python - 使用 NSGA-II 算法的 pymoo 多目标投资组合优化

Question

I am trying to use pymoo's NSGA-II algorithm to carry out portfolio optimization.

from pymoo.algorithms.moo.nsga2 import NSGA2
from pymoo.core.problem import Problem
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter

v = df_cov
m = df_mr
K = 10
print("v=", v, "m=", m, "K=", K, "n=", n)

#Examples
x=np.ones(n)/n
print("x=", x, np.sum(x))
print("Risk = ", np.sum(np.dot(x.T,(np.dot(v,x)))))
print(np.dot(x.T,(np.dot(v,x))).shape)
print(x.T.shape, np.dot(v,x).shape)
print("Return = ", np.dot(x,m))

v is an nxn matrix containing the covariance values between n number of assets. m is an array of mean returns of those assets.

I have defined the problem as the following:

class MyProblem(Problem):

   def __init__(self, m, v):
       super().__init__(n_var=n,
                        n_obj=2,
                        n_constr=0,
                        xl=np.array([0 for _ in range(n)]),
                        xu=np.array([1 for _ in range(n)]))
       self.m = m
       self.v = v
   def _evaluate(self, x, out, *args, **kwargs):
       f1 = np.dot(np.array(x).T, (np.dot(self.v, np.array(x))))
       f2 = -(np.dot(np.array(x), self.m))
       #g1 = np.sum(np.array(x))-1
       #g2 = np.sum(len(np.array(x)))-K
    
       out["F"] = np.column_stack([f1, f2])
       #out["G"] = [g1,g2]

problem = MyProblem(m,v)

algorithm = NSGA2(pop_size=100)

from pymoo.factory import get_termination

termination = get_termination("n_gen", 200)

from pymoo.optimize import minimize

res = minimize(problem,
               algorithm,
               termination,
               seed=1,
               save_history=True,
               verbose=True)

X = res.X
F = res.F

I am firstly trying to run the algorithm without any constraints, however when I run the algorithm I receive this error:

ValueError: shapes (31,31) and (100,31) not aligned: 31 (dim 1) != 100 (dim 0)

It appears that the population size is being passed through the algorithm creating a matrix with the incorrect dimensions. (in this example n=31)

Is there a way to fix this error?

The data used was acquired fromhttp://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/port1.txt

Below is the code used to prepare the data:

import numpy
import pandas as pd
import numpy as np

#read in the chosen dataset 
df = pd.read_fwf(
    'port1.txt', sep=" ",header=None)

#define n as the number of assets in the dataset
n = int(df[0].iloc[0])

#split the dataframe into two data frames
df_RR = df.iloc[1:n+1]
df_CV = df.iloc[n+1:]

#split the single column into two and give headings to both
df_RR['mean returns'] = [d.split()[0] for d in df_RR[0]]
df_RR['sd'] = [d.split()[1] for d in df_RR[0]]
del df_RR[0]
df_RR = df_RR.reset_index(drop=True)


#split the single column into three and give headings to each
df_CV['i'] = [d.split()[0] for d in df_CV[0]]
df_CV['j'] = [d.split()[1] for d in df_CV[0]]
df_CV['correlation'] = [d.split()[2] for d in df_CV[0]]
del df_CV[0]
df_CV = df_CV.reset_index(drop=True)

#convert variables to correct type (numeric)
df_CV = df_CV.apply(pd.to_numeric)
df_RR = df_RR.apply(pd.to_numeric)

#create correlation matrix
df2 = df_CV.pivot(index='i', columns='j', values='correlation')
df3 = np.triu(df2)
iu = np.triu_indices(n,1)
il = (iu[1],iu[0])
df3[il]=df3[iu]

#create sd array
df_std = np.asarray(df_RR['sd'])

#create covariance matrix
df4 = np.multiply(df3, df_std)
df_cov = np.multiply(df4, df3)

#create mean returns array
df_mr = np.asarray(df_RR['mean returns']) 

Answer 1

Can you post the code to reproduce the error? The code snippets above are unfortunately not enough to debug and see where the error lies.

In general, you intend to use NSGA-II with a population size of 100. That means if you overwrite the problem's _evaluate method, the input of x will be of shape (100, n_var) . Since you are setting n_obj to 2, that means out["F"] is supposed to have the shape (100,2) . Analogously, the constraints need to be set to out["G"] . I recommended checking the shapes and trying to find where the error lies. If you post some source code that is ready to run, I can also have a look at it quickly.