Differential Evolution in Scipy with Data

Question

I have two dataframes (df_1, df_2):

df_1 = pd.DataFrame({'O' : [1,2,3], 'M' : [2,8,3]})

df_2 = pd.DataFrame({'O' : [1,1,1, 2,2,2, 3,3,3],
                     'M' : [9,2,4, 6,7,8, 5,3,4],
                     'X' : [2,4,6, 4,8,7, 3,1,9],
                     'Y' : [3,6,1, 4,6,5, 1,0,7],
                     'Z' : [2,4,8, 3,5,4, 7,5,1]})

and a function (fun):

# Index
df_1 = df_1.set_index('O')
df_1_M = df_1.M
df_1_M = df_1_M.sort_index()

# Fun
def fun(z, *params):
    A,B,C = z
        
    # Score
    df_2['S'] = df_2['X']*A + df_2['Y']*B + df_2['Z']*C
    
    # Top score
    df_Sort = df_2.sort_values(['S', 'X', 'M'], ascending=[False, True, True])
    df_O    = df_Sort.set_index('O')
    M_Top   = df_O[~df_O.index.duplicated(keep='first')].M
    M_Top   = M_Top.sort_index()
        
    # Compare the top scoring row for each O to df_1
    df_1_R = df_1_M.reindex(M_Top.index) # Nan
    T_N_T  = M_Top == df_1_R

    # Record the results for the given values of A,B,C
    df_Res = pd.DataFrame({'it_is':T_N_T}) # is this row of df_1 the same as this row of M_Top?
        
    # p_hat =         TP / (TP + FP)
    p_hat = df_Res.sum() / len(df_Res.index)
        
    return -p_hat

I can optimise it using brute force:

from scipy.optimize import brute

# Range
min_ = -2
max_ = 2
step = .5
ran_ge = slice(min_, max_+step, step)
ranges = (ran_ge,ran_ge,ran_ge)

# Params
params = (df_1, df_2)

# Brute
resbrute = brute(fun,ranges,args=params,full_output=True,finish=None)

print('Global maximum ',                   resbrute[0])
print('Function value at global maximum ',-resbrute[1])

Which gives:

Global maximum  [-2.   0.5  1.5]
Function value at global maximum  0.6666666666666666

But that takes too long when the dimensionality and the resolution increase. To save time, I would like to optimise it by differential evolution (DE) please. I tried:

from scipy.optimize import differential_evolution

# Bounds
min_ = -2
max_ = 2
ran_ge = (min_, max_)
bounds = [ran_ge,ran_ge,ran_ge]

# Params
params = (df_1, df_2)

# DE
DE = differential_evolution(fun,bounds,args=params)

But I got:

ValueError: The truth value of a Series is ambiguous. Use a.empty, a.bool(), a.item(), a.any() or a.all().

Any ideas why it works by brute force but not by differential evolution please? How do I get it working by differential evolution?

score 2 · Accepted Answer · answered Sep 12 '20 at 19:37

Looking at the code, the fun(z, *params) functions return a series, and differential_evolution doesn't know how to handle it.

# pandas.core.series.Series
type(p_hat)

Changed the return value of fun(z, *params) to:

return -p_hat[0]

We get the correct answer:

# Function value at global maximum  0.6666666666666666
print('Function value at global maximum ',-DE.fun)

Code Fix:

import pandas as pd

df_1 = pd.DataFrame({'O' : [1,2,3], 'M' : [2,8,3]})

df_2 = pd.DataFrame({'O' : [1,1,1, 2,2,2, 3,3,3],
                     'M' : [9,2,4, 6,7,8, 5,3,4],
                     'X' : [2,4,6, 4,8,7, 3,1,9],
                     'Y' : [3,6,1, 4,6,5, 1,0,7],
                     'Z' : [2,4,8, 3,5,4, 7,5,1]})

# Index
df_1 = df_1.set_index('O')
df_1_M = df_1.M
df_1_M = df_1_M.sort_index()


# Fun
def fun(z, *params):
    A, B, C = z

    # Score
    df_2['S'] = df_2['X'] * A + df_2['Y'] * B + df_2['Z'] * C

    # Top score
    df_Sort = df_2.sort_values(['S', 'X', 'M'], ascending=[False, True, True])
    df_O = df_Sort.set_index('O')
    M_Top = df_O[~df_O.index.duplicated(keep='first')].M
    M_Top = M_Top.sort_index()

    # Compare the top scoring row for each O to df_1
    df_1_R = df_1_M.reindex(M_Top.index)  # Nan
    T_N_T = M_Top == df_1_R

    # Record the results for the given values of A,B,C
    df_Res = pd.DataFrame({'it_is': T_N_T})  # is this row of df_1 the same as this row of M_Top?

    # p_hat =         TP / (TP + FP)
    p_hat = df_Res.sum() / len(df_Res.index)

    return -p_hat[0]

from scipy.optimize import differential_evolution

# Bounds
min_ = -2
max_ = 2
ran_ge = (min_, max_)
bounds = [ran_ge,ran_ge,ran_ge]

# Params
params = (df_1, df_2)

# DE
DE = differential_evolution(fun,bounds,args=params)

print('Function value at global maximum ',-DE.fun)

Differential Evolution in Scipy with Data

1 Answers1