Gekko - if3() statement for choosing between two expressions in ODE

Question

I tried solving a differential equation having a logical condition in Gekko. I know that Gekko does not like these things but I supposed that simple if3() function in order to switch between the two given expressions (R1,R2) will get some solution. Here is a simple example code that failed - Solution not found.

import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt

A=1
B=1e-5
C=2
D=0.01 
G=1
y0=120

m = GEKKO()    # create GEKKO model
nt = 101
m.time = np.linspace(0,100,nt) # time points

y = m.Var(y0) # create GEKKO variable

R1 = m.Intermediate(-(y+A-A/(y/C+1)**(B/D))/G*(D*y+D*C))
R2 = m.Intermediate(-0.1*y)

z = m.Var()              # This way - Solution not found
z = m.if3(y-60,R1,R2)    #
m.Equation(y.dt()== z)   # 

#m.Equation(y.dt()== R1)
#m.Equation(y.dt()== R2)

# solve ODE
m.options.IMODE = 4
m.options.NODES = 5
m.solve(disp=False)

# plot results
plt.plot(m.time,y)
plt.xlabel('time')
plt.ylabel('y(t)')

Unfortunately, it seems I did not figure out yet how to overcome these problems by reading the article about Logical conditions in Optimization.

Best Regards,

Radovan

user_2366941 · Answer

The posted script gives the error:

Exception:  @error: Solution Not Found

To see additional details about the error, turn on the display with disp=True. This gives additional detail that indicates that the problem is infeasible.

 Number of state variables:    2800
 Number of total equations: -  2000
 Number of slack variables: -  800
 ---------------------------------------
 Degrees of freedom       :    0
 
 ----------------------------------------------
 Dynamic Simulation with APOPT Solver
 ----------------------------------------------
Iter:     1 I: -1 Tm:     13.07 NLPi:    9 Dpth:    0 Lvs:    0 Obj:  0.00E+00 Gap:       NaN
 Warning: no more possible trial points and no integer solution
 Maximum iterations
 
 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :  13.116200000000001 sec
 Objective      :  0.
 Unsuccessful with error code  0
 ---------------------------------------------------
 
 Creating file: infeasibilities.txt
 Use command apm_get(server,app,'infeasibilities.txt') to retrieve file
 @error: Solution Not Found

A couple issues with the model:

z = m.Var() is not needed because the z = if3() function defines the variable.
IMODE=6 is needed because there are slack variables in the problem and an optimization mode is needed to solve the problem.
Try if2() instead of if3(). It seems to work better with the MPCC form than the Mixed Integer form.
Solver APOPT performs better for this problem. Try m.options.SOLVER=1.

import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt

A=1; B=1e-5; C=2; D=0.01; G=1
y0=120

m = GEKKO(remote=False)    # create GEKKO model
nt = 101
m.time = np.linspace(0,50,nt) # time points

y = m.Var(y0) # create GEKKO variable

R1 = m.Intermediate(-(y+A-A/(y/C+1)**(B/D))/G*(D*y+D*C))
R2 = m.Intermediate(-0.1*y)

z = m.if2(y-60,0,1) 
m.Equation(y.dt()== (1-z)*R1+z*R2)

# solve ODE
m.options.IMODE  = 6
m.options.SOLVER = 1
m.options.NODES  = 5
m.solve(disp=True)

# plot results
plt.subplot(2,1,1)
plt.plot(m.time,y)
plt.plot([0,50],[60,60],'r--')
plt.ylabel('y(t)'); plt.grid()
plt.subplot(2,1,2)
plt.plot(m.time,z)
plt.ylabel('z(t)'); plt.grid()
plt.xlabel('time')
plt.show()

The alternative to using an if statement in the model is to integrate in a loop and check the condition y>60 to switch to the other model.

Gekko - if3() statement for choosing between two expressions in ODE

1 Answers