Scipy.optimize：最小化 function 产生错误

Question

我正在尝试使用scipy.optimize优化预测参数。 我按照教程进行操作，并在 stackoverflow 上找到了一些不错的示例，但我遇到了一个无法解决的问题。 我开始怀疑使用 pandas 是否是 scipy 的糟糕选择？

我已将我的代码设置如下：

import simpy
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
import pandas as pd
import statistics as stat
import math as m
#from sklearn.grid_search import ParameterGrid
from scipy.optimize import minimize

###dataframe for the simulation

df = pd.read_csv('simulation_df_data_2018_2.csv')
with pd.option_context("max_rows", None,"max_columns", None):
    print(df.head())


for i in df.index:
    alpha = 0.2
    beta = 0.3
    
    x = np.array([alpha, beta])

 
    def holts(x):

        LO = np.int(df['average_demand'].loc[i])
        print(type(LO))

        TO = ((df['m2'].loc[i] - df['m3'].loc[i]) + (df['m1'].loc[i] - df['m2'].loc[i])) / 2
        L1 = round(x[0] * df['m3'].loc[i] + (1 - x[0]) * (
                LO + TO))
        T1 = x[1] * (L1 - LO) + (1 - x[1]) * TO

        L2 = round(x[0] * df['m2'].loc[i] + (1 - x[0]) * (
                L1 + T1))
        T2 = x[1] * (L2 - L1) + (1 - x[1]) * T1
        L3 = round(x[0] * df['m1'].loc[i] + (1 - x[0]) * (
                L2 + T2))
        T3 = beta * (L3 - L2) + (1 - beta) * T2
        LT1 = round(L3 + 1 * T3)
        MSE = ((df['m3'].loc[i] - L1) + (df['m2'].loc[i] - L2) + (
                df['m2'].loc[i] - L3)) ** 2 / 3

        return MSE
    #print(holts(x))

    x0 = [0.1,0.1]

    result = minimize(holts, x0, bounds=[(0,1),(0,1)], method="SLSQP")
    print(result)
    print(x)

和 df 看起来像这样：

     m1     m2     m3     m4     m5     m6     m7     m8     m9    m10    m11  \
0   0.0    8.0    2.0    0.0   14.0    0.0    5.0    2.0    4.0    4.0   10.0   
1   4.0   55.0    2.0   72.0   38.0   87.0  113.0    2.0    0.0  165.0    2.0   
2  18.0   34.0    6.0   63.0   14.0   18.0   33.0   35.0   51.0    0.0   24.0   
3   0.0   21.0    3.0   10.0   15.0    0.0   32.0    1.0    3.0   17.0    0.0   
4  96.0  106.0  237.0  136.0  138.0  116.0  167.0  158.0  110.0  115.0  161.0   

     m12   m13   m14   m15   m16    m17   m18   m19   m20    m21    m22  \
0    0.0   6.0  10.0   0.0   2.0    2.0  17.0   0.0   0.0    0.0    0.0   
1   35.0   7.0  88.0   6.0   3.0  103.0  18.0  59.0   6.0   20.0  152.0   
2    6.0   5.0  99.0   7.0  17.0   15.0   8.0   3.0  21.0    6.0    4.0   
3   30.0   5.0  88.0   1.0   6.0   10.0   9.0  17.0   9.0    0.0    1.0   
4  116.0  77.0  48.0  96.0  69.0   77.0  96.0  74.0  94.0  101.0  115.0   

     m23    m24  average_demand  low_demand  high_demand  
0    0.0    0.0        3.583333         0.0         17.0  
1    6.0    0.0       43.458333         0.0        165.0  
2   14.0   12.0       21.375000         0.0         99.0  
3    0.0    0.0       11.583333         0.0         88.0  
4  158.0  167.0      117.833333        48.0        237.0  

我对不断收到的错误感到非常困惑，这是回溯

Traceback (most recent call last):
  File "/Users/pierre/Desktop/simul/forecast_holts_alpha.py", line 121, in <module>
    result = minimize(holts, x0, args= coef_list,bounds=[(0,1),(0,1)], method="SLSQP")
  File "/Users/pierre/Desktop/Django-app/lib/python3.7/site-packages/scipy/optimize/_minimize.py", line 618, in minimize
    constraints, callback=callback, **options)
  File "/Users/pierre/Desktop/Django-app/lib/python3.7/site-packages/scipy/optimize/slsqp.py", line 399, in _minimize_slsqp
    fx = func(x)
  File "/Users/pierre/Desktop/Django-app/lib/python3.7/site-packages/scipy/optimize/optimize.py", line 327, in function_wrapper
    return function(*(wrapper_args + args))
  File "/Users/pierre/Desktop/simul/forecast_holts_alpha.py", line 63, in holts
    LO = np.int(df['average_demand'].loc[i])
IndexError: only integers, slices (`:`), ellipsis (`...`), numpy.newaxis (`None`) and integer or boolean arrays are valid indices

我不明白为什么会出现这个错误，特别是因为如果我搜索 LO 的类型，我会得到这个：

print(type(LO))

<class 'int'>

我不是经验丰富的程序员，所以我很难弄清楚发生了什么，任何帮助将不胜感激！

更新：

   fun: 56.333333333333336
     jac: array([0., 0.])
 message: 'Optimization terminated successfully.'
    nfev: 4
     nit: 1
    njev: 1
  status: 0
 success: True
       x: array([0.1, 0.1])
[0.2,0.3]

OUTPUT 看起来像这样，但似乎没有优化任何东西

Answer 1

由于我不知道您的代码到底在做什么，所以我无法判断以下代码是否正确。 但只是为了指导如何使用scipy.optimize.minimize function，它应该类似于以下内容：

import numpy as np
import pandas as pd
from scipy.optimize import minimize

df = pd.read_csv('simulation_df_data_2018_2.csv')

for i in df.index:
    # Since you said "alpha" and "beta" are the variable of "holts" function
    # I changed all "alpha" and "beta" to "x[0]" and "x[1]" respectively.
    def holts(x):
        LO = np.int(df['average_demand'].loc[i])
        TO = ((df['m2'].loc[i] - df['m3'].loc[i]) + (df['m1'].loc[i] - df['m2'].loc[i])) / 2
        L1 = x[0] * df['m3'].loc[i] + (1 - x[0]) * (LO + TO)
        T1 = x[1] * (L1 - LO) + (1 - x[1]) * TO
        L2 = x[0] * df['m2'].loc[i] + (1 - x[0]) * (L1 + T1)
        T2 = x[1] * (L2 - L1) + (1 - x[1]) * T1
        L3 = x[0] * df['m1'].loc[i] + (1 - x[0]) * (L2 + T2)
        MSE = ((df['m3'].loc[i] - L1) + (df['m2'].loc[i] - L2) + (df['m2'].loc[i] - L3)) ** 2 / 3
        return MSE


    x0 = np.array([0.1, 0.1])  # initial guess for the points "x" which "holts(x)" attains its minimum.

    result = minimize(holts, x0, bounds=[(0, 1), (0, 1)], method="SLSQP", options={'disp': True})
    print(result)
    print()

哪个打印

Optimization terminated successfully    (Exit mode 0)
            Current function value: 16.921875002444228
            Iterations: 5
            Function evaluations: 15
            Gradient evaluations: 5
     fun: 16.921875002444228
     jac: array([ 8.06808472e-04, -6.23427415e+00])
 message: 'Optimization terminated successfully'
    nfev: 15
     nit: 5
    njev: 5
  status: 0
 success: True
       x: array([0.75000606, 1.        ])

Optimization terminated successfully    (Exit mode 0)
            Current function value: 3.0792324286388828e-09
            Iterations: 7
            Function evaluations: 24
            Gradient evaluations: 7
     fun: 3.0792324286388828e-09
     jac: array([-0.00833083, -0.00081578])
 message: 'Optimization terminated successfully'
    nfev: 24
     nit: 7
    njev: 7
  status: 0
 success: True
       x: array([0.1495232 , 0.25665903])

Optimization terminated successfully    (Exit mode 0)
            Current function value: 1.9951658230345873e-10
            Iterations: 9
            Function evaluations: 32
            Gradient evaluations: 9
     fun: 1.9951658230345873e-10
     jac: array([0.03791677, 0.00858221])
 message: 'Optimization terminated successfully'
    nfev: 32
     nit: 9
    njev: 9
  status: 0
 success: True
       x: array([0.37155192, 0.19218713])

Optimization terminated successfully    (Exit mode 0)
            Current function value: 114.53090716252409
            Iterations: 11
            Function evaluations: 37
            Gradient evaluations: 11
     fun: 114.53090716252409
     jac: array([ 3.06129456e-04, -3.04457455e+01])
 message: 'Optimization terminated successfully'
    nfev: 37
     nit: 11
    njev: 11
  status: 0
 success: True
       x: array([0.7171298, 1.       ])

Optimization terminated successfully    (Exit mode 0)
            Current function value: 33.333333333333336
            Iterations: 2
            Function evaluations: 6
            Gradient evaluations: 2
     fun: 33.333333333333336
     jac: array([-403.33331966,   -0.        ])
 message: 'Optimization terminated successfully'
    nfev: 6
     nit: 2
    njev: 2
  status: 0
 success: True
       x: array([1., 1.])

UPDATE : It seems that the round function is the reason minimize function is not working, since round function would create many plateaus on the graph of holts function. 我删除了round函数并更新了打印的结果。