I am trying to understand how gekko and its different types of custom variables work. So I wrote a very simple optimization problem, but it won’t find the optimal solution, at least this is what i think the error message means.
The code is a simple set switch combination (braco_gas and braco_eh, both binaries) multiplied by some weights (vazao and volume, both continuos).
I want to find which combination of switches and weights yields the maximum objective value. See below the objective:
Objective = vazao_gas * braco_gas_1 + volume_gas * braco_gas_2 + vazao_eh * braco_eh_1 + volume_eh * braco_eh_2
See the code below:
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from gekko import GEKKO2
import numpy as np3
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m = GEKKO(remote=False)5
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# binary variables7
braco_gas_1 = m.Var(integer=True, lb=0,ub=1)8
braco_eh_1 = m.Var(integer=True, lb=0,ub=1)9
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braco_gas_2 = m.Var(integer=True, lb=0,ub=1)11
braco_eh_2 = m.Var(integer=True, lb=0,ub=1)12
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# continuous variables14
vazao_gas = m.Var(value=100,lb=0,ub=150)15
vazao_eh = m.Var(value=100,lb=0,ub=150)16
17
#constants18
volume_gas = 100019
volume_eh = 200020
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# I want to see each parcel of the objective22
tempo_b1 = m.MV(vazao_gas*braco_gas_1 + volume_gas*braco_gas_2)23
tempo_b1.STATUS=124
tempo_b2 = m.MV(vazao_eh*braco_eh_1 + volume_eh*braco_eh_2)25
tempo_b2.STATUS=126
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# that is supposed to be the objective28
tempo_total = m.MV(tempo_b1+tempo_b2, lb=0, ub = 4000)29
tempo_total.STATUS=130
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# Only of binary variable of each group can be true32
m.Equation (braco_gas_1+braco_gas_2 == 1)33
m.Equation (braco_eh_1+braco_eh_2 == 1)34
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# I want to maximize the objective36
m.Maximize(tempo_b1+tempo_b2)37
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m.options.SOLVER = 139
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m.solve() # solve41
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print('Braco_gas_1:'+str(braco_gas_1.value))43
print('Braco_gas_2:'+str(braco_gas_2.value))44
print('Braco_eh_1:'+str(braco_eh_1.value))45
print('Braco_eh_2:'+str(braco_eh_2.value))46
print('vazao_gas:'+str(vazao_gas.value))47
print('vazao_eh:'+str(vazao_eh.value))48
print('volume_gas:'+str(volume_gas))49
print('volume_eh:'+str(volume_eh))50
print('tempo_b1:'+str(tempo_b1.value))51
print('tempo_b2:'+str(tempo_b2.value))52
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print('tempo_total:'+str(tempo_total.value))54
Following the error message:
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----------------------------------------------------------------2
APMonitor, Version 1.0.03
APMonitor Optimization Suite4
----------------------------------------------------------------5
6
7
--------- APM Model Size ------------8
Each time step contains9
Objects : 010
Constants : 011
Variables : 912
Intermediates: 013
Connections : 014
Equations : 315
Residuals : 316
17
Number of state variables: 918
Number of total equations: - 219
Number of slack variables: - 020
---------------------------------------21
Degrees of freedom : 722
23
----------------------------------------------24
Steady State Optimization with APOPT Solver25
----------------------------------------------26
Iter: 1 I: 0 Tm: 0.00 NLPi: 4 Dpth: 0 Lvs: 3 Obj: -1.00E+15 Gap: NaN27
Iter: 2 I: -1 Tm: 0.00 NLPi: 0 Dpth: 1 Lvs: 2 Obj: -1.00E+15 Gap: NaN28
Iter: 3 I: -2 Tm: 0.00 NLPi: 2 Dpth: 1 Lvs: 1 Obj: -1.00E+15 Gap: NaN29
Iter: 4 I: -2 Tm: 0.00 NLPi: 2 Dpth: 1 Lvs: 0 Obj: -1.00E+15 Gap: NaN30
Warning: no more possible trial points and no integer solution31
Maximum iterations32
33
---------------------------------------------------34
Solver : APOPT (v1.0)35
Solution time : 0.0208 sec36
Objective : -1.E+1537
Unsuccessful with error code 038
---------------------------------------------------39
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Creating file: infeasibilities.txt41
Use command apm_get(server,app,'infeasibilities.txt') to retrieve file42
@error: Solution Not Found43
44
---------------------------------------------------------------------------45
Exception Traceback (most recent call last)46
~AppDataLocalTemp/ipykernel_10100/3307325789.py in <module>47
32 m.options.SOLVER = 148
33 49
---> 34 m.solve() # solve50
35 51
36 print('Braco_gas_1:'+str(braco_gas_1.value))52
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~Anaconda3libsite-packagesgekkogekko.py in solve(self, disp, debug, GUI, **kwargs)54
2138 print("Error:", errs)55
2139 if (debug >= 1) and record_error:56
-> 2140 raise Exception(apm_error)57
2141 58
2142 else: #solve on APM server59
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Exception: @error: Solution Not Found61
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Answer
The problem is currently unbounded (see Objective: -1.E+15).
Use m.Intermediate() instead of m.MV(). An MV (Manipulated Variable) is a degree of freedom that the optimizer can use to achieve an optimal objective among all of the feasible solutions. Because tempo_b1, tempo_b2, and tempo_total all have equations associated with solving them, they need to either be:
- Regular variables with
m.Var()and a correspondingm.Equation()definition - Intermediate variables with
m.Intermediate()to define the variable and equation with one line.
Here is the solution to the simple Mixed Integer Linear Programming (MINLP) optimization problem.
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----------------------------------------------------------------2
APMonitor, Version 1.0.13
APMonitor Optimization Suite4
----------------------------------------------------------------5
6
--------- APM Model Size ------------7
Each time step contains8
Objects : 09
Constants : 010
Variables : 711
Intermediates: 212
Connections : 013
Equations : 614
Residuals : 415
16
Number of state variables: 717
Number of total equations: - 318
Number of slack variables: - 019
---------------------------------------20
Degrees of freedom : 421
22
----------------------------------------------23
Steady State Optimization with APOPT Solver24
----------------------------------------------25
Iter: 1 I: 0 Tm: 0.00 NLPi: 4 Dpth: 0 Lvs: 0 Obj: -3.00E+03 Gap: 0.00E+0026
Successful solution27
28
---------------------------------------------------29
Solver : APOPT (v1.0)30
Solution time : 1.529999999911524E-002 sec31
Objective : -3000.00000000000 32
Successful solution33
---------------------------------------------------34
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Braco_gas_1:[0.0]2
Braco_gas_2:[1.0]3
Braco_eh_1:[0.0]4
Braco_eh_2:[1.0]5
vazao_gas:[150.0]6
vazao_eh:[150.0]7
volume_gas:10008
volume_eh:20009
tempo_b1:[1000.0]10
tempo_b2:[2000.0]11
tempo_total:[3000.0]12
The complete script:
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from gekko import GEKKO2
import numpy as np3
4
m = GEKKO(remote=False)5
6
# binary variables7
braco_gas_1 = m.Var(integer=True, lb=0,ub=1)8
braco_eh_1 = m.Var(integer=True, lb=0,ub=1)9
10
braco_gas_2 = m.Var(integer=True, lb=0,ub=1)11
braco_eh_2 = m.Var(integer=True, lb=0,ub=1)12
13
# continuous variables14
vazao_gas = m.Var(value=100,lb=0,ub=150)15
vazao_eh = m.Var(value=100,lb=0,ub=150)16
17
#constants18
volume_gas = 100019
volume_eh = 200020
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# I want to see each parcel of the objective22
tempo_b1 = m.Intermediate(vazao_gas*braco_gas_1 + volume_gas*braco_gas_2)23
tempo_b2 = m.Intermediate(vazao_eh*braco_eh_1 + volume_eh*braco_eh_2)24
25
# that is supposed to be the objective26
tempo_total = m.Var(lb=0, ub = 4000)27
m.Equation(tempo_total==tempo_b1+tempo_b2)28
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# Only of binary variable of each group can be true30
m.Equation (braco_gas_1+braco_gas_2 == 1)31
m.Equation (braco_eh_1+braco_eh_2 == 1)32
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# I want to maximize the objective34
m.Maximize(tempo_b1+tempo_b2)35
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m.options.SOLVER = 137
m.solve() # solve38
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print('Braco_gas_1:'+str(braco_gas_1.value))40
print('Braco_gas_2:'+str(braco_gas_2.value))41
print('Braco_eh_1:'+str(braco_eh_1.value))42
print('Braco_eh_2:'+str(braco_eh_2.value))43
print('vazao_gas:'+str(vazao_gas.value))44
print('vazao_eh:'+str(vazao_eh.value))45
print('volume_gas:'+str(volume_gas))46
print('volume_eh:'+str(volume_eh))47
print('tempo_b1:'+str(tempo_b1.value))48
print('tempo_b2:'+str(tempo_b2.value))49
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print('tempo_total:'+str(tempo_total.value))51
Additional tutorials are available in the documentation or in the 18 example problems (with videos).