y11': 0.26734367215858723, 'x12': 0.7900280102106726, 'y12': 0.8859497883230742, 'x13': 0.06049916040817749, 'y13': 0.5787331254042741, 'x14': 0.9661015932158041, 'y14': 0.9966011198525705, 'x15': 0.9287323371755268, 'y15': 0.47746606671692177, 'x16': 0.8210172664541819, 'y16': 0.37816898941792365, 'x17': 0.5719401893304894, 'y17': 0.51546981643742, 'x18': 0.7320273502944299, 'y18': 0.4611940516103817, 'x19': 0.547767364368474, 'y19': 0.09651766587258592}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,040][0m Trial 53 finished with value: 0.08440871398658656 and parameters: {'x0': 0.11431905667897457, 'y0': 0.17385734200005684, 'x1': 0.4116391020407413, 'y1': 0.5139664765337144, 'x2': 0.6151042069114182, 'y2': 0.9971314320198409, 'x3': 0.04375967194702174, 'y3': 0.16299930138935342, 'x4': 0.4354609441401591, 'y4': 0.39175574762454923, 'x5': 0.09934351567062255, 'y5': 0.19253005300274917, 'x6': 0.39304227974022815, 'y6': 0.8407033047941345, 'x7': 0.5720698303252925, 'y7': 0.46377521250815573, 'x8': 0.7449714761229743, 'y8': 0.8862106815749724, 'x9': 0.8895853375330092, 'y9': 0.9030133228632738, 'x10': 0.5550928501306526, 'y10': 0.15036481638259508, 'x11': 0.5903304565970776, 'y11': 0.13890606608654776, 'x12': 0.8928257565071706, 'y12': 0.9437764576686944, 'x13': 0.7371356315408877, 'y13': 0.6357469573028066, 'x14': 0.42601726373196885, 'y14': 0.8527222878767383, 'x15': 0.787354126490897, 'y15': 0.8007352807698739, 'x16': 0.9526530467572252, 'y16': 0.4678764863139027, 'x17': 0.09400316099296961, 'y17': 0.5253458886108122, 'x18': 0.9038450940307372, 'y18': 0.5598412280045836, 'x19': 0.32346770529132146, 'y19': 0.24610247016501385}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,107][0m Trial 54 finished with value: 0.06746407051291736 and parameters: {'x0': 0.4820393235432027, 'y0': 0.9627730684041991, 'x1': 0.33994706884727316, 'y1': 0.6258669096200784, 'x2': 0.550877434132548, 'y2': 0.6614213932362262, 'x3': 0.3937484915177627, 'y3': 0.3049984507792757, 'x4': 0.38175048570572623, 'y4': 0.25871657946539617, 'x5': 0.03617732807267174, 'y5': 0.05148317061568236, 'x6': 0.4276226716860437, 'y6': 0.404618420558001, 'x7': 0.234448014185604, 'y7': 0.40186596007845027, 'x8': 0.6520910272867019, 'y8': 0.6703979641535742, 'x9': 0.9326301505254267, 'y9': 0.9985589845504033, 'x10': 0.6460541939595974, 'y10': 0.0380337760444002, 'x11': 0.2572559572561465, 'y11': 0.3588915579609817, 'x12': 0.7074944647557135, 'y12': 0.4587512648164368, 'x13': 0.5759559984553413, 'y13': 0.46638218993966996, 'x14': 0.6545399908704412, 'y14': 0.8970662205899141, 'x15': 0.856898456291206, 'y15': 0.9205406864379977, 'x16': 0.5240188675735372, 'y16': 0.37639019458836487, 'x17': 0.5659899498244592, 'y17': 0.6717092544256014, 'x18': 0.7729719028991991, 'y18': 0.6062328974344738, 'x19': 0.5994786927916071, 'y19': 0.16718766582962688}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,170][0m Trial 55 finished with value: 0.2308895131368468 and parameters: {'x0': 0.38731919377305335, 'y0': 0.03157551122003503, 'x1': 0.664279663813123, 'y1': 0.8586951050312701, 'x2': 0.6719602778790295, 'y2': 0.7812652990749909, 'x3': 0.29084045606438663, 'y3': 0.4428200790931275, 'x4': 0.284994197884089, 'y4': 0.4490701841412204, 'x5': 0.34560170948042784, 'y5': 0.30123137930378363, 'x6': 0.5148301028684845, 'y6': 0.5044592450667846, 'x7': 0.3378570590043335, 'y7': 0.5785267731037971, 'x8': 0.8323351411780363, 'y8': 0.5485025688545657, 'x9': 0.7551087832776453, 'y9': 0.9535956262621432, 'x10': 0.5096842899195653, 'y10': 0.10799747722230046, 'x11': 0.5255122282486406, 'y11': 0.08386487275813603, 'x12': 0.8429999927741725, 'y12': 0.5868995080751234, 'x13': 0.6950222437198943, 'y13': 0.4994548164858399, 'x14': 0.5226265843752215, 'y14': 0.8023048098952474, 'x15': 0.727209999178271, 'y15': 0.735807410134138, 'x16': 0.9299284847550453, 'y16': 0.5416612946949102, 'x17': 0.43231802387625323, 'y17': 0.46220026554854016, 'x18': 0.8531576163459981, 'y18': 0.33419861870547346, 'x19': 0.27738817155991036, 'y19': 0.3426763221885239}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,236][0m Trial 56 finished with value: 0.13341745279130618 and parameters: {'x0': 0.32943932462985087, 'y0': 0.23572755194338182, 'x1': 0.23640993230418808, 'y1': 0.962753665439661, 'x2': 0.8190257282104162, 'y2': 0.8335238273307827, 'x3': 0.21194494439712383, 'y3': 0.5145895456221738, 'x4': 0.4735342330514003, 'y4': 0.14579224232562704, 'x5': 0.4339507546398267, 'y5': 0.15488984705084335, 'x6': 0.37127197352128033, 'y6': 0.14529086604651148, 'x7': 0.4569515412342089, 'y7': 0.6684908500867737, 'x8': 0.67582158789285, 'y8': 0.7400241463274606, 'x9': 0.8205095291598027, 'y9': 0.8665730115864386, 'x10': 0.6118336186363565, 'y10': 0.0025973605383699805, 'x11': 0.35072348416165744, 'y11': 0.029486093158560434, 'x12': 0.7519219007132008, 'y12': 0.8346776036476218, 'x13': 0.6201746267308971, 'y13': 0.6303783527363237, 'x14': 0.6097917411254857, 'y14': 0.9983875181369264, 'x15': 0.928306180034562, 'y15': 0.9795224289583898, 'x16': 0.9755448799109082, 'y16': 0.6544399988100421, 'x17': 0.6454795556410726, 'y17': 0.40924958720787774, 'x18': 0.6765044357416593, 'y18': 0.757990939647589, 'x19': 0.3659112071741139, 'y19': 0.22013172487046886}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,302][0m Trial 57 finished with value: 0.3508472187863114 and parameters: {'x0': 0.25769289137805146, 'y0': 0.28515038813809523, 'x1': 0.5055617023536167, 'y1': 0.1860269302457872, 'x2': 0.9316112813280345, 'y2': 0.8866986161621677, 'x3': 0.15124385842355276, 'y3': 0.38786084749728206, 'x4': 0.6031840919598321, 'y4': 0.9451660055179356, 'x5': 0.1652822886661506, 'y5': 0.35298885158848586, 'x6': 0.28227460180508834, 'y6': 0.33601904147971245, 'x7': 0.5860595981124623, 'y7': 0.7941160741357212, 'x8': 0.622046541415662, 'y8': 0.44087685561592044, 'x9': 0.8771504025083477, 'y9': 0.9244213387303987, 'x10': 0.4764665309227792, 'y10': 0.2253436888701221, 'x11': 0.4701204289147437, 'y11': 0.2508644269451634, 'x12': 0.6117861411878044, 'y12': 0.7142990637899155, 'x13': 0.3955893375441115, 'y13': 0.9190314294605311, 'x14': 0.6995571251154382, 'y14': 0.9288875631745385, 'x15': 0.81153691729831, 'y15': 0.5311636656209862, 'x16': 0.4553439112739711, 'y16': 0.9000278722461222, 'x17': 0.02624990555067184, 'y17': 0.7621235838131752, 'x18': 0.8038596396909595, 'y18': 0.07173055604917039, 'x19': 0.22233982607361236, 'y19': 0.4137490214850128}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,376][0m Trial 58 finished with value: 0.4103035690712338 and parameters: {'x0': 0.45140572409385893, 'y0': 0.11884261090192977, 'x1': 0.4476842384339367, 'y1': 0.40306638126911587, 'x2': 0.7758960901516323, 'y2': 0.945237830009489, 'x3': 0.07623548623714144, 'y3': 0.666616050469059, 'x4': 0.42093750204606606, 'y4': 0.7122773196713991, 'x5': 0.2201517788449136, 'y5': 0.037707641598120054, 'x6': 0.4869790607110373, 'y6': 0.19940215162748715, 'x7': 0.3792344610296346, 'y7': 0.9151364208532429, 'x8': 0.5389387538729165, 'y8': 0.9486084491354939, 'x9': 0.6592738369527557, 'y9': 0.8093470486189415, 'x10': 0.5768248657009494, 'y10': 0.05383231821987806, 'x11': 0.6314650320036701, 'y11': 0.4201864391584416, 'x12': 0.9249254036446046, 'y12': 0.7877122672405791, 'x13': 0.5588257406726489, 'y13': 0.7471012829077592, 'x14': 0.3182266859012027, 'y14': 0.86259154655722, 'x15': 0.9404773868888924, 'y15': 0.5828200357065724, 'x16': 0.89288818826936, 'y16': 0.8405155856540741, 'x17': 0.726750792170602, 'y17': 0.22114562725940498, 'x18': 0.9812611935739576, 'y18': 0.6611172405397385, 'x19': 0.5195188781258866, 'y19': 0.11609711434327345}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,440][0m Trial 59 finished with value: 0.28350483707637336 and parameters: {'x0': 0.6533341402991526, 'y0': 0.41566341675168866, 'x1': 0.3876716799512949, 'y1': 0.1069639003708703, 'x2': 0.8731953539131609, 'y2': 0.525313810033779, 'x3': 0.4773899948674468, 'y3': 0.27171928355863445, 'x4': 0.7147018193959649, 'y4': 0.3888098648687916, 'x5': 0.26207774968453823, 'y5': 0.10010260267092075, 'x6': 0.31660061761352787, 'y6': 0.2995399032924913, 'x7': 0.5050832867563029, 'y7': 0.5419286025863441, 'x8': 0.34490502549853275, 'y8': 0.7966804847625995, 'x9': 0.9495179734868948, 'y9': 0.4191251490197454, 'x10': 0.6857643098966169, 'y10': 0.1480007726947229, 'x11': 0.5587465156258855, 'y11': 0.17753982186227807, 'x12': 0.9532616131621234, 'y12': 0.9502263220753921, 'x13': 0.45517403973538345, 'y13': 0.8353166717982433, 'x14': 0.7371427132491376, 'y14': 0.9607478866279975, 'x15': 0.8663342824964531, 'y15': 0.3797976407240646, 'x16': 0.7177012014678914, 'y16': 0.6893215276335067, 'x17': 0.09659890164458389, 'y17': 0.2896776731426477, 'x18': 0.7389550056361864, 'y18': 0.23940845507183933, 'x19': 0.42931049748284583, 'y19': 0.1785789241480411}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,504][0m Trial 60 finished with value: 0.3145558592635692 and parameters: {'x0': 0.9868788484403823, 'y0': 0.1987436887916499, 'x1': 0.5990265739648479, 'y1': 0.7009018902912667, 'x2': 0.5985214562181606, 'y2': 0.7097410189666035, 'x3': 0.0005077001421321167, 'y3': 0.03317045785278455, 'x4': 0.537134926119002, 'y4': 0.3123160986336786, 'x5': 0.11664229611529212, 'y5': 0.20862294411760562, 'x6': 0.4344002506792955, 'y6': 0.25050294207403917, 'x7': 0.08407684674807613, 'y7': 0.333324799460665, 'x8': 0.48055660963666763, 'y8': 0.8942511052726189, 'x9': 0.7543876635549016, 'y9': 0.964775559864696, 'x10': 0.42865764112083227, 'y10': 0.9333811347601677, 'x11': 0.42706223016526607, 'y11': 0.10294250016751891, 'x12': 0.8278398340455461, 'y12': 0.8676119736140123, 'x13': 0.8360538912791293, 'y13': 0.546160368252185, 'x14': 0.6699163006713403, 'y14': 0.895052769737406, 'x15': 0.4339221432784605, 'y15': 0.8645879875345562, 'x16': 0.805368288697808, 'y16': 0.30842941831593856, 'x17': 0.5453380119220719, 'y17': 0.6002025991659499, 'x18': 0.8802201315632727, 'y18': 0.5176241798717242, 'x19': 0.6346623573509713, 'y19': 0.2628294621230855}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,566][0m Trial 61 finished with value: 0.11969628602868476 and parameters: {'x0': 0.500775727344277, 'y0': 0.3527148323271666, 'x1': 0.5481623710109735, 'y1': 0.24925249482530887, 'x2': 0.795494994290724, 'y2': 0.8507676131031817, 'x3': 0.11983833858245892, 'y3': 0.5892284486694304, 'x4': 0.950258046699584, 'y4': 0.21765023740271214, 'x5': 0.3617434459660974, 'y5': 0.021340232374439244, 'x6': 0.34071926112776785, 'y6': 0.06925047652991745, 'x7': 0.15782813799295575, 'y7': 0.7529511184925552, 'x8': 0.8334235792822897, 'y8': 0.9590139899753065, 'x9': 0.8542313763100926, 'y9': 0.8887764893015716, 'x10': 0.37255185258243106, 'y10': 0.15801191032042466, 'x11': 0.5961076899971707, 'y11': 0.1881572782145097, 'x12': 0.9803555415839951, 'y12': 0.9993379646442313, 'x13': 0.6384536260489905, 'y13': 0.6791135587371734, 'x14': 0.5884954705414774, 'y14': 0.8091279090537518, 'x15': 0.9491745376197891, 'y15': 0.7073940282434389, 'x16': 0.861083373418011, 'y16': 0.9629010690044303, 'x17': 0.26728183791817517, 'y17': 0.04979558857926176, 'x18': 0.5491646659381781, 'y18': 0.34893058903261187, 'x19': 0.6428150686312004, 'y19': 0.28586870176339046}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,639][0m Trial 62 finished with value: 0.30676433215653387 and parameters: {'x0': 0.5933871096457529, 'y0': 0.28219040906782034, 'x1': 0.6633163758375965, 'y1': 0.27876800949000574, 'x2': 0.8346268870586344, 'y2': 0.8850325513710113, 'x3': 0.03452568686260232, 'y3': 0.5328664295907172, 'x4': 0.3491209226569937, 'y4': 0.14274391122087215, 'x5': 0.3021976194051304, 'y5': 0.00011762765788367324, 'x6': 0.379706563265279, 'y6': 0.9915209595154861, 'x7': 0.26145596607964877, 'y7': 0.8394077339370181, 'x8': 0.7080683951200256, 'y8': 0.8300464615136154, 'x9': 0.7995334973362611, 'y9': 0.5921270417922164, 'x10': 0.3419719823460133, 'y10': 0.3155156687123313, 'x11': 0.7967870247831106, 'y11': 0.32632999344162045, 'x12': 0.8910722673361295, 'y12': 0.9197731686513448, 'x13': 0.6250836309020391, 'y13': 0.6664410843599883, 'x14': 0.5052662085303532, 'y14': 0.8215802074450949, 'x15': 0.9056172375447803, 'y15': 0.7613810084347807, 'x16': 0.8462288663734071, 'y16': 0.8885150455190586, 'x17': 0.4728678661062678, 'y17': 0.099759275225248, 'x18': 0.8236140306329283, 'y18': 0.4335766414393486, 'x19': 0.5614241260121294, 'y19': 0.495062992234644}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,709][0m Trial 63 finished with value: 0.11825550098962301 and parameters: {'x0': 0.42976834696929644, 'y0': 0.3967172239136923, 'x1': 0.47139558577535773, 'y1': 0.35840465926608156, 'x2': 0.7375554517891196, 'y2': 0.7796080188124037, 'x3': 0.13842297600352135, 'y3': 0.47066759898878485, 'x4': 0.1902178987981259, 'y4': 0.319154855637924, 'x5': 0.4041225810195399, 'y5': 0.09879669620959794, 'x6': 0.23766727141861643, 'y6': 0.0928959457349247, 'x7': 0.2963308006583236, 'y7': 0.6184263797515512, 'x8': 0.9293496070963321, 'y8': 0.9018137904982718, 'x9': 0.6138203813420551, 'y9': 0.7300734620935271, 'x10': 0.39430491531035333, 'y10': 0.08590625777394861, 'x11': 0.7075785272611204, 'y11': 0.19505738526928285, 'x12': 0.9723659877909085, 'y12': 0.9681805440496877, 'x13': 0.6753334162269528, 'y13': 0.7752253453886748, 'x14': 0.622596962551087, 'y14': 0.8439316358576956, 'x15': 0.8474776393573464, 'y15': 0.679565973271048, 'x16': 0.9293635489579, 'y16': 0.9470116612184559, 'x17': 0.12887790050755335, 'y17': 0.044434701112949726, 'x18': 0.48631169335224717, 'y18': 0.48142547279454434, 'x19': 0.4845957160455765, 'y19': 0.3475407060260913}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,776][0m Trial 64 finished with value: 0.28071134004821635 and parameters: {'x0': 0.5256463287616207, 'y0': 0.46221645318411597, 'x1': 0.5882647155774748, 'y1': 0.39512228179850567, 'x2': 0.6456602206221589, 'y2': 0.823616280820265, 'x3': 0.22775396631262312, 'y3': 0.6177186890198962, 'x4': 0.6537271234798284, 'y4': 0.23917157138789544, 'x5': 0.1983791496167884, 'y5': 0.1355232085561121, 'x6': 0.4389116636768883, 'y6': 0.17399115902053522, 'x7': 0.13439212766305128, 'y7': 0.9328166372935983, 'x8': 0.5933742261125815, 'y8': 0.8485861291934566, 'x9': 0.6986738510550309, 'y9': 0.8034281457837894, 'x10': 0.5159106956305666, 'y10': 0.17891905680497425, 'x11': 0.5151002753883093, 'y11': 0.14476426650335508, 'x12': 0.4748366553317274, 'y12': 0.8261103177019389, 'x13': 0.5021975903925522, 'y13': 0.5890555846588457, 'x14': 0.7874038538174478, 'y14': 0.9550110397368957, 'x15': 0.9021911719090171, 'y15': 0.8028284480646928, 'x16': 0.8845187734973923, 'y16': 0.8281002512583191, 'x17': 0.27873718026756217, 'y17': 0.14237147299511566, 'x18': 0.938860349385528, 'y18': 0.5965674882644709, 'x19': 0.5983136314986344, 'y19': 0.4045455248789887}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,844][0m Trial 65 finished with value: 0.10751438293604143 and parameters: {'x0': 0.3714413717887032, 'y0': 0.3444876805309339, 'x1': 0.7303836627005498, 'y1': 0.48035322140326486, 'x2': 0.2003643457668266, 'y2': 0.6695639566514562, 'x3': 0.09571922131014905, 'y3': 0.5704718690524175, 'x4': 0.4794164714115398, 'y4': 0.2749936808668756, 'x5': 0.15413501396096405, 'y5': 0.2839323688400254, 'x6': 0.12140992958290725, 'y6': 0.03770280154543211, 'x7': 0.18340978059610857, 'y7': 0.6764712349804272, 'x8': 0.7500909341922718, 'y8': 0.9897247555608, 'x9': 0.998107958990959, 'y9': 0.9292487735202253, 'x10': 0.5545626290352359, 'y10': 0.11245249203291992, 'x11': 0.3699210706020438, 'y11': 0.24105366399764006, 'x12': 0.8619745695460822, 'y12': 0.9989406684746563, 'x13': 0.7467783765322041, 'y13': 0.6867365891649115, 'x14': 0.19928062248913053, 'y14': 0.9009012527143074, 'x15': 0.7955733279606823, 'y15': 0.5045626489451813, 'x16': 0.9718934436081937, 'y16': 0.9806548511199522, 'x17': 0.00026248765123020534, 'y17': 0.034573961756149386, 'x18': 0.3770186463512222, 'y18': 0.41607648037816614, 'x19': 0.7194299149743434, 'y19': 0.27785907086169476}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,908][0m Trial 66 finished with value: 0.39073072226267286 and parameters: {'x0': 0.6221494345238561, 'y0': 0.3104430527018121, 'x1': 0.6237727372857527, 'y1': 0.5485209810975902, 'x2': 0.6952039505489589, 'y2': 0.7459478996711537, 'x3': 0.16709203294126856, 'y3': 0.4841492879103386, 'x4': 0.3755882196411488, 'y4': 0.3722404631374241, 'x5': 0.3147541871412298, 'y5': 0.04778278258413638, 'x6': 0.35999886306264023, 'y6': 0.12622802573077357, 'x7': 0.04955392679846838, 'y7': 0.4337258453186307, 'x8': 0.2982920068823779, 'y8': 0.9324208725882417, 'x9': 0.9449278233898515, 'y9': 0.8643271033284023, 'x10': 0.4659346706503225, 'y10': 0.03533168992431365, 'x11': 0.45968491147995155, 'y11': 0.21509521124143904, 'x12': 0.995797653144948, 'y12': 0.11268369491014929, 'x13': 0.8090386488248987, 'y13': 0.45140636352234903, 'x14': 0.5780503253247848, 'y14': 0.5534945629120729, 'x15': 0.7478350365963882, 'y15': 0.7059772584144355, 'x16': 0.8322325676501625, 'y16': 0.9186501895973542, 'x17': 0.0781402005738348, 'y17': 0.3339724578216028, 'x18': 0.7799638322346565, 'y18': 0.5746459444688565, 'x19': 0.7467294473567736, 'y19': 0.14952177146092663}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:25,977][0m Trial 67 finished with value: 0.15721799217691007 and parameters: {'x0': 0.4694308757336722, 'y0': 0.16939109278420716, 'x1': 0.518192334523199, 'y1': 0.34059624449497483, 'x2': 0.7987478466301512, 'y2': 0.8581701756149, 'x3': 0.3220108024022713, 'y3': 0.7892670808953896, 'x4': 0.9908742152982307, 'y4': 0.239031073158677, 'x5': 0.2712389505807697, 'y5': 0.07414855304602212, 'x6': 0.5818076410828522, 'y6': 0.20427068373440713, 'x7': 0.08651241958222788, 'y7': 0.5092344586550468, 'x8': 0.8175590209764445, 'y8': 0.8693741719310168, 'x9': 0.8706049599084099, 'y9': 0.6624520843089882, 'x10': 0.5300286174552882, 'y10': 0.45968510980536487, 'x11': 0.30212262299442777, 'y11': 0.0758369691005727, 'x12': 0.7746439014413771, 'y12': 0.889491407110511, 'x13': 0.7647525705574327, 'y13': 0.5605255816558418, 'x14': 0.6863896681241185, 'y14': 0.9710992662870558, 'x15': 0.9620703773994105, 'y15': 0.8904128000145853, 'x16': 0.999246383752797, 'y16': 0.8526785829618528, 'x17': 0.19459927999729348, 'y17': 0.5446919526625768, 'x18': 0.6481565762014764, 'y18': 0.4624096263357935, 'x19': 0.5161742950642006, 'y19': 0.23652763115775183}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,047][0m Trial 68 finished with value: 0.3062111317508078 and parameters: {'x0': 0.5402790458391739, 'y0': 0.09810835463043618, 'x1': 0.4770826360847813, 'y1': 0.21128259244773043, 'x2': 0.8913814927809636, 'y2': 0.41744890994264916, 'x3': 0.2685176990996747, 'y3': 0.6759261121384517, 'x4': 0.2963309328829806, 'y4': 0.32850814316825355, 'x5': 0.5538456846976342, 'y5': 0.15775816333810286, 'x6': 0.4787306888401205, 'y6': 0.24054733136332707, 'x7': 0.8795950852962096, 'y7': 0.6053336368477533, 'x8': 0.762981960526269, 'y8': 0.9579069287572456, 'x9': 0.8189982940641111, 'y9': 0.9756021213802318, 'x10': 0.43812558241893673, 'y10': 0.22047653319238733, 'x11': 0.6389213257613886, 'y11': 0.12185056037579436, 'x12': 0.9164492876257422, 'y12': 0.7312826844315308, 'x13': 0.6425831096555313, 'y13': 0.6194480530412716, 'x14': 0.45042168534195764, 'y14': 0.7402520480040282, 'x15': 0.9958377957841333, 'y15': 0.6278638704050192, 'x16': 0.9366758453185946, 'y16': 0.6036828273612533, 'x17': 0.03355663526058822, 'y17': 0.48427899299977567, 'x18': 0.7057698438720926, 'y18': 0.5205862061346426, 'x19': 0.6657513094670748, 'y19': 0.06654079846338809}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,111][0m Trial 69 finished with value: 0.32265694448158044 and parameters: {'x0': 0.5727100713449415, 'y0': 0.4325392648522454, 'x1': 0.5602767831525358, 'y1': 0.1543783943042602, 'x2': 0.9482287946069059, 'y2': 0.605002020391707, 'x3': 0.032650580018123314, 'y3': 0.44590211187214046, 'x4': 0.1461011494737095, 'y4': 0.4598520542557084, 'x5': 0.047670585670033794, 'y5': 0.47190637095408167, 'x6': 0.5353898453027213, 'y6': 0.152797850420965, 'x7': 0.2326823652215091, 'y7': 0.561801681011656, 'x8': 0.8593858445470447, 'y8': 0.9958409508036536, 'x9': 0.4408294068267686, 'y9': 0.8428420667448518, 'x10': 0.6313610067488522, 'y10': 0.2743099347458755, 'x11': 0.5713476969199182, 'y11': 0.027714780487871113, 'x12': 0.7020987026804999, 'y12': 0.9688513768219913, 'x13': 0.35424454154974755, 'y13': 0.747846502543829, 'x14': 0.824584532971672, 'y14': 0.7776338117493637, 'x15': 0.7178520973579914, 'y15': 0.5697144958262167, 'x16': 0.8845633156574421, 'y16': 0.92918990460979, 'x17': 0.1619585690407892, 'y17': 0.07914996368664971, 'x18': 0.7479163908486428, 'y18': 0.36915206599865724, 'x19': 0.8603190189829824, 'y19': 0.3216912502628533}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,181][0m Trial 70 finished with value: 0.13065007962036995 and parameters: {'x0': 0.22363110915296025, 'y0': 0.5837646418285485, 'x1': 0.05091380682220997, 'y1': 0.29440850835393173, 'x2': 0.850659884408307, 'y2': 0.3000109613576612, 'x3': 0.08067493306745804, 'y3': 0.09171104150565701, 'x4': 0.5527979610914787, 'y4': 0.5094805906640645, 'x5': 0.22161737373300938, 'y5': 0.6098153323371058, 'x6': 0.4079511165794088, 'y6': 0.268335214009621, 'x7': 0.31391541414051205, 'y7': 0.04651951511204678, 'x8': 0.8801298732089444, 'y8': 0.7863663338590606, 'x9': 0.9223624187867226, 'y9': 0.5518777293461818, 'x10': 0.38026878980472506, 'y10': 0.06311507409618848, 'x11': 0.80044003176995, 'y11': 0.2886306522823254, 'x12': 0.7968893096574751, 'y12': 0.9203283184937902, 'x13': 0.5539288978529014, 'y13': 0.16648057788792714, 'x14': 0.5264931456321166, 'y14': 0.9242581070394226, 'x15': 0.6570485581457981, 'y15': 0.9526948559241207, 'x16': 0.781160199162513, 'y16': 0.9723019778077464, 'x17': 0.2168721376786137, 'y17': 0.1230792293474553, 'x18': 0.5663757845075713, 'y18': 0.6979118732924416, 'x19': 0.3918166830008183, 'y19': 0.3616900251785619}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,248][0m Trial 71 finished with value: 0.008151912208648304 and parameters: {'x0': 0.5096070633223229, 'y0': 0.30897992020459547, 'x1': 0.5658752718462577, 'y1': 0.442231846663611, 'x2': 0.9143624431947482, 'y2': 0.6528794034469594, 'x3': 0.1013127614945207, 'y3': 0.4096416197225818, 'x4': 0.5878182870102489, 'y4': 0.3531793290590801, 'x5': 0.2976937325901601, 'y5': 0.10659371864648491, 'x6': 0.4496228614977504, 'y6': 0.27895835962305504, 'x7': 0.17544160853851706, 'y7': 0.5207709096670503, 'x8': 0.7802461266970695, 'y8': 0.9184187980249784, 'x9': 0.8977324080770973, 'y9': 0.9027511921548409, 'x10': 0.4844625820978977, 'y10': 0.18672609224093545, 'x11': 0.677375221070219, 'y11': 0.23506674435674121, 'x12': 0.8525623605341281, 'y12': 0.8851848945526706, 'x13': 0.5881859968315178, 'y13': 0.7005210070539971, 'x14': 0.5577243533715582, 'y14': 0.9774368189688051, 'x15': 0.8836616781772838, 'y15': 0.6458302399628774, 'x16': 0.872301794730471, 'y16': 0.894611766229322, 'x17': 0.02953849353635821, 'y17': 0.08279869198689827, 'x18': 0.5937813978113953, 'y18': 0.4252017648592923, 'x19': 0.6968923420558211, 'y19': 0.390714482590352}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,316][0m Trial 72 finished with value: 0.1149335512939591 and parameters: {'x0': 0.5122850032445406, 'y0': 0.29970143761866086, 'x1': 0.6807097787742526, 'y1': 0.41965576046814096, 'x2': 0.9272085549489395, 'y2': 0.6470316546714843, 'x3': 0.12712142372794571, 'y3': 0.3356352396373423, 'x4': 0.6135620565918427, 'y4': 0.4200521317243826, 'x5': 0.33052145851410375, 'y5': 0.09297892768717064, 'x6': 0.44797178218847994, 'y6': 0.2226075084665606, 'x7': 0.1309293297095941, 'y7': 0.6562995878220981, 'x8': 0.6625041455697048, 'y8': 0.9175379145764508, 'x9': 0.5181535565028333, 'y9': 0.9414388322982079, 'x10': 0.4855535802273482, 'y10': 0.17782067327750153, 'x11': 0.6886851380283293, 'y11': 0.16569902096183803, 'x12': 0.8671113854517492, 'y12': 0.8696262925488069, 'x13': 0.7063875816707124, 'y13': 0.9645112956120081, 'x14': 0.6053583252249978, 'y14': 0.9670984322324361, 'x15': 0.8765611267656072, 'y15': 0.6591167809451127, 'x16': 0.9127615549429314, 'y16': 0.8898404746511315, 'x17': 0.03465118635198727, 'y17': 0.031787526272643404, 'x18': 0.4843266780871681, 'y18': 0.28975029995749163, 'x19': 0.7776099542545382, 'y19': 0.4471639708751643}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,381][0m Trial 73 finished with value: 0.26079335800833575 and parameters: {'x0': 0.4270717022820564, 'y0': 0.2331841370992987, 'x1': 0.6280117496622305, 'y1': 0.49328328660974524, 'x2': 0.3179429347323022, 'y2': 0.6979105275417398, 'x3': 0.0947644374846244, 'y3': 0.4122980897872429, 'x4': 0.24396570342416107, 'y4': 0.29648424515701793, 'x5': 0.41890450161045395, 'y5': 0.02581116123742057, 'x6': 0.3415941459054384, 'y6': 0.28899432906114253, 'x7': 0.2053442038054415, 'y7': 0.4802837205795899, 'x8': 0.7197003845736336, 'y8': 0.9055172780054096, 'x9': 0.89645560489732, 'y9': 0.9136996930887455, 'x10': 0.5714147909132434, 'y10': 0.12237001265715658, 'x11': 0.6128562745041728, 'y11': 0.2100182853416307, 'x12': 0.9320131921595838, 'y12': 0.8996763019909395, 'x13': 0.6164747640527646, 'y13': 0.6916005942589801, 'x14': 0.6727647760691216, 'y14': 0.9991021978299761, 'x15': 0.8316108145875053, 'y15': 0.5935013408763714, 'x16': 0.966017647344387, 'y16': 0.7933444429850199, 'x17': 0.1173964636234853, 'y17': 0.9848190368972987, 'x18': 0.38316705154707337, 'y18': 0.48600408893626784, 'x19': 0.6242693567468178, 'y19': 0.3835803521474538}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,446][0m Trial 74 finished with value: 0.42152540560227825 and parameters: {'x0': 0.4652918791812271, 'y0': 0.3512700115403337, 'x1': 0.5334535585305276, 'y1': 0.5868608082066649, 'x2': 0.45457990502847934, 'y2': 0.7987278773436802, 'x3': 0.03625902723728518, 'y3': 0.540104297391349, 'x4': 0.5690130725732657, 'y4': 0.37161625139697063, 'x5': 0.00040595708796575813, 'y5': 0.218511681088298, 'x6': 0.6543037596844407, 'y6': 0.34828354303707865, 'x7': 0.19035696196495883, 'y7': 0.5279463017684498, 'x8': 0.1385079755357616, 'y8': 0.8317858702365339, 'x9': 0.9637462769364156, 'y9': 0.99102603738612, 'x10': 0.4969418449857289, 'y10': 0.07992732701980314, 'x11': 0.7235776711433998, 'y11': 0.2582801792183474, 'x12': 0.895121027348765, 'y12': 0.7638274760796863, 'x13': 0.583882533745294, 'y13': 0.6516769210761814, 'x14': 0.5845271858437088, 'y14': 0.8940402432159762, 'x15': 0.9063377767145872, 'y15': 0.5131843693294998, 'x16': 0.6661040006856487, 'y16': 0.45689435713824683, 'x17': 0.07012253650335522, 'y17': 0.17278679624243348, 'x18': 0.8431926754445817, 'y18': 0.25703795357605497, 'x19': 0.6751659581478224, 'y19': 0.3111636331488482}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,512][0m Trial 75 finished with value: 0.0446114623072299 and parameters: {'x0': 0.5577476511412308, 'y0': 0.1457328072450803, 'x1': 0.5892620241239407, 'y1': 0.5350498961600904, 'x2': 0.996240216101188, 'y2': 0.7588045837250853, 'x3': 0.1825201266989577, 'y3': 0.367406295675503, 'x4': 0.5085758147155377, 'y4': 0.1640922469030138, 'x5': 0.10876904344443902, 'y5': 0.12777094104131317, 'x6': 0.39227065166253, 'y6': 0.18399385916995714, 'x7': 0.4122006005804399, 'y7': 0.20718604455127954, 'x8': 0.7808092657259127, 'y8': 0.9690450022797225, 'x9': 0.8394193257418954, 'y9': 0.8799271342086679, 'x10': 0.4147090854704396, 'y10': 0.16171714349134064, 'x11': 0.5419695542203246, 'y11': 0.11377244633901942, 'x12': 0.8189659779760858, 'y12': 0.95295232019619, 'x13': 0.4762370950570105, 'y13': 0.5116721983273417, 'x14': 0.5438350167342573, 'y14': 0.946572064879226, 'x15': 0.3287450131770502, 'y15': 0.7222329128170032, 'x16': 0.8597308251144018, 'y16': 0.9429493607926959, 'x17': 0.01703603859947786, 'y17': 0.08595664312678951, 'x18': 0.8004055334174961, 'y18': 0.5426067056846701, 'x19': 0.5787800444034567, 'y19': 0.2810301918690496}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,578][0m Trial 76 finished with value: 0.1411964445839125 and parameters: {'x0': 0.6524026498674841, 'y0': 0.25850040354513765, 'x1': 0.4891232931080887, 'y1': 0.9231851864481935, 'x2': 0.8728069518414725, 'y2': 0.7277565754100525, 'x3': 0.6269788640374094, 'y3': 0.4958349124857582, 'x4': 0.7061904674187187, 'y4': 0.33881034141973865, 'x5': 0.2837953188023097, 'y5': 0.18395689578830732, 'x6': 0.29201519606170523, 'y6': 0.044305222125778025, 'x7': 0.36258961557980285, 'y7': 0.5593693624707258, 'x8': 0.5468245111212298, 'y8': 0.8690859029671862, 'x9': 0.9007595225751222, 'y9': 0.7949558148231517, 'x10': 0.33398854382720544, 'y10': 0.021315775883928245, 'x11': 0.4855164316568951, 'y11': 0.41693226979932135, 'x12': 0.8419694884399943, 'y12': 0.8277285523845385, 'x13': 0.6643619200737204, 'y13': 0.8153064233007917, 'x14': 0.6424262699269717, 'y14': 0.8431811251110224, 'x15': 0.9548972670452245, 'y15': 0.45327864413827434, 'x16': 0.8166408201050229, 'y16': 0.8402309742891299, 'x17': 0.605575727325848, 'y17': 0.13152822918985627, 'x18': 0.6773106815148306, 'y18': 0.44218189794730695, 'x19': 0.6467899031098095, 'y19': 0.22364165210534387}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,656][0m Trial 77 finished with value: 0.2570864373664349 and parameters: {'x0': 0.8919273480905363, 'y0': 0.3770442110210572, 'x1': 0.4481377529502592, 'y1': 0.459305683223967, 'x2': 0.01166686065935002, 'y2': 0.5705302213399595, 'x3': 0.22429440731239736, 'y3': 0.45600945487803113, 'x4': 0.41744441434146706, 'y4': 0.5475576703007176, 'x5': 0.16136922499530496, 'y5': 0.07977758103186414, 'x6': 0.5074625785692053, 'y6': 0.40449590463663376, 'x7': 0.4726140206595083, 'y7': 0.4498103656624428, 'x8': 0.6140842238523643, 'y8': 0.9443068991585237, 'x9': 0.9322539622931135, 'y9': 0.8483883143083857, 'x10': 0.45286355755075547, 'y10': 0.21891732345582793, 'x11': 0.6688490782359319, 'y11': 0.30628037232363914, 'x12': 0.9569102161550125, 'y12': 0.9350980941399719, 'x13': 0.42230930917885706, 'y13': 0.8953606737464153, 'x14': 0.48413757870971286, 'y14': 0.9154763612168325, 'x15': 0.8764227874799434, 'y15': 0.682964043891502, 'x16': 0.7400252735122934, 'y16': 0.8896784507384319, 'x17': 0.15169336265266803, 'y17': 0.2154567459180181, 'x18': 0.5143155825222756, 'y18': 0.39943068547654903, 'x19': 0.8151726702999857, 'y19': 0.19371233040843044}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,729][0m Trial 78 finished with value: 0.022849316356090665 and parameters: {'x0': 0.3530852949074378, 'y0': 0.3128352961430749, 'x1': 0.41293446069166495, 'y1': 0.37142494137307847, 'x2': 0.9065587159489028, 'y2': 0.9105946416737415, 'x3': 0.13868654256838042, 'y3': 0.5650235446302281, 'x4': 0.44540277177683585, 'y4': 0.2645398176060693, 'x5': 0.2314473627566625, 'y5': 0.27154032899196695, 'x6': 0.21686094631865782, 'y6': 0.10466098559365088, 'x7': 0.2614671286898645, 'y7': 0.29795401189576143, 'x8': 0.395411534579341, 'y8': 0.5445858655755795, 'x9': 0.7755520527002259, 'y9': 0.2756398303187275, 'x10': 0.5890730800109383, 'y10': 0.05175093109170693, 'x11': 0.6155772811887177, 'y11': 0.1555882474457168, 'x12': 0.7693900074492155, 'y12': 0.8582129920548912, 'x13': 0.5132648366131306, 'y13': 0.5916429310861565, 'x14': 0.9430289243886008, 'y14': 0.8748917604471359, 'x15': 0.7601912522286776, 'y15': 0.82203028925803, 'x16': 0.90985733216818, 'y16': 0.9681904709856812, 'x17': 0.04917098111085151, 'y17': 0.011590754940290507, 'x18': 0.6329544503220291, 'y18': 0.371802750953778, 'x19': 0.721028781682285, 'y19': 0.3581959836047694}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,795][0m Trial 79 finished with value: 0.271499905878534 and parameters: {'x0': 0.292085724567583, 'y0': 0.32358644735422065, 'x1': 0.36511096212843813, 'y1': 0.37695219014096304, 'x2': 0.9114704019085549, 'y2': 0.9601122267458004, 'x3': 0.06582488698366021, 'y3': 0.42819174469607973, 'x4': 0.4944811368215871, 'y4': 0.4408022961415208, 'x5': 0.23942597402573093, 'y5': 0.26720261618973, 'x6': 0.22109094460571688, 'y6': 0.3218382564268033, 'x7': 0.21927463925068896, 'y7': 0.40152816120041507, 'x8': 0.2902648555957964, 'y8': 0.5217320801370737, 'x9': 0.738889094735891, 'y9': 0.18772405087784882, 'x10': 0.580918627387668, 'y10': 0.04738536133714133, 'x11': 0.5738513769129389, 'y11': 0.059330971818197874, 'x12': 0.7711366311315622, 'y12': 0.7682021913919177, 'x13': 0.5210922047334832, 'y13': 0.5956039345703771, 'x14': 0.9217612548371862, 'y14': 0.87321909160279, 'x15': 0.7590000459016158, 'y15': 0.826110890351736, 'x16': 0.0544357559293307, 'y16': 0.8692118015855571, 'x17': 0.060766807690203456, 'y17': 0.02829127024533315, 'x18': 0.6409607422212377, 'y18': 0.3568861305278279, 'x19': 0.7137552504818436, 'y19': 0.3677924966568058}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,862][0m Trial 80 finished with value: 0.006449656502852452 and parameters: {'x0': 0.3546678626465461, 'y0': 0.09094419591307173, 'x1': 0.40224663639355435, 'y1': 0.4168167975511889, 'x2': 0.9619420245912803, 'y2': 0.90469102990043, 'x3': 0.7740203557471246, 'y3': 0.9163344069374231, 'x4': 0.4586623932535163, 'y4': 0.8564943956348388, 'x5': 0.19974305815510984, 'y5': 0.38383265986320325, 'x6': 0.13051969721748913, 'y6': 0.12674667295373754, 'x7': 0.2619862550743603, 'y7': 0.2861273458496825, 'x8': 0.39713733032720494, 'y8': 0.4549441702119209, 'x9': 0.688607946311335, 'y9': 0.2924401095042828, 'x10': 0.5355246157964686, 'y10': 0.10685818603249841, 'x11': 0.6345780116892423, 'y11': 0.15176058977347193, 'x12': 0.7321524214899467, 'y12': 0.6651340934070122, 'x13': 0.450981172892372, 'y13': 0.5581768053189782, 'x14': 0.8681605573302607, 'y14': 0.9774476223240431, 'x15': 0.80850507202571, 'y15': 0.7863045470734458, 'x16': 0.9440855896612761, 'y16': 0.42263648962397066, 'x17': 0.08664653316972015, 'y17': 0.15397236594049946, 'x18': 0.7141100854054007, 'y18': 0.634111950182952, 'x19': 0.7363494660888878, 'y19': 0.4657550735486818}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,929][0m Trial 81 finished with value: 0.03672429882499895 and parameters: {'x0': 0.3530868975754317, 'y0': 0.09837957752640661, 'x1': 0.33545929946455566, 'y1': 0.422498106265856, 'x2': 0.9668768248567542, 'y2': 0.9042790528115142, 'x3': 0.7664953929354539, 'y3': 0.9304071720194349, 'x4': 0.5363839168602722, 'y4': 0.7990686953335956, 'x5': 0.1963597657611677, 'y5': 0.3539692541332591, 'x6': 0.03571084176372291, 'y6': 0.14184257754086343, 'x7': 0.25330377019581246, 'y7': 0.14259910474401435, 'x8': 0.3910234543994982, 'y8': 0.5694487457572339, 'x9': 0.7934933903009264, 'y9': 0.23860989707444602, 'x10': 0.6016127393600148, 'y10': 0.09828072088776496, 'x11': 0.615321198724863, 'y11': 0.16816231193666892, 'x12': 0.6389087145400151, 'y12': 0.6605168600945917, 'x13': 0.4498403643901312, 'y13': 0.5753412948242191, 'x14': 0.8836008958389174, 'y14': 0.9784520102117807, 'x15': 0.7984384069996301, 'y15': 0.7789660169338501, 'x16': 0.9449183635462874, 'y16': 0.39585393106229344, 'x17': 0.08429463011958303, 'y17': 0.10607031761544487, 'x18': 0.5775569492296606, 'y18': 0.6477404324630056, 'x19': 0.7694148745214737, 'y19': 0.47581452633181226}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:26,999][0m Trial 82 finished with value: 0.03882535248504093 and parameters: {'x0': 0.3843760188148181, 'y0': 0.21035092785140352, 'x1': 0.4063214162527614, 'y1': 0.4502258228211863, 'x2': 0.9309973693383744, 'y2': 0.9192025921440654, 'x3': 0.7782643909169465, 'y3': 0.39291888574442296, 'x4': 0.4491835379974858, 'y4': 0.8692021915820629, 'x5': 0.13741739645660356, 'y5': 0.37497598298645884, 'x6': 0.13722318450424426, 'y6': 0.10958221380140934, 'x7': 0.18028723316040823, 'y7': 0.29313549672939926, 'x8': 0.4390320234997628, 'y8': 0.44707870582715525, 'x9': 0.6952256587731808, 'y9': 0.3608089371969869, 'x10': 0.5412392137561014, 'y10': 0.003047760640225043, 'x11': 0.6478803598352929, 'y11': 0.13566333790592555, 'x12': 0.7211360274441843, 'y12': 0.8539360455911879, 'x13': 0.4965372129940544, 'y13': 0.5347712709606389, 'x14': 0.9799878392839425, 'y14': 0.9369773521948571, 'x15': 0.8396831719489002, 'y15': 0.8660549237186074, 'x16': 0.9175067643790078, 'y16': 0.48757648076814397, 'x17': 0.047471128691559276, 'y17': 0.15538074937763946, 'x18': 0.7141064178721309, 'y18': 0.6281732709529979, 'x19': 0.7391000389930431, 'y19': 0.39598382900948914}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,073][0m Trial 83 finished with value: 0.2788695087656629 and parameters: {'x0': 0.33681911245419577, 'y0': 0.240477571719649, 'x1': 0.43552380420890496, 'y1': 0.4905215049986037, 'x2': 0.9529367949844112, 'y2': 0.8696402686311506, 'x3': 0.8430779235862202, 'y3': 0.8628563118460479, 'x4': 0.4067755358829465, 'y4': 0.9786007364367884, 'x5': 0.24650423324279733, 'y5': 0.42784445547130806, 'x6': 0.09621651446096403, 'y6': 0.22396703070405197, 'x7': 0.2723771916177432, 'y7': 0.24572348792862314, 'x8': 0.3801707142967503, 'y8': 0.40145524966339363, 'x9': 0.7751806890070151, 'y9': 0.29242707671723794, 'x10': 0.6722324957335892, 'y10': 0.124047766192794, 'x11': 0.5467031842490863, 'y11': 0.09002371603723518, 'x12': 0.798323819873319, 'y12': 0.7890136355982397, 'x13': 0.3613879086497774, 'y13': 0.6211945047920635, 'x14': 0.8578802494812527, 'y14': 0.0667417649162314, 'x15': 0.7730314781131936, 'y15': 0.7980191398849696, 'x16': 0.8880060489007622, 'y16': 0.3130670876682466, 'x17': 0.10564615154047052, 'y17': 0.058740154524555915, 'x18': 0.6102517998036339, 'y18': 0.5635448050889817, 'x19': 0.85317743170421, 'y19': 0.5843895678268509}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,147][0m Trial 84 finished with value: 0.056731640946878215 and parameters: {'x0': 0.3872403559901344, 'y0': 0.0245258901997214, 'x1': 0.399758600659543, 'y1': 0.3694471862835849, 'x2': 0.8793779777808569, 'y2': 0.8403230462773168, 'x3': 0.9997048092983563, 'y3': 0.8953316045294267, 'x4': 0.5898108757038654, 'y4': 0.2631515016556031, 'x5': 0.18809576564260036, 'y5': 0.1793491469838755, 'x6': 0.26301865116617856, 'y6': 0.271805551197998, 'x7': 0.22889142718201738, 'y7': 0.37059801306823525, 'x8': 0.4658308104739221, 'y8': 0.6091832851994192, 'x9': 0.8556437825541077, 'y9': 0.042332445772540195, 'x10': 0.522205814004434, 'y10': 0.08139813652261911, 'x11': 0.5977386937738342, 'y11': 0.6921400743525965, 'x12': 0.6882416206010885, 'y12': 0.6036290126946342, 'x13': 0.2918081656676383, 'y13': 0.4949741556748251, 'x14': 0.9561907517277761, 'y14': 0.9848472600538292, 'x15': 0.8195165756388874, 'y15': 0.7504040500105449, 'x16': 0.9765936467237387, 'y16': 0.5201562997066171, 'x17': 0.02047937936663878, 'y17': 0.08928176566535329, 'x18': 0.7658322959112789, 'y18': 0.5882440260440484, 'x19': 0.01576440086634978, 'y19': 0.4744974393537088}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,217][0m Trial 85 finished with value: 0.3078149013600526 and parameters: {'x0': 0.2781245458673258, 'y0': 0.15727192423442576, 'x1': 0.2563888589908351, 'y1': 0.3217015099271154, 'x2': 0.8336279696014872, 'y2': 0.13860431967604114, 'x3': 0.021943996169578768, 'y3': 0.3466378112565735, 'x4': 0.6332839001640536, 'y4': 0.2960207174709406, 'x5': 0.10022668549200865, 'y5': 0.21125139991234354, 'x6': 0.16596801408692063, 'y6': 0.1608714061234563, 'x7': 0.30003465620528874, 'y7': 0.31315035431574195, 'x8': 0.32696681696831675, 'y8': 0.47799054635157096, 'x9': 0.6340066712744223, 'y9': 0.1213144893585267, 'x10': 0.6345793594084678, 'y10': 0.13262353037972346, 'x11': 0.5067631117154708, 'y11': 0.2339560994512713, 'x12': 0.7481857527530773, 'y12': 0.8806971710257645, 'x13': 0.570300044561914, 'y13': 0.5541424911711317, 'x14': 0.9884647383497515, 'y14': 0.9462109130406982, 'x15': 0.7240379791672733, 'y15': 0.8233489475920711, 'x16': 0.2781307517209164, 'y16': 0.9261593784048839, 'x17': 0.001671771901083443, 'y17': 0.38375152045888916, 'x18': 0.6660155208549811, 'y18': 0.5249985239134096, 'x19': 0.6884978632662264, 'y19': 0.33190961098841243}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,287][0m Trial 86 finished with value: 0.1323894045650036 and parameters: {'x0': 0.4175805990633144, 'y0': 0.07274928178810514, 'x1': 0.3688407726518357, 'y1': 0.5845777270093562, 'x2': 0.8962973048378591, 'y2': 0.6354749585491162, 'x3': 0.5516506283045604, 'y3': 0.7741519380741934, 'x4': 0.49153062211179266, 'y4': 0.6349880422602501, 'x5': 0.2170117715966409, 'y5': 0.32514742086963355, 'x6': 0.5371919781554911, 'y6': 0.6013377222702138, 'x7': 0.33935174060204704, 'y7': 0.5079227476807628, 'x8': 0.4044239527000737, 'y8': 0.23787300826868327, 'x9': 0.9671551150625872, 'y9': 0.31722242733258, 'x10': 0.48610567312721914, 'y10': 0.06070890853652588, 'x11': 0.6830857932967125, 'y11': 0.03981266305768161, 'x12': 0.8708821368392891, 'y12': 0.8137475638811617, 'x13': 0.5298474593290033, 'y13': 0.6518809909846064, 'x14': 0.9517368289675312, 'y14': 0.914046126603469, 'x15': 0.8550375211476349, 'y15': 0.6080606932895463, 'x16': 0.9463570345159883, 'y16': 0.998814870982506, 'x17': 0.04944004374257873, 'y17': 0.24085840427938143, 'x18': 0.6261427135950568, 'y18': 0.6788545103820354, 'x19': 0.6113918234974378, 'y19': 0.43090798086752635}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,356][0m Trial 87 finished with value: 0.32340716086288135 and parameters: {'x0': 0.23312141036709103, 'y0': 0.18617912962101638, 'x1': 0.4964801417268653, 'y1': 0.4020560235334101, 'x2': 0.9975801634379776, 'y2': 0.9647498603036172, 'x3': 0.1427398713414344, 'y3': 0.702899003929462, 'x4': 0.45477850246366386, 'y4': 0.3839680624522497, 'x5': 0.16739319587473703, 'y5': 0.14564630537634637, 'x6': 0.4698038936907381, 'y6': 0.08780736575610487, 'x7': 0.1366273256253639, 'y7': 0.6008624943738964, 'x8': 0.7282253574972501, 'y8': 0.40367145934195575, 'x9': 0.8251325607170301, 'y9': 0.23714200624858953, 'x10': 0.5618058497664495, 'y10': 0.025843282330186262, 'x11': 0.6334762526373432, 'y11': 0.1469929349513321, 'x12': 0.7681226589444539, 'y12': 0.8485997985236903, 'x13': 0.4256493389644875, 'y13': 0.525763431964663, 'x14': 0.8897280657848988, 'y14': 0.8697942666640296, 'x15': 0.9014578549090035, 'y15': 0.892748132489542, 'x16': 0.9182850392555447, 'y16': 0.3554023142122507, 'x17': 0.9016023535258924, 'y17': 0.17678950862157597, 'x18': 0.872397656897062, 'y18': 0.5007116480651148, 'x19': 0.7215236917561434, 'y19': 0.5162003252056849}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,434][0m Trial 88 finished with value: 0.22755368753594718 and parameters: {'x0': 0.31940681179574343, 'y0': 0.26913734032335873, 'x1': 0.4600052822179192, 'y1': 0.4699283163683328, 'x2': 0.5294448024737213, 'y2': 0.7667682684712083, 'x3': 0.6390107404762633, 'y3': 0.8193845600043523, 'x4': 0.5587018895592993, 'y4': 0.4784629468579212, 'x5': 0.26208732307126975, 'y5': 0.24140041778297594, 'x6': 0.21590169618095173, 'y6': 0.2021483381514725, 'x7': 0.09969154886542375, 'y7': 0.2758425239889662, 'x8': 0.2659873730277738, 'y8': 0.3455733792253479, 'x9': 0.6840687336389634, 'y9': 0.21166438041409252, 'x10': 0.5105625711708246, 'y10': 0.8295581975833193, 'x11': 0.5787927767519317, 'y11': 0.19090708603402257, 'x12': 0.7326239639304982, 'y12': 0.5418636409929182, 'x13': 0.31899201527814547, 'y13': 0.7245908680419124, 'x14': 0.916600718790932, 'y14': 0.9771609906218052, 'x15': 0.8125933247520806, 'y15': 0.6542200973589414, 'x16': 0.8377335296788053, 'y16': 0.18403518528897306, 'x17': 0.12890976269788995, 'y17': 0.00319164894789907, 'x18': 0.7256591064375058, 'y18': 0.4194261912696036, 'x19': 0.7974644254835455, 'y19': 0.2612727401058161}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,510][0m Trial 89 finished with value: 0.05593124767986579 and parameters: {'x0': 0.45194118699443625, 'y0': 0.49588694928209914, 'x1': 0.5277696257695643, 'y1': 0.522715651650681, 'x2': 0.8570872141046901, 'y2': 0.8925415859939785, 'x3': 0.3934279114050047, 'y3': 0.31865024113813417, 'x4': 0.3508350898411402, 'y4': 0.3440777308242444, 'x5': 0.08539883268667627, 'y5': 0.11131912639039121, 'x6': 0.3234124713020961, 'y6': 0.3075894097258919, 'x7': 0.16996275454397303, 'y7': 0.7032560230266188, 'x8': 0.49861808071603364, 'y8': 0.5064254842361137, 'x9': 0.7323507160131831, 'y9': 0.45061041477333996, 'x10': 0.7213090289327367, 'y10': 0.6262504852842229, 'x11': 0.5309849237806029, 'y11': 0.9113916695084547, 'x12': 0.8230009836323332, 'y12': 0.9177005859539014, 'x13': 0.6030757484614382, 'y13': 0.43589499587170477, 'x14': 0.8557015391375946, 'y14': 0.8865090593924592, 'x15': 0.6815948271829979, 'y15': 0.8489581960353005, 'x16': 0.8740810961401992, 'y16': 0.42019500045017005, 'x17': 0.08646042257374643, 'y17': 0.07267740376201319, 'x18': 0.7915582850121382, 'y18': 0.3095073038593349, 'x19': 0.5697577085845849, 'y19': 0.308022240809999}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,581][0m Trial 90 finished with value: 0.30566960889638156 and parameters: {'x0': 0.3531414676015363, 'y0': 0.11147355144847584, 'x1': 0.5557226391798592, 'y1': 0.4363213028354993, 'x2': 0.7541366502586848, 'y2': 0.6743916395123397, 'x3': 0.051150216690312146, 'y3': 0.5048516809066089, 'x4': 0.5238259237436828, 'y4': 0.4113416871188425, 'x5': 0.9064467029349647, 'y5': 0.28872960610051635, 'x6': 0.19686396591937544, 'y6': 0.2417359032587185, 'x7': 0.5424483055288787, 'y7': 0.650559885114477, 'x8': 0.6386358787279056, 'y8': 0.4718335033909707, 'x9': 0.006777772458628484, 'y9': 0.9459244642497878, 'x10': 0.4605097420332682, 'y10': 0.10880986337081572, 'x11': 0.4315815876509185, 'y11': 0.10164240482085288, 'x12': 0.6506639574465847, 'y12': 0.728355822050897, 'x13': 0.4736504433829045, 'y13': 0.6015372440056849, 'x14': 0.9284996170259837, 'y14': 0.9331204702747841, 'x15': 0.9209681458611897, 'y15': 0.945729235947288, 'x16': 0.9784923037444526, 'y16': 0.5536620382864048, 'x17': 0.039477619329317426, 'y17': 0.122642047974165, 'x18': 0.8303133568901409, 'y18': 0.4593822602754028, 'x19': 0.5213382551546496, 'y19': 0.35859543585306664}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,661][0m Trial 91 finished with value: 0.08623542554542507 and parameters: {'x0': 0.6042415231504813, 'y0': 0.40721078599908894, 'x1': 0.6549438116165489, 'y1': 0.29039333667143663, 'x2': 0.7959144470619525, 'y2': 0.7992400730778224, 'x3': 0.5048898114275666, 'y3': 0.529082342006394, 'x4': 0.014375104404841355, 'y4': 0.22447496972541148, 'x5': 0.3702218000348063, 'y5': 0.038394296449366594, 'x6': 0.4146148681456941, 'y6': 0.12584777700391397, 'x7': 0.03033927860260096, 'y7': 0.5485320192032355, 'x8': 0.3571944242277846, 'y8': 0.9172107568589827, 'x9': 0.8808486074409144, 'y9': 0.9804455430202873, 'x10': 0.535435586792241, 'y10': 0.20181755298439855, 'x11': 0.7794631356087662, 'y11': 0.20895856533297152, 'x12': 0.9014451494410249, 'y12': 0.9780672870373004, 'x13': 0.6531337611811778, 'y13': 0.6727486153194648, 'x14': 0.6169846374851612, 'y14': 0.8439158150924426, 'x15': 0.9724235932931218, 'y15': 0.7800812482005084, 'x16': 0.9086680567283921, 'y16': 0.9654199992527689, 'x17': 0.07032514245313332, 'y17': 0.025634020904087382, 'x18': 0.6808759409756282, 'y18': 0.3958501010421553, 'x19': 0.654812097795926, 'y19': 0.2492060962776452}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,733][0m Trial 92 finished with value: 0.11618711782267499 and parameters: {'x0': 0.5442271684545271, 'y0': 0.3258631306540657, 'x1': 0.6147763886209178, 'y1': 0.36028937204823386, 'x2': 0.7180623554163672, 'y2': 0.9223495737510696, 'x3': 0.11209436156895641, 'y3': 0.5648576104252071, 'x4': 0.815945131098337, 'y4': 0.11717546135201645, 'x5': 0.31246366278601945, 'y5': 0.0632088721850834, 'x6': 0.3736989056395142, 'y6': 0.0584087262543119, 'x7': 0.250073377710744, 'y7': 0.13748595606347083, 'x8': 0.8133717313405666, 'y8': 0.9741590318676447, 'x9': 0.7711088613176573, 'y9': 0.3516768108130006, 'x10': 0.5888910838601517, 'y10': 0.14650451795454436, 'x11': 0.7252949658431905, 'y11': 0.16612940583232141, 'x12': 0.8498139130474658, 'y12': 0.8992547842681441, 'x13': 0.5466175852021021, 'y13': 0.6305370516595138, 'x14': 0.5406803108751175, 'y14': 0.694008590789381, 'x15': 0.8797933292352644, 'y15': 0.6971021161678973, 'x16': 0.8490295426899107, 'y16': 0.9074671421389251, 'x17': 0.17352857309305997, 'y17': 0.05875802495717575, 'x18': 0.7473568244744392, 'y18': 0.6133245067768835, 'x19': 0.6989632525332669, 'y19': 0.2898865420082222}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,806][0m Trial 93 finished with value: 0.03201796306735061 and parameters: {'x0': 0.48954295451874535, 'y0': 0.3022980393671278, 'x1': 0.577025613390035, 'y1': 0.33361412537754725, 'x2': 0.8166670871780722, 'y2': 0.8187983011948908, 'x3': 0.08099807709640144, 'y3': 0.6142424259421434, 'x4': 0.3962330744697848, 'y4': 0.18445878143845446, 'x5': 0.233709140420936, 'y5': 0.11762538613550882, 'x6': 0.43916116166001873, 'y6': 0.0994763384050632, 'x7': 0.20641135172071534, 'y7': 0.4723200588202308, 'x8': 0.9651511358598496, 'y8': 0.6631619195475287, 'x9': 0.8051839347632936, 'y9': 0.9065708234058251, 'x10': 0.3904600242894584, 'y10': 0.07215164941747984, 'x11': 0.6646527780793267, 'y11': 0.3695568539772731, 'x12': 0.8794234595937105, 'y12': 0.9610972027157331, 'x13': 0.7282231472340501, 'y13': 0.7063124317521509, 'x14': 0.5720721578401076, 'y14': 0.7954916888250666, 'x15': 0.8394874224737134, 'y15': 0.5529434522966378, 'x16': 0.9486027080552427, 'y16': 0.9361837057935812, 'x17': 0.11596412739888085, 'y17': 0.4387543222394684, 'x18': 0.7592734534495686, 'y18': 0.3388043249397547, 'x19': 0.3426118047555482, 'y19': 0.11971950123134828}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,880][0m Trial 94 finished with value: 0.023446897183439508 and parameters: {'x0': 0.508211134127496, 'y0': 0.37207006015693267, 'x1': 0.5100451918114142, 'y1': 0.22766305236632786, 'x2': 0.927059522033021, 'y2': 0.8358470601211537, 'x3': 0.15524580853590775, 'y3': 0.6464859220506735, 'x4': 0.4293946554412813, 'y4': 0.7594499707407443, 'x5': 0.13012744938944507, 'y5': 0.17272221928691484, 'x6': 0.2830640192366841, 'y6': 0.1829038994684493, 'x7': 0.15051081061372423, 'y7': 0.03977354584888887, 'x8': 0.4369438453321225, 'y8': 0.38412839140994737, 'x9': 0.9092744374585777, 'y9': 0.5081379341700413, 'x10': 0.4191887645232574, 'y10': 0.16687256953345536, 'x11': 0.8579985433635378, 'y11': 0.3309783671236341, 'x12': 0.8054125109549948, 'y12': 0.9350620628115527, 'x13': 0.5096577126409633, 'y13': 0.5637994546462033, 'x14': 0.722665634723534, 'y14': 0.9545415507033017, 'x15': 0.9164438004099948, 'y15': 0.7181437334205167, 'x16': 0.8001676339310624, 'y16': 0.43406505772544934, 'x17': 0.02448314958813648, 'y17': 0.0001277711226015544, 'x18': 0.7036863858082897, 'y18': 0.3796912247828816, 'x19': 0.619532644252442, 'y19': 0.38945075469075696}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:27,953][0m Trial 95 finished with value: 0.012901170286832797 and parameters: {'x0': 0.5786477344136592, 'y0': 0.4392709074348745, 'x1': 0.4363097246614184, 'y1': 0.2756601136951151, 'x2': 0.6424128955292353, 'y2': 0.8713216927247313, 'x3': 0.007645602463433879, 'y3': 0.17576369580999213, 'x4': 0.3598734916254739, 'y4': 0.30614926207397414, 'x5': 0.28391777155601006, 'y5': 0.21205942898351868, 'x6': 0.4873267633027487, 'y6': 0.14239482855019614, 'x7': 0.2932956088972728, 'y7': 0.21286304362562197, 'x8': 0.6880921177761763, 'y8': 0.548188104678227, 'x9': 0.8387299106679759, 'y9': 0.291795530376936, 'x10': 0.3127690967881466, 'y10': 0.04432326206306189, 'x11': 0.6095750321483815, 'y11': 0.2332310729727235, 'x12': 0.5185535625396867, 'y12': 0.872526643367391, 'x13': 0.6835536935363529, 'y13': 0.7579523275344642, 'x14': 0.7801220560453617, 'y14': 0.914557843650386, 'x15': 0.9432975070528173, 'y15': 0.7453607645496652, 'x16': 0.8742748908773577, 'y16': 0.9678940378818304, 'x17': 0.00025526864498932113, 'y17': 0.09830501801912402, 'x18': 0.7853645883037152, 'y18': 0.3137760754188636, 'x19': 0.6783459825865273, 'y19': 0.33863615259194957}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:28,026][0m Trial 96 finished with value: 0.0048852825906344766 and parameters: {'x0': 0.5800386778635127, 'y0': 0.6737503242638181, 'x1': 0.42442072829452326, 'y1': 0.1923480957958664, 'x2': 0.66853554092768, 'y2': 0.9923865887895431, 'x3': 0.05167249882526104, 'y3': 0.24115748364120082, 'x4': 0.30932825244834644, 'y4': 0.3564705123654738, 'x5': 0.2864258814191172, 'y5': 0.2737038379177163, 'x6': 0.48811453246660474, 'y6': 0.14441300588306288, 'x7': 0.2920368737799322, 'y7': 0.22683270793915553, 'x8': 0.6808818105177615, 'y8': 0.539745471624064, 'x9': 0.8516725881284786, 'y9': 0.2998412042569586, 'x10': 0.29652813415270046, 'y10': 0.04030661941436667, 'x11': 0.616321425261072, 'y11': 0.26560737953200003, 'x12': 0.33018588271908034, 'y12': 0.40790681149691654, 'x13': 0.6771564113766314, 'y13': 0.8546105673095225, 'x14': 0.7812958805242581, 'y14': 0.9148985294267052, 'x15': 0.9468043417878922, 'y15': 0.7442491200407869, 'x16': 0.8908325175638958, 'y16': 0.9590730335093282, 'x17': 0.05597117790079806, 'y17': 0.10556383425245963, 'x18': 0.7965536895509644, 'y18': 0.20854456886264564, 'x19': 0.7546240861793962, 'y19': 0.4613980353776152}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:28,098][0m Trial 97 finished with value: 0.06874093734947762 and parameters: {'x0': 0.5913719191819161, 'y0': 0.7071088810352045, 'x1': 0.43901413137550727, 'y1': 0.19573949103755212, 'x2': 0.6271373834893705, 'y2': 0.9971532373360371, 'x3': 0.001197649972191803, 'y3': 0.16633113335610902, 'x4': 0.28990399750175133, 'y4': 0.3609858351230463, 'x5': 0.2737828194486082, 'y5': 0.20391294724072034, 'x6': 0.5560738781670302, 'y6': 0.14702984592500648, 'x7': 0.29296350908513213, 'y7': 0.1313315859965199, 'x8': 0.6962148478638467, 'y8': 0.5298485144199114, 'x9': 0.9753448143290128, 'y9': 0.33263039589987853, 'x10': 0.2904026601252749, 'y10': 0.03717986700076405, 'x11': 0.559055832684821, 'y11': 0.2552068723887627, 'x12': 0.38591805135295804, 'y12': 0.38051414474976925, 'x13': 0.691121777106211, 'y13': 0.8713731724590339, 'x14': 0.7851401418070116, 'y14': 0.9107753907810997, 'x15': 0.9413775992363321, 'y15': 0.746144616664595, 'x16': 0.8772644014928759, 'y16': 0.8243181809658859, 'x17': 0.018447558511455, 'y17': 0.1585638657277669, 'x18': 0.9046182016065757, 'y18': 0.18769992974310773, 'x19': 0.7581182645366211, 'y19': 0.42540749292813784}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:28,172][0m Trial 98 finished with value: 0.2974860428304429 and parameters: {'x0': 0.6962800289485551, 'y0': 0.8561856560758355, 'x1': 0.4830108539451241, 'y1': 0.08087034605079281, 'x2': 0.6611892181290788, 'y2': 0.9496905358293881, 'x3': 0.023303636415720613, 'y3': 0.12018605059167231, 'x4': 0.3546948161414506, 'y4': 0.3144515943251926, 'x5': 0.35671385744333634, 'y5': 0.14927220562025864, 'x6': 0.5132798147396554, 'y6': 0.20481346966718827, 'x7': 0.4007361508522207, 'y7': 0.2418064464785096, 'x8': 0.7687835797974095, 'y8': 0.5884590378156859, 'x9': 0.9423304446383625, 'y9': 0.26376634935096, 'x10': 0.19822601777608673, 'y10': 0.09866030429193567, 'x11': 0.6492450815195769, 'y11': 0.3022728618312728, 'x12': 0.13439153464893233, 'y12': 0.29627631035231633, 'x13': 0.7949908941391837, 'y13': 0.7827764949428055, 'x14': 0.7474365877391955, 'y14': 0.976948574005436, 'x15': 0.46122132788986975, 'y15': 0.6219165337841768, 'x16': 0.18390190716532306, 'y16': 0.8695324544016249, 'x17': 0.5225886500752781, 'y17': 0.13528205440020974, 'x18': 0.8183314206650371, 'y18': 0.22032329855668836, 'x19': 0.2814979728733895, 'y19': 0.46529140667761915}. Best is trial 35 with value: 0.0034136459197382507.[0m
[32m[I 2022-01-18 06:52:28,252][0m Trial 99 finished with value: 0.12036324220005201 and parameters: {'x0': 0.6698511273372065, 'y0': 0.4404316355126148, 'x1': 0.3803108197781073, 'y1': 0.26870056970360534, 'x2': 0.5796138156794659, 'y2': 0.9760285301403557, 'x3': 0.04703064601308656, 'y3': 0.1913299151777945, 'x4': 0.22364825890928092, 'y4': 0.8805932384060209, 'x5': 0.20286478133681038, 'y5': 0.2387594577269527, 'x6': 0.4781530760235914, 'y6': 0.27567606913868303, 'x7': 0.34867354636466796, 'y7': 0.582295697252534, 'x8': 0.6808511026838009, 'y8': 0.7308210971017639, 'x9': 0.8827839997532685, 'y9': 0.2969421704094559, 'x10': 0.13573306050340167, 'y10': 0.018031753016144302, 'x11': 0.141487901184066, 'y11': 0.2758730314181824, 'x12': 0.5446890553665602, 'y12': 0.440600768908776, 'x13': 0.7581993236839744, 'y13': 0.7522097538810101, 'x14': 0.8306676524448797, 'y14': 0.997971810740511, 'x15': 0.8652650374812382, 'y15': 0.7922039517073058, 'x16': 0.9920506025516742, 'y16': 0.9049003291440642, 'x17': 0.0965016539891573, 'y17': 0.10514552544134947, 'x18': 0.7871306280322209, 'y18': 0.12451136297131588, 'x19': 0.07336241738707477, 'y19': 0.5175976248093392}. Best is trial 35 with value: 0.0034136459197382507.[0m

結果の表示

トライアル回数が少なかったせいか、ぴったり0.63にはなかなかならないようです。

import matplotlib.pyplot as plt

X = objective.best_X
Y = objective.best_Y
coeff = np.corrcoef(X, Y)[0, 1]
plt.figure(figsize=(5,5))
plt.title("correlation coefficient = {0:.3f}".format(coeff))
plt.scatter(X, Y)
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.grid()
plt.show()

トライアル回数を増やす

１０００回もトライアルすればぴったり0.63になってくれるだろ。知らんけど。えいっ。

import optuna

optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

for _ in range(10):
    objective = Objective()
    study = optuna.create_study()
    study.optimize(objective, n_trials=1000)
    X = objective.best_X
    Y = objective.best_Y
    coeff = np.corrcoef(X, Y)[0, 1]
    plt.figure(figsize=(5,5))
    plt.title("correlation coefficient = {0:.3f}".format(coeff))
    plt.scatter(X, Y)
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.grid()
    plt.show()

こうやって見ると、相関係数＝0.63といっても色々あって、味わい深いですね。

相関係数0.63で、データを１つ取り除くと相関係数0.84

次に、相関係数0.63で、データを１つ取り除くと相関係数0.84になるデータを作成しましょう。そのためには、目的関数を次のように改変します。

class Objective:
    def __init__(self, n_data = 20, target_coeff = 0.63, target_coeff2 = 0.84):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None
        self.target_coeff = target_coeff
        self.target_coeff2 = target_coeff2

    def __call__(self, trial):
        self.X = []
        self.Y = []
        for i in range(n_data):
            self.X.append(trial.suggest_uniform("x{}".format(i), 0, 1))
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        coeff = np.corrcoef(self.X, self.Y)[0, 1]
        coeff2 = np.corrcoef(self.X[:-1], self.Y[:-1])[0, 1]
        score = abs(coeff - self.target_coeff) + abs(coeff2 - self.target_coeff2)
        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

そうすると次のような散布図が得られました。トライアルを２０００回にしても、なかなかピッタリの値にはなりにくいですね。左の数字が全体の相関係数、右の数字が外れ値を１つ除いた時の相関係数です。

import optuna

optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

for _ in range(10):
    objective = Objective()
    study = optuna.create_study()
    study.optimize(objective, n_trials=2000, show_progress_bar=True)
    X = objective.best_X
    Y = objective.best_Y
    coeff = np.corrcoef(X, Y)[0, 1]
    coeff2 = np.corrcoef(X[:-1], Y[:-1])[0, 1]
    plt.figure(figsize=(5,5))
    plt.title("correlation coefficient = {0:.3f}, {1:.3f}".format(coeff, coeff2))
    plt.scatter(X, Y)
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.grid()
    plt.show()

いやー、これはなかなかの鑑識眼が必要だわ。

外れ値を１つ除外すると相関係数が大きく変わる散布図

次は、外れ値を１つ除外すると相関係数が大きく変わる散布図を作成してみましょう。外れ値の除外による相関係数の変化が最大になるように最適化してみます。

左の数字が全体の相関係数、右の数字が外れ値を１つ除いた時の相関係数です。

class Objective:
    def __init__(self, n_data = 20):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None

    def __call__(self, trial):
        self.X = []
        self.Y = []
        for i in range(n_data):
            self.X.append(trial.suggest_uniform("x{}".format(i), 0, 1))
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        coeff = np.corrcoef(self.X, self.Y)[0, 1]
        coeff2 = np.corrcoef(self.X[:-1], self.Y[:-1])[0, 1]
        score = coeff - coeff2
        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

データ数が２０個しかないこともあり、外れ値の影響が大きいですね。

データ数が変化した時の外れ値の影響

それでは、データ数が変化した時に、外れ値の影響によって相関係数がどの程度変化するかを調べてみましょう。

先ほどと同様、外れ値を１つ除外した時に生じる相関係数の変化が最大になるような散布図を計算しますが、その時のデータ数を変化させてみます。

import numpy as np
import optuna

optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

n_opt = 10 # 最適化計算を行う回数
n_trials = 100 # １回の最適化計算あたりのトライアル数
result = {}

# さまざまなデータサイズで外れ値の影響を調べる
for n_data in [20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 400]:
    result[n_data] = []
    for iteration in range(n_opt):
        print(n_data, iteration)
        objective = Objective(n_data=n_data)
        study = optuna.create_study()
        study.optimize(objective, n_trials=n_trials, show_progress_bar=True)
        X = objective.best_X
        Y = objective.best_Y
        coeff = np.corrcoef(X, Y)[0, 1]
        coeff2 = np.corrcoef(X[:-1], Y[:-1])[0, 1]
        sa = coeff2 - coeff # 外れ値を除いた相関係数と、除かなかった相関係数の差
        result[n_data].append(sa)

得られた結果をswarmplotで可視化しましょう。

import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt

df = pd.DataFrame(result)
fig = plt.figure(figsize=(16, 4))
ax = fig.add_subplot(1, 1, 1)
sns.swarmplot(data=df, ax=ax)
ax.set_xlabel('data size')
ax.set_ylabel('Difference in correlation coefficient')
plt.grid()
plt.show()

データ数が多い時は、外れ値が１つある程度では相関係数に対する影響は小さいですが、データ数が４０個よりも小さくなると、外れ値が１個あるだけで相関係数が 0.1 以上も変化してしまうことがあります。データ数が２０個の場合、外れ値が１個あるだけで相関係数が0.4近くも変わってしまう場合があります。これは、解釈に気をつけなければいけませんね。

無相関検定

では、相関があるかないか、どのように判定すれば良いでしょうか。無相関検定という方法があります。その理屈については各自でググっていただくとして、scipy に scipy.stats.pearsonr という便利ツールがあります。それを使えば、相関の有無を p 値で見積もることができます。

相関係数と p 値の関係が、データ数とどのような関係にあるか計算してみましょう。そのために目的関数の部分を少し改良します。

class Objective:
    def __init__(self, n_data = 20, target_coeff = 0.63):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None
        self.target_coeff = target_coeff

    def __call__(self, trial):
        self.X = np.linspace(0.05, 0.95, n_data) # 書き換えた部分
        self.Y = []
        for i in range(n_data):
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        coeff = np.corrcoef(self.X, self.Y)[0, 1]
        score = abs(coeff - self.target_coeff)
        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

さまざまなサイズのデータセットを、相関係数が 0.0 〜 0.9 になるように最適化し、その相関係数と p 値を集計します。

import numpy as np
import optuna
import matplotlib.pyplot as plt
from scipy.stats import pearsonr

optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

n_opt = 5
n_trials = 100
target_delta = 1e-3

result = []
for target_coeff in [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]:
    for n_data in [10, 20, 30, 40, 50, 60, 80, 100]:
        objective = Objective(n_data=n_data, target_coeff=target_coeff)
        study = optuna.create_study()
        n_optimize = 0
        while objective.best_score > target_delta:
            study.optimize(objective, n_trials=n_trials, show_progress_bar=False)
            print(n_data, target_coeff, objective.best_score)
            n_optimize += 1
            if n_optimize == n_opt:
                break
        X = objective.best_X
        Y = objective.best_Y
        r, p = pearsonr(X, Y)
        result.append([n_data, r, p])

結果をプロットします。薄くバックグラウンドかけた部分は、有意差検定を行うときによく用いられる p = 0.05 〜 p = 0.01 の範囲です。

Xh = {}
Yh = {}
for res in result:
    if res[0] not in Xh.keys():
        Xh[res[0]] = []
        Yh[res[0]] = []
    Xh[res[0]].append(res[1])
    Yh[res[0]].append(res[2])

plt.figure(figsize=(12,12))
for x in Xh.keys():
    plt.plot(Xh[x], Yh[x], label="data size = {}".format(x), marker="o")
plt.fill_between([0.0, 1.0], [0.01, 0.01], [0.05, 0.05], label="p=0.01 - 0.05", alpha=0.2)
plt.grid()
plt.legend()
plt.ylabel("p")
plt.xlabel("correlation coefficient")
plt.yscale("log")
plt.show()

よく使われる p = 0.05 を使って判定するならば、データ数が１０個の場合は相関係数0.7くらいでようやく「相関がある」一方、データ数が１００個の場合は相関係数0.2でも「相関がある」、そう考えるのが良さそうですね。

無相関検定の有意差ギリギリの散布図

最後に（たぶんこれで最後：何かネタを思いついたらまた追加するかも）、有意差検定でよく用いられる閾値である p = 0.05 や p = 0.01 ピッタリの散布図を作ってみましょう。

目的関数を次のように改変します。

from scipy.stats import pearsonr

class Objective:
    def __init__(self, n_data = 20, target_p = 0.05):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None
        self.target_p = target_p

    def __call__(self, trial):
        self.X = np.linspace(0.05, 0.95, n_data)
        self.Y = []
        for i in range(n_data):
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        r, p = pearsonr(self.X, self.Y)
        if r > 0:
            score = abs(np.log(p) - np.log(self.target_p))
        else:
            score = 530000
        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

データサイズを変化させながら、p値が p = 0.05 や p = 0.01 ピッタリになるような散布図を作っていきます。

import numpy as np
import optuna
import matplotlib.pyplot as plt
from scipy.stats import pearsonr

optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

n_opt = 20
n_trials = 100
target_delta = 1e-3

result = []
for n_data in [10, 20, 30, 40, 50, 60, 80, 100]:
    Xs = []
    Ys = []
    Rs = []
    Ps = []
    for target_p in [0.05, 0.01]:
        objective = Objective(n_data=n_data, target_p=target_p)
        study = optuna.create_study()
        n_optimize = 0
        while objective.best_score > target_delta:
            study.optimize(objective, n_trials=n_trials, show_progress_bar=False)
            print(n_data, target_p, objective.best_score)
            n_optimize += 1
            if n_optimize == n_opt:
                break
        X = objective.best_X
        Y = objective.best_Y
        r, p = pearsonr(X, Y)
        Xs.append(X)
        Ys.append(Y)
        Rs.append(r)
        Ps.append(p)
        result.append([n_data, r, target_p])

    fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(8, 4))
    axes[0].set_title("data size={0}, r={1:.3f}, p={2:.3f}".format(
        n_data, Rs[0], Ps[0]))
    axes[0].scatter(Xs[0], Ys[0])
    axes[0].grid()
    axes[0].set_xlim([-0.01, 1.01])
    axes[0].set_ylim([-0.01, 1.01])
    axes[1].set_title("data size={0}, r={1:.3f}, p={2:.3f}".format(
        n_data, Rs[1], Ps[1]))
    axes[1].scatter(Xs[1], Ys[1])
    axes[1].grid()
    axes[1].set_xlim([-0.01, 1.01])
    axes[1].set_ylim([-0.01, 1.01])
    plt.show()

その結果を集計して可視化します。

Xh = {}
Yh = {}
for res in result:
    if res[2] not in Xh.keys():
        Xh[res[2]] = []
        Yh[res[2]] = []
    Xh[res[2]].append(res[0])
    Yh[res[2]].append(res[1])

plt.figure(figsize=(6,6))
for x in Xh.keys():
    plt.plot(Xh[x], Yh[x], label="p = {}".format(x), marker="o")
plt.grid()
plt.legend()
plt.ylabel("correlation coefficient")
plt.xlabel("data size")
plt.show()

これまでの議論からよく分かるように、データ数が少ない場合は相関係数が大きくないと「相関あり」と見なされないわけですが、データ数が大きくなると、意外なほど小さい相関係数の値でも p 値が有意水準以下になるのですね。

その散布図の例をこれから列挙していきましょう。

まずはデータサイズが１０の場合です。左が p=0.05 右が p=0.01 の散布図になります。

うん、まあ確かに「相関あり」と言えそうな散布図ですが、ここからちょっとでも違ったら「相関なし」という判定になってしまうギリギリの散布図であることにご注意ください。

次に、データサイズが２０の場合です。左が p=0.05 右が p=0.01 の散布図になります。

うーん、まあ、「相関あり」かな...でもここからちょっとでも違ったら「相関なし」判定になってしまうギリギリの散布図なんだよな...

データサイズが３０の場合です。左が p=0.05 右が p=0.01 の散布図になります。

なんか分からなくなってきたぞ...

データサイズが４０の場合です。左が p=0.05 右が p=0.01 の散布図になります。

うーん...

データサイズが５０の場合です。

データサイズが６０の場合です。

データサイズが８０の場合です。

データサイズが１００の場合です。

何度も言いますが、これらは p=0.05 または p=0.01 ピッタリの散布図です。p値だけを信頼した場合、「相関あり」と判定されるか「相関なし」と判定されるかギリギリの散布図です。

...分からん...

データ数が多くなるほど「p値は低いけど、ほんとに相関あるん？」って言いたくなる気がしますね。

相関係数の95%信頼区間の下限がギリギリ0.2の散布図

相関係数の区間推定についてアドバイスをいただきましたので、95%信頼区間の下限がギリギリ0.2の散布図を作成してみました。相関係数0.2とは、「弱い相関
がある」と「相関がない」の境界として使われる（ことがある）相関係数です。

まずは https://bellcurve.jp/statistics/course/9591.html を参考に、相関係数の区間推定をするための関数を自作します。

import numpy as np
from scipy.stats import pearsonr, norm

def corr_confidence_interval(X, Y, alpha = 0.95):
    r, p = pearsonr(X, Y)
    z = np.log((1 + r) / (1 - r)) / 2
    z_a_half = norm.ppf(0.5 + 0.5 * alpha) 
    z_L = z - z_a_half * np.sqrt(1 / (len(X) - 3))
    z_U = z + z_a_half * np.sqrt(1 / (len(X) - 3))
    r_L = (np.exp(2 * z_L) - 1)/ (np.exp(2 * z_L) + 1)
    r_U = (np.exp(2 * z_U) - 1)/ (np.exp(2 * z_U) + 1)
    return r_L, r, r_U, p

この r_L が、相関係数の信頼区間の下限になります。その値が 0.2 になるように散布図を最適化するよう目的関数を設計します。

from scipy.stats import pearsonr

class Objective:
    def __init__(self, n_data = 20, target_r_L = 0.2, alpha=0.95):
        self.X = []
        self.Y = []
        self.best_score = 530000
        self.best_X = None
        self.best_Y = None
        self.target_r_L = target_r_L
        self.alpha = alpha
        self.n_data = n_data

    def __call__(self, trial):
        self.X = np.linspace(0.05, 0.95, self.n_data)
        self.Y = []
        for i in range(self.n_data):
            self.Y.append(trial.suggest_uniform("y{}".format(i), 0, 1))
        r_L, r, r_U, p = corr_confidence_interval(self.X, self.Y, self.alpha)
        score = abs(r_L - self.target_r_L)

        if self.best_score > score:
            self.best_score = score
            self.best_X = self.X
            self.best_Y = self.Y
        return score

それでは、さまざまなサイズのデータに対して、95%信頼区間の下限がギリギリ0.2の散布図を作成してみましょう。

import matplotlib.pyplot as plt
import optuna
optuna.logging.set_verbosity(optuna.logging.WARN) # 途中経過メッセージを省略する

delta = 0.001
n_trials = 100
max_trial = 1000
results = []
for n_data in [10, 20, 30, 40, 50, 60, 80, 100]:
    objective = Objective(n_data=n_data)
    study = optuna.create_study()
    study.optimize(objective, n_trials=n_trials, show_progress_bar=False)
    for _ in range(int(max_trial / n_trials)):
        if objective.best_score < delta:
            break
        study.optimize(objective, n_trials=n_trials, show_progress_bar=False)
        print(objective.n_data, objective.best_score)

    r_L, r, r_U, p = corr_confidence_interval(objective.best_X, objective.best_Y)
    results.append([n_data, r_L, r, r_U, p])
    plt.figure(figsize=(6,6))
    plt.title("datasize={4}, r={0:.3f}, CI=[{1:.3f}, {2:.3f}], p={3:.2e}".format(r, r_L, r_U, p, objective.n_data))
    plt.scatter(objective.best_X, objective.best_Y)
    plt.xlim([-0.01, 1.01])
    plt.ylim([-0.01, 1.01])
    plt.grid()
    plt.show()

どれも相関はありそうに見える気がしますね。95%信頼区間の下限が0.2ですからね。

それでは、相関係数の95%信頼区間の下限がギリギリ0.2の散布図を作成したときに、その相関係数と95%信頼区間の上限が、データサイズに応じてどのように変化するかを図示してみましょう。濃い青の線が相関係数、薄い青の領域が95%信頼区間です（下限は0.2で固定になってます）。

import pandas as pd

results = pd.DataFrame(results)
fig = plt.figure(figsize=(8, 4))
plt.xlabel("data size")
plt.ylabel("correlation coefficient")
plt.plot(results[0], results[2], marker='o')
plt.fill_between(results[0], results[1], results[3], alpha=0.3)
plt.grid()
plt.show()

なるほど、データ数が 20 くらい少なくなると、95%の信頼性で「弱い相関がある（相関係数0.2以上）」と言いたいときには相関係数が 0.6 くらいはないといけないということですね。

結論

相関は、そう簡単に分からない。