機械学習と数理最適化の融合

MOAI Project

from typing import List, Optional, Union, Tuple, Dict, Any
from pydantic import BaseModel, Field, ValidationError, validator, confloat, conint, constr, Json
from pydantic.tools import parse_obj_as
import pandas as pd
import numpy as np
import fastai.tabular.core as ft

文脈から問題例を生成する関数 instance_generation

引数：

文脈（Context；たとえば日付）を表すデータフレーム
他のTabularPandasの引数

返値： - 問題例を生成

これは，表データから表データを生成する深層学習モデルなので， fastaiの TabularPandas で代用できる．複数ラベル回帰を用いる．顧客数だけを予測してから，点の座標を予測する．その後，予測した点の数だけサンプリングする．

https://docs.fast.ai/tabular.core.html#tabularpandas

他の方法としては，問題例をクラスタリングして分類ラベルを付与し，与えられた文脈からラベルを当てる分類を適当な機械学習で行うことも考えられる．

#Context（日付）
df = pd.DataFrame({'date': pd.date_range(
    start='2021/1/1',
    freq='d',
    periods=30
)})
#ft.make_date(df, 'date')
ft.add_datepart(df, "date")
df.head()

	Year	Month	Week	Day	Dayofweek	Dayofyear	Is_month_end	Is_month_start	Is_quarter_end	Is_quarter_start	Is_year_end	Is_year_start	Elapsed
0	2021	1	53	1	4	1	False	True	False	True	False	True	1.609459e+09
1	2021	1	53	2	5	2	False	False	False	False	False	False	1.609546e+09
2	2021	1	53	3	6	3	False	False	False	False	False	False	1.609632e+09
3	2021	1	1	4	0	4	False	False	False	False	False	False	1.609718e+09
4	2021	1	1	5	1	5	False	False	False	False	False	False	1.609805e+09

問題例を入力とし，過去の学習データから解の情報を返す関数

問題例間の距離を定義する必要がある．

Instanceクラス

たとえばTSPなら点数と座標の列や地点間の移動費用，時間の行列；　点の座標は（たとえば北東方向に）大きい順に並べておく．
他の問題例との距離計算（輸送問題を解く）割当問題の解法 https://scmopt.github.io/opt100/33ap.html#%E5%89%B2%E5%BD%93%E5%95%8F%E9%A1%8C
問題例をクラスタリングしたときのラベル
対応する文脈データフレーム

Solutionクラス

対応するInstance

class Instance():
        
    def __init__(self, context=None, data=None, feature=None):
        self.context = context
        self.data = data
        self.feature = self.extract_feature(data)
    
    def extract_feature(self, data=None):
        pass
    
    def distance(self, another):
        pass
        
    class Config:
        arbitrary_types_allowed = True
        
class Solution():
    pass

an_instance = Instance()

#Dayによって顧客数や分布が異なるように設定
n_max, n_min = 100, 50 #平日と休日の平均顧客数
sd = 10 #standard deviation 
data = []
for row in df.itertuples():
    if row.Dayofweek<=4:
        loc = np.random.normal( loc= 0, scale = sd, size= (n_max,2) )
        instance = Instance(numpyArray=loc)
    else:
        loc = np.random.normal( loc= 0, scale = sd, size= (n_min,2) )
        instance = Instance(numpyArray=loc)
    
    new_loc = np.concatenate( ((loc[:,0] + loc[:,1]).reshape( (-1,1) ), loc ), axis=1 )
    new_loc.sort(axis=0)
    sorted_loc = new_loc[:,1:]
    
    data.append( sorted_loc.flatten() )

new_loc = np.concatenate( ((loc[:,0] + loc[:,1]).reshape( (-1,1) ), loc ), axis=1 )

new_loc.sort(axis=0)
sorted_loc = new_loc[:,1:]
sorted_loc

array([[-20.19666462, -24.74534989],
       [-13.69222509, -17.30384304],
       [-12.33393609, -15.45093693],
       [-10.53916806, -15.32671206],
       [ -9.35126821, -15.22409121],
       [ -8.822563  , -14.52154506],
       [ -8.73932943, -12.28191137],
       [ -8.36073931, -12.13593063],
       [ -8.02864509, -11.33781158],
       [ -7.74814991, -11.22964621],
       [ -7.7033224 , -10.10622249],
       [ -7.42682121,  -8.17208738],
       [ -6.55308268,  -7.914439  ],
       [ -5.66587855,  -6.38066481],
       [ -5.282336  ,  -6.34512238],
       [ -4.90897862,  -4.69273309],
       [ -3.94285144,  -4.53736864],
       [ -3.23423259,  -4.38628677],
       [ -3.16378394,  -4.35164651],
       [ -2.82444794,  -3.8416044 ],
       [ -2.72227564,  -3.29531517],
       [ -2.62622257,  -2.25543761],
       [ -2.40086914,  -2.03813249],
       [ -1.5312655 ,  -1.94330015],
       [ -1.5306093 ,  -1.57389452],
       [ -1.24658262,  -0.88679573],
       [ -1.03659721,  -0.83513033],
       [ -0.64599481,  -0.72145542],
       [  1.16255704,   1.08847602],
       [  2.35537998,   1.26442765],
       [  2.54497356,   2.33036034],
       [  4.16398703,   3.35935826],
       [  4.19791133,   3.81257709],
       [  4.6522782 ,   3.85829137],
       [  4.83735901,   3.99427655],
       [  4.96292333,   4.71795374],
       [  5.65189015,   5.10307142],
       [  5.75416739,   6.04482509],
       [  6.40985136,   6.39549295],
       [  7.24370719,   6.71061287],
       [  7.25471248,   7.65835066],
       [  8.06849262,   7.83926117],
       [  8.6756994 ,   8.892523  ],
       [ 11.8957031 ,   9.88954257],
       [ 12.03415855,  10.10811007],
       [ 12.91862634,  10.68724123],
       [ 14.15213083,  12.69164302],
       [ 15.66748155,  12.73932924],
       [ 23.25826818,  13.61147835],
       [ 29.68281631,  22.75131276]])

sorted_loc.flatten()

array([-20.19666462, -24.74534989, -13.69222509, -17.30384304,
       -12.33393609, -15.45093693, -10.53916806, -15.32671206,
        -9.35126821, -15.22409121,  -8.822563  , -14.52154506,
        -8.73932943, -12.28191137,  -8.36073931, -12.13593063,
        -8.02864509, -11.33781158,  -7.74814991, -11.22964621,
        -7.7033224 , -10.10622249,  -7.42682121,  -8.17208738,
        -6.55308268,  -7.914439  ,  -5.66587855,  -6.38066481,
        -5.282336  ,  -6.34512238,  -4.90897862,  -4.69273309,
        -3.94285144,  -4.53736864,  -3.23423259,  -4.38628677,
        -3.16378394,  -4.35164651,  -2.82444794,  -3.8416044 ,
        -2.72227564,  -3.29531517,  -2.62622257,  -2.25543761,
        -2.40086914,  -2.03813249,  -1.5312655 ,  -1.94330015,
        -1.5306093 ,  -1.57389452,  -1.24658262,  -0.88679573,
        -1.03659721,  -0.83513033,  -0.64599481,  -0.72145542,
         1.16255704,   1.08847602,   2.35537998,   1.26442765,
         2.54497356,   2.33036034,   4.16398703,   3.35935826,
         4.19791133,   3.81257709,   4.6522782 ,   3.85829137,
         4.83735901,   3.99427655,   4.96292333,   4.71795374,
         5.65189015,   5.10307142,   5.75416739,   6.04482509,
         6.40985136,   6.39549295,   7.24370719,   6.71061287,
         7.25471248,   7.65835066,   8.06849262,   7.83926117,
         8.6756994 ,   8.892523  ,  11.8957031 ,   9.88954257,
        12.03415855,  10.10811007,  12.91862634,  10.68724123,
        14.15213083,  12.69164302,  15.66748155,  12.73932924,
        23.25826818,  13.61147835,  29.68281631,  22.75131276])

#dfに追加（顧客数も追加）
loc_df = pd.DataFrame(data)

pd.concat( [df, loc_df], axis=1 )

	Year	Month	Week	Day	Dayofweek	Dayofyear	Is_month_end	Is_month_start	Is_quarter_end	Is_quarter_start	...	190	191	192	193	194	195	196	197	198	199
0	2021	1	53	1	4	1	False	True	False	True	...	14.470132	20.842812	14.809092	22.660701	15.209006	22.725063	18.868986	23.626687	29.370445	28.334336
1	2021	1	53	2	5	2	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	2021	1	53	3	6	3	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
3	2021	1	1	4	0	4	False	False	False	False	...	14.920890	16.903697	15.339421	18.232201	15.420866	18.901594	16.108396	24.803074	17.458791	26.837565
4	2021	1	1	5	1	5	False	False	False	False	...	16.620776	13.192277	17.113658	13.442796	17.145945	13.689042	18.394004	20.106800	23.705008	25.717087
5	2021	1	1	6	2	6	False	False	False	False	...	19.174283	15.499169	19.307015	16.227055	21.029683	17.517485	22.046130	17.754123	26.434196	20.584023
6	2021	1	1	7	3	7	False	False	False	False	...	19.204572	17.585625	21.110851	17.667264	21.812600	19.550941	24.309018	22.560459	25.161768	23.408903
7	2021	1	1	8	4	8	False	False	False	False	...	15.978173	15.930315	16.300432	17.716276	18.003666	20.133823	20.179454	22.199705	20.717632	24.163873
8	2021	1	1	9	5	9	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
9	2021	1	1	10	6	10	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
10	2021	1	2	11	0	11	False	False	False	False	...	18.734432	15.311818	19.974946	16.032423	20.910366	20.280738	23.157091	20.382886	26.204243	21.547111
11	2021	1	2	12	1	12	False	False	False	False	...	14.473795	17.296738	18.006466	19.308644	18.114859	19.789006	19.152658	20.259421	23.773261	24.067777
12	2021	1	2	13	2	13	False	False	False	False	...	16.047620	11.983234	16.662413	14.059299	18.522118	15.099365	19.265778	15.182389	19.778607	18.048300
13	2021	1	2	14	3	14	False	False	False	False	...	20.008937	16.221666	20.111617	16.348063	21.458096	16.614298	29.560323	18.886797	33.268425	24.639888
14	2021	1	2	15	4	15	False	False	False	False	...	15.167943	17.820723	16.650802	19.963430	17.963204	22.391149	18.381884	23.846735	22.882777	24.703841
15	2021	1	2	16	5	16	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
16	2021	1	2	17	6	17	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
17	2021	1	3	18	0	18	False	False	False	False	...	17.136287	17.469488	17.142804	17.516448	18.589927	17.575417	21.233247	19.700874	26.086480	22.692306
18	2021	1	3	19	1	19	False	False	False	False	...	15.395525	14.435958	17.677362	15.293260	20.340947	16.074834	25.272895	18.181873	27.679798	24.392501
19	2021	1	3	20	2	20	False	False	False	False	...	18.327361	20.267441	18.634094	20.791375	20.257293	20.978126	21.129962	22.456371	26.234376	23.942431
20	2021	1	3	21	3	21	False	False	False	False	...	16.626384	16.446960	18.830958	17.035065	20.053474	18.842837	20.223198	24.516268	20.841600	25.171439
21	2021	1	3	22	4	22	False	False	False	False	...	22.943273	16.232633	23.352425	16.451594	23.798254	16.814654	27.866677	18.287373	28.669873	18.924273
22	2021	1	3	23	5	23	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
23	2021	1	3	24	6	24	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
24	2021	1	4	25	0	25	False	False	False	False	...	13.051126	16.176910	14.691632	21.956990	14.696065	22.078566	15.721047	22.890334	24.247104	27.744182
25	2021	1	4	26	1	26	False	False	False	False	...	17.066672	18.071581	19.149347	18.227819	19.395548	18.514316	22.566636	19.413032	23.693322	25.134841
26	2021	1	4	27	2	27	False	False	False	False	...	14.615501	18.174073	14.895239	19.835223	16.661473	20.114736	22.003240	23.647944	23.992727	29.237498
27	2021	1	4	28	3	28	False	False	False	False	...	16.130062	16.489784	16.364160	17.313268	17.327189	17.666102	18.210826	20.392974	20.443050	22.736248
28	2021	1	4	29	4	29	False	False	False	False	...	19.313625	17.858271	20.281820	17.864886	21.246656	20.640586	30.321315	23.640204	30.574485	31.760287
29	2021	1	4	30	5	30	False	False	False	False	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

30 rows × 213 columns