# python – Gekko seems to ignore the single equation

I’ve been using Gekko for the last three years for optimization purposes. As a matter of fact, I’m using `Gekko` version `1.0.4`. Recently, I’ve been trying to solve an ESG-MVP problem developed by (Vo, He et al. 2019):

Considering `sum(wesg)` should be equal to 1 and `0 ≤ wesg_i ≤ 1 for iε[0, 1, 2,..., 23]`. In this model, I’m trying to find the best values ​​of `wesg_i` for the model above. Hence, according to the information provided, I have to find the value of 24 variables through an optimization model. My code is available for you to test on your computer with all the vital data needed.

## Libraries

``````from gekko import GEKKO
import numpy as np
import pandas as pd
``````

## Data Section

Make sure copy it all.

``````esg_scores_df = pd.DataFrame({'Score 2019': {'MSFT': 7,'PEP': 7,'TSLA': 4,'AMZN': 6,'LKQ': 3,'ABMD': 3,'MSI': 10,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 4,'GS': 6,'EQIX': 9,'EA': 7,'AAP': 6,'TEL': 9,'DG': 6,'EXR': 5,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 9},
'Score 2020': {'MSFT': 6,'PEP': 11,'TSLA': 4,'AMZN': 6,'LKQ': 4,'ABMD': 4,'MSI': 8,'PH': 8,'NKE': 6,'TM': 7,'EOG': 7,'GOOGL': 5,'NFLX': 3,'GS': 6,'EQIX': 9,'EA': 6,'AAP': 7,'TEL': 9,'DG': 6,'EXR': 4,'MDLZ': 6,'FIS': 8,'CRL': 8,'RCL': 7}})

predicted_return_dataframe = pd.DataFrame({'MSFT': 1.0982472257593677e-15,'PEP': 4.567069595849647e-09,'TSLA': 7.439258841202596e-10,'AMZN': 3.176883309676764e-07,'LKQ': 4.825709334830293e-05,'ABMD': 2.0608058642685837e-05,'MSI': -3.1789250961959136e-12,'PH': -2.257237871892785e-07,'NKE': -4.737530217609426e-07,'TM': 9.951932427172896e-07,'EOG': 1.184074639824261e-08,'GOOGL': -1.7027206923083418e-10,'NFLX': 2.948344729885545e-05,'GS': 1.458862302453713e-07,'EQIX': 4.620207503091301e-07,'EA': -1.297137640100873e-06,'AAP': -3.493153382990658e-07,'TEL': 8.202463568291799e-08,'DG': 2.743802312024829e-05,'EXR': 1.971994818465128e-11,'MDLZ': 1.578772827915881e-08,'FIS': 1.3314663987166631e-08,'CRL': 4.112083587242872e-05,'RCL': -1.470829206425942e-09} , index = [0])

r = pd.DataFrame({'MSFT': -0.029838842874655123,'PEP': -0.012265555866403165,'TSLA': -0.053599428210690636,'AMZN': -0.02614876342440773,'LKQ': -0.026658034482507052,'ABMD': -0.017274321994365294,'MSI': -0.018624198080929168,'PH': -0.02871952268633362,'NKE': -0.028820168231794074,'TM': -0.011208781085200492,'EOG': -0.04606883798249617,'GOOGL': -0.027983366801701926,'NFLX': -0.0070609860042608165,'GS': -0.02429261616692462,'EQIX': -0.015181566244607758,'EA': -0.012009295653284258,'AAP': -0.011979871239295382,'TEL': -0.021782414925879602,'DG': -0.009820085124020328,'EXR': -0.012233190959318829,'MDLZ': -0.015917631061436933,'FIS': -0.023877815976094417,'CRL': -0.020169902356185498,'RCL': -0.06831607178882856} , index = [0])

sigma = pd.DataFrame(np.array([[ 1.02188994e-04,  3.16399586e-05,  8.54243667e-05,
7.14148287e-05,  3.55313650e-05,  5.44796564e-05,
3.39128448e-05,  6.65003271e-05,  5.42932808e-05,
2.29333906e-05,  4.26407605e-05,  7.92791756e-05,
9.28910574e-05,  6.36770764e-05,  3.75024646e-05,
5.13720672e-05,  1.33646720e-05,  6.21865710e-05,
4.72888751e-05,  2.35546749e-06,  2.49700413e-05,
6.74503236e-05,  7.08948785e-05,  5.55096135e-05],
[ 3.16399586e-05,  6.47824823e-05, -2.57461009e-05,
1.81931187e-05,  2.11795049e-05,  1.01708683e-05,
3.33739243e-05,  1.23893822e-05,  2.74825418e-05,
1.35954411e-05,  2.37108310e-06,  2.34208728e-05,
1.96972793e-05,  1.09335123e-05,  4.26042775e-05,
2.76849308e-05,  6.01821651e-06,  8.04387109e-06,
3.10892437e-05,  2.79970364e-05,  3.70572613e-05,
3.08215527e-05,  2.57244480e-05,  8.72002781e-06],
[ 8.54243667e-05, -2.57461009e-05,  8.84138653e-04,
6.16478906e-05, -1.78063009e-05,  3.62712388e-05,
-6.15200573e-05,  8.63597848e-05,  2.12571109e-05,
3.21749681e-05,  6.54693912e-05,  7.95298035e-05,
1.53917874e-04,  8.06306277e-05, -5.27893372e-06,
2.60899474e-05,  4.29017379e-05,  6.13689353e-05,
2.30097086e-06, -4.45963115e-05, -2.83669072e-06,
2.95395217e-05,  4.53889239e-05,  3.11615533e-05],
[ 7.14148287e-05,  1.81931187e-05,  6.16478906e-05,
1.19357840e-04,  5.48763301e-05,  5.55161292e-05,
2.77288469e-05,  6.25231790e-05,  5.19494452e-05,
1.93193913e-05,  4.28946368e-05,  7.00210371e-05,
9.92756795e-05,  6.54630027e-05,  1.73935405e-05,
4.46819063e-05,  2.94199398e-05,  5.76749375e-05,
3.75634244e-05, -5.53847280e-06,  9.72193169e-06,
4.42756733e-05,  4.21469376e-05,  4.35344231e-05],
[ 3.55313650e-05,  2.11795049e-05, -1.78063009e-05,
5.48763301e-05,  3.49607174e-04,  1.58156275e-04,
-1.64565378e-05,  5.95602984e-05,  3.36138721e-05,
2.25095973e-05,  4.90144491e-05,  5.60207136e-05,
3.73119885e-05,  8.65010497e-05, -1.68774498e-05,
1.06928038e-05,  3.53732120e-05,  8.46071106e-05,
3.89200328e-05, -1.10740797e-05,  4.20238479e-06,
2.07371361e-05,  2.27640364e-05,  7.39017715e-05],
[ 5.44796564e-05,  1.01708683e-05,  3.62712388e-05,
5.55161292e-05,  1.58156275e-04,  1.12266763e-03,
2.49786917e-05,  5.60053839e-05, -2.57686022e-05,
3.00855419e-05,  2.09079416e-04,  1.21797841e-04,
3.80689080e-06,  1.17305259e-04, -4.95192897e-05,
5.56059321e-05,  2.87765760e-06,  1.13640096e-04,
-2.73690072e-05,  2.17458024e-05, -1.24009254e-05,
6.11287657e-05,  1.12849096e-04,  1.17234141e-04],
[ 3.39128448e-05,  3.33739243e-05, -6.15200573e-05,
2.77288469e-05, -1.64565378e-05,  2.49786917e-05,
1.84271573e-04, -2.99455473e-06,  3.56885701e-05,
1.53451236e-05,  3.20222217e-06,  3.00619247e-05,
5.17902613e-05,  1.69851832e-05,  7.75007583e-05,
7.49839347e-06, -3.78485373e-05, -1.28942631e-05,
4.36657573e-05,  3.97590833e-05,  4.04704969e-05,
4.05201790e-05,  4.01384618e-05,  4.82818631e-06],
[ 6.65003271e-05,  1.23893822e-05,  8.63597848e-05,
6.25231790e-05,  5.95602984e-05,  5.60053839e-05,
-2.99455473e-06,  2.86568704e-04,  6.55278686e-05,
4.08938883e-05,  1.18822482e-04,  9.32577766e-05,
7.92498191e-05,  1.38967662e-04, -1.64128182e-05,
4.16393158e-05,  1.06300676e-04,  1.31672888e-04,
6.64839109e-05, -5.14108669e-05, -1.03044572e-05,
1.59107041e-05,  7.65457600e-05,  1.31611693e-04],
[ 5.42932808e-05,  2.74825418e-05,  2.12571109e-05,
5.19494452e-05,  3.36138721e-05, -2.57686022e-05,
3.56885701e-05,  6.55278686e-05,  1.36374334e-04,
1.36781102e-05,  2.38544176e-05,  5.90104054e-05,
6.20754315e-05,  5.84082445e-05,  3.96422393e-05,
2.96064418e-05,  5.54456912e-05,  5.69396332e-05,
7.28867485e-05,  7.92870807e-06,  3.79528145e-05,
3.38036564e-05,  3.47015652e-05,  3.86545249e-05],
[ 2.29333906e-05,  1.35954411e-05,  3.21749681e-05,
1.93193913e-05,  2.25095973e-05,  3.00855419e-05,
1.53451236e-05,  4.08938883e-05,  1.36781102e-05,
5.30619573e-05,  4.42693706e-05,  2.92937393e-05,
1.15184525e-05,  3.04141154e-05,  1.11981894e-06,
1.29388215e-05,  1.41913521e-05,  2.37704063e-05,
1.27983719e-05, -3.53963791e-06,  5.41505031e-06,
1.21874870e-05,  2.04099948e-05,  2.89151466e-05],
[ 4.26407605e-05,  2.37108310e-06,  6.54693912e-05,
4.28946368e-05,  4.90144491e-05,  2.09079416e-04,
3.20222217e-06,  1.18822482e-04,  2.38544176e-05,
4.42693706e-05,  5.01946804e-04,  7.79572195e-05,
7.61563242e-05,  1.31597522e-04, -2.43789107e-05,
6.77962026e-05,  5.39745318e-05,  9.05223133e-05,
-1.88433584e-06, -1.63784490e-05, -1.04001201e-05,
1.79450881e-05,  5.33951974e-05,  1.07102393e-04],
[ 7.92791756e-05,  2.34208728e-05,  7.95298035e-05,
7.00210371e-05,  5.60207136e-05,  1.21797841e-04,
3.00619247e-05,  9.32577766e-05,  5.90104054e-05,
2.92937393e-05,  7.79572195e-05,  1.10688236e-04,
8.13294795e-05,  8.72981821e-05,  2.13737337e-05,
4.33439061e-05,  3.06090710e-05,  7.60853329e-05,
4.44363057e-05,  3.33458671e-06,  1.60908360e-05,
4.09067616e-05,  5.72051871e-05,  6.05239478e-05],
[ 9.28910574e-05,  1.96972793e-05,  1.53917874e-04,
9.92756795e-05,  3.73119885e-05,  3.80689080e-06,
5.17902613e-05,  7.92498191e-05,  6.20754315e-05,
1.15184525e-05,  7.61563242e-05,  8.13294795e-05,
3.77348891e-04,  8.99709029e-05,  2.58732673e-05,
8.24015922e-05,  2.77333081e-05,  4.74146019e-05,
3.76467363e-05, -5.60031564e-06,  2.25653918e-05,
6.22679966e-05,  3.92394407e-05,  6.47067147e-05],
[ 6.36770764e-05,  1.09335123e-05,  8.06306277e-05,
6.54630027e-05,  8.65010497e-05,  1.17305259e-04,
1.69851832e-05,  1.38967662e-04,  5.84082445e-05,
3.04141154e-05,  1.31597522e-04,  8.72981821e-05,
8.99709029e-05,  1.54802097e-04, -1.57072336e-05,
3.58129141e-05,  5.52667399e-05,  1.02065825e-04,
4.96942712e-05, -2.44193897e-05, -5.66188177e-06,
2.35884764e-05,  5.15584350e-05,  9.98376706e-05],
[ 3.75024646e-05,  4.26042775e-05, -5.27893372e-06,
1.73935405e-05, -1.68774498e-05, -4.95192897e-05,
7.75007583e-05, -1.64128182e-05,  3.96422393e-05,
1.11981894e-06, -2.43789107e-05,  2.13737337e-05,
2.58732673e-05, -1.57072336e-05,  1.54605175e-04,
1.07085192e-05, -1.14274871e-05, -1.26204468e-05,
2.50810750e-05,  5.60340845e-05,  4.60520336e-05,
4.29696767e-05,  5.33004299e-05, -1.56063893e-05],
[ 5.13720672e-05,  2.76849308e-05,  2.60899474e-05,
4.46819063e-05,  1.06928038e-05,  5.56059321e-05,
7.49839347e-06,  4.16393158e-05,  2.96064418e-05,
1.29388215e-05,  6.77962026e-05,  4.33439061e-05,
8.24015922e-05,  3.58129141e-05,  1.07085192e-05,
1.32544808e-04,  3.15561503e-05,  3.62681876e-05,
1.76503394e-05,  1.90982407e-07,  1.02992114e-05,
2.81341342e-05,  2.81970597e-05,  3.94413355e-05],
[ 1.33646720e-05,  6.01821651e-06,  4.29017379e-05,
2.94199398e-05,  3.53732120e-05,  2.87765760e-06,
-3.78485373e-05,  1.06300676e-04,  5.54456912e-05,
1.41913521e-05,  5.39745318e-05,  3.06090710e-05,
2.77333081e-05,  5.52667399e-05, -1.14274871e-05,
3.15561503e-05,  2.71861487e-04,  6.04272650e-05,
3.55256428e-05, -2.37123843e-05, -1.99844011e-05,
-2.02943319e-07, -4.12746174e-07,  6.80701129e-05],
[ 6.21865710e-05,  8.04387109e-06,  6.13689353e-05,
5.76749375e-05,  8.46071106e-05,  1.13640096e-04,
-1.28942631e-05,  1.31672888e-04,  5.69396332e-05,
2.37704063e-05,  9.05223133e-05,  7.60853329e-05,
4.74146019e-05,  1.02065825e-04, -1.26204468e-05,
3.62681876e-05,  6.04272650e-05,  1.67171047e-04,
5.06392219e-05, -1.02673299e-05,  1.64715372e-05,
2.50897861e-05,  5.81836032e-05,  1.00294572e-04],
[ 4.72888751e-05,  3.10892437e-05,  2.30097086e-06,
3.75634244e-05,  3.89200328e-05, -2.73690072e-05,
4.36657573e-05,  6.64839109e-05,  7.28867485e-05,
1.27983719e-05, -1.88433584e-06,  4.44363057e-05,
3.76467363e-05,  4.96942712e-05,  2.50810750e-05,
1.76503394e-05,  3.55256428e-05,  5.06392219e-05,
1.99771178e-04,  4.70710752e-06,  3.76160380e-05,
2.30014580e-05,  3.12554634e-05,  5.94948441e-06],
[ 2.35546749e-06,  2.79970364e-05, -4.45963115e-05,
-5.53847280e-06, -1.10740797e-05,  2.17458024e-05,
3.97590833e-05, -5.14108669e-05,  7.92870807e-06,
-3.53963791e-06, -1.63784490e-05,  3.33458671e-06,
-5.60031564e-06, -2.44193897e-05,  5.60340845e-05,
1.90982407e-07, -2.37123843e-05, -1.02673299e-05,
4.70710752e-06,  8.86508330e-05,  4.02039134e-05,
2.39025489e-05, -5.94660474e-06, -1.92301274e-05],
[ 2.49700413e-05,  3.70572613e-05, -2.83669072e-06,
9.72193169e-06,  4.20238479e-06, -1.24009254e-05,
4.04704969e-05, -1.03044572e-05,  3.79528145e-05,
5.41505031e-06, -1.04001201e-05,  1.60908360e-05,
2.25653918e-05, -5.66188177e-06,  4.60520336e-05,
1.02992114e-05, -1.99844011e-05,  1.64715372e-05,
3.76160380e-05,  4.02039134e-05,  8.23927778e-05,
3.21948208e-05,  3.50482953e-05, -1.97971783e-07],
[ 6.74503236e-05,  3.08215527e-05,  2.95395217e-05,
4.42756733e-05,  2.07371361e-05,  6.11287657e-05,
4.05201790e-05,  1.59107041e-05,  3.38036564e-05,
1.21874870e-05,  1.79450881e-05,  4.09067616e-05,
6.22679966e-05,  2.35884764e-05,  4.29696767e-05,
2.81341342e-05, -2.02943319e-07,  2.50897861e-05,
2.30014580e-05,  2.39025489e-05,  3.21948208e-05,
1.20680211e-04,  5.96710279e-05,  3.14411495e-05],
[ 7.08948785e-05,  2.57244480e-05,  4.53889239e-05,
4.21469376e-05,  2.27640364e-05,  1.12849096e-04,
4.01384618e-05,  7.65457600e-05,  3.47015652e-05,
2.04099948e-05,  5.33951974e-05,  5.72051871e-05,
3.92394407e-05,  5.15584350e-05,  5.33004299e-05,
2.81970597e-05, -4.12746174e-07,  5.81836032e-05,
3.12554634e-05, -5.94660474e-06,  3.50482953e-05,
5.96710279e-05,  1.65974972e-04,  5.42453625e-05],
[ 5.55096135e-05,  8.72002781e-06,  3.11615533e-05,
4.35344231e-05,  7.39017715e-05,  1.17234141e-04,
4.82818631e-06,  1.31611693e-04,  3.86545249e-05,
2.89151466e-05,  1.07102393e-04,  6.05239478e-05,
6.47067147e-05,  9.98376706e-05, -1.56063893e-05,
3.94413355e-05,  6.80701129e-05,  1.00294572e-04,
5.94948441e-06, -1.92301274e-05, -1.97971783e-07,
3.14411495e-05,  5.42453625e-05,  1.92061080e-04]]))

sigma_bar = pd.DataFrame(np.array([[ 1.26820873e-09,  9.99357360e-01,  9.96834344e-01,
9.99572167e-01,  9.42281243e-01,  9.97900189e-01,
9.99540337e-01,  9.98601652e-01,  9.99273813e-01,
9.97018616e-01, -9.73801139e-01,  9.99572102e-01,
9.99493833e-01,  9.98516049e-01,  9.99016459e-01,
9.99032878e-01, -9.44718270e-01,  9.99102498e-01,
9.99273586e-01,  9.97964072e-01,  9.98809893e-01,
9.99306302e-01,  9.98670142e-01,  9.89075401e-01],
[ 9.99357360e-01,  8.85756152e-04,  9.96279483e-01,
9.99197947e-01,  9.41407791e-01,  9.97899466e-01,
9.99417552e-01,  9.98836192e-01,  9.99109838e-01,
9.97212584e-01, -9.74070678e-01,  9.99506469e-01,
9.99304970e-01,  9.98532839e-01,  9.99435799e-01,
9.99191149e-01, -9.45834544e-01,  9.99087732e-01,
9.99237110e-01,  9.98261304e-01,  9.98920402e-01,
9.99254574e-01,  9.98828941e-01,  9.88935866e-01],
[ 9.96834344e-01,  9.96279483e-01,  4.28636430e-07,
9.96600181e-01,  9.47870932e-01,  9.95399154e-01,
9.96381458e-01,  9.96592822e-01,  9.96914826e-01,
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9.89492504e-01,  9.74895278e-01,  9.90401184e-01,
9.89348747e-01,  9.92893798e-01,  9.91294961e-01,
9.87014134e-01, -9.49332577e-01,  9.89982094e-01,
9.88011557e-01,  9.92133050e-01,  9.90282263e-01,
9.88600916e-01, -9.20277725e-01,  9.90680163e-01,
9.89226980e-01,  9.86577350e-01,  9.89489744e-01,
9.90734007e-01,  9.91199840e-01,  9.41720628e-08]]))
``````

## Algorithm Section

``````N = 24
model = GEKKO(remote=False)
wesg = model.Array(model.Var , N , value = 1/N , lb=0 , ub=1)
model.Equation = (sum(wesg) == 1)

def obj(rf = 0.02):
esg_portfo = 0
for i in range(N):
esg_portfo += model.Intermediate(wesg[i] * ((esg_scores_df["Score 2019"][i] + esg_scores_df["Score 2020"][i])/2))

return_portfo = 0
for i in range(N):
return_portfo += model.Intermediate(wesg[i]*((predicted_return_dataframe.iloc[0 , i] + r.iloc[0 ,i])/2))

sigma_portfo = 0
for i in range(N):
for j in range(N):
sigma_portfo += model.Intermediate(wesg[i] * ((sigma.iloc[i,j] + sigma_bar.iloc[i,j])/2) * wesg[j])

return -esg_portfo * ((return_portfo - rf)/sigma_portfo)

model.Minimize(obj())
model.solve(disp=False)
wesg = np.array( [item[0] for item in wesg], dtype=float)
print(wesg)
``````

## Results

The code results in:

``````[0.00000000e+00 1.31172076e-07 0.00000000e+00 0.00000000e+00
1.88847768e-01 1.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00
1.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00
0.00000000e+00 0.00000000e+00 1.00000000e+00 1.00000000e+00
9.07168980e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00]
``````

But, there are many ones in the result!! I have a constraint of `sum(wesg) == 1`! But the result indicates that somehow, Gekko doesn’t consider the constraint. If you try `print(wesg.sum())`then it will result:

``````7.096016879722077
``````

Which I expected to be exact 1!
How can I fix this issue, and where is the problem? Any help would be appreciated.