在 Python Gekko 中使用 APMonitor model

Question

Is there a way to use an APMonitor model directly within Gekko? For example, could I solve the Hock Schittkowski benchmark problems without re-writing them in Gekko but still solve them with Gekko? Example is problem 43, the Rosen-Suzuki problem. In APMonitor it is:

File: hs043.apm

Model hs43
  Variables
    x[1:4] = 0
    obj
  End Variables

  Equations
    x[1]^2 +x[2]^2 +x[3]^2 +x[4]^2 +x[1] -x[2] +x[3] -x[4] <= 8
    x[1]^2 +2*x[2]^2 +x[3]^2 +2*x[4]^2 -x[1] -x[4] <= 10
    2*x[1]^2 +x[2]^2 +x[3]^2 +2*x[1] -x[2] -x[4] <= 5          

    ! best known objective = -44
    ! best known solution
    ! x[1] = 0
    ! x[2] = 1
    ! x[3] = 2
    ! x[4] = -1
    obj = x[1]^2 + x[2]^2 + 2*x[3]^2 + x[4]^2 - 5*x[1] - 5*x[2] - 21*x[3] + 7*x[4]
  End Equations
End Model

The model in Gekko is similar:

Python Gekko

from gekko import GEKKO
m = GEKKO(remote=False)
x1,x2,x3,x4 = m.Array(m.Var,4)
m.Equation(x1**2+x2**2+x3**2+x4**2+x1-x2+x3-x4<=8)
m.Equation(x1**2+2*x2**2+x3**2+2*x4**2-x1-x4<=10)
m.Equation(2*x1**2+x2**2+x3**2+2*x1-x2-x4<=5)
m.Minimize(x1**2+x2**2+2*x3**2+x4**2-5*x1-5*x2-21*x3+7*x4)
m.solve()
print(x1,x2,x3,x4)
print('Objective: ',m.options.OBJFCNVAL)

When I open the run folder with m.open_folder() with the Gekko application, I see that Gekko is writing an APMonitor file gk_model0.apm .

Model
Variables
    v1 = 0
    v2 = 0
    v3 = 0
    v4 = 0
End Variables
Equations
    (((((((((v1)^(2))+((v2)^(2)))+((v3)^(2)))+((v4)^(2)))+v1)-v2)+v3)-v4)<=8
    (((((((v1)^(2))+((2)*(((v2)^(2)))))+((v3)^(2)))+((2)*(((v4)^(2)))))-v1)-v4)<=10
    (((((((2)*(((v1)^(2))))+((v2)^(2)))+((v3)^(2)))+((2)*(v1)))-v2)-v4)<=5
    minimize (((((((((v1)^(2))+((v2)^(2)))+((2)*(((v3)^(2)))))+((v4)^(2)))-((5)*(v1)))-((5)*(v2)))-((21)*(v3)))+((7)*(v4)))
End Equations

End Model

Could I use hs043.apm instead?

Answer 1

The m.Raw() function allows you to use APMonitor code in Gekko, although it isn't recommended except for advanced users. Here is hs043.apm in gekko.

model = '''
Model hs43
  Variables
    x[1:4] = 0
    obj
  End Variables

  Equations
    x[1]^2 +x[2]^2 +x[3]^2 +x[4]^2 +x[1] -x[2] +x[3] -x[4] <= 8
    x[1]^2 +2*x[2]^2 +x[3]^2 +2*x[4]^2 -x[1] -x[4] <= 10
    2*x[1]^2 +x[2]^2 +x[3]^2 +2*x[1] -x[2] -x[4] <= 5          

    ! best known objective = -44
    ! best known solution
    ! x[1] = 0
    ! x[2] = 1
    ! x[3] = 2
    ! x[4] = -1
    obj = x[1]^2 + x[2]^2 + 2*x[3]^2 + x[4]^2 &
          - 5*x[1] - 5*x[2] - 21*x[3] + 7*x[4]
  End Equations
End Model
'''

from gekko import GEKKO
m = GEKKO(remote=False)
m.Raw(model)
m.solve()
print('Objective: ', m.options.OBJFCNVAL)

It solves with Objective: -44.00000003 , the same as the Python gekko application. One drawback to using an APMonitor model is that you'll need to retrieve the results because they won't be loaded back into Python variables.

import json
with open(m.path+'//results.json') as f:
    results = json.load(f)
print(results)

Here is the results dictionary:

{'time': [0.0], 'hs43.x[1]': [1.1795097003e-09], \
 'hs43.x[2]': [1.0000000007], 'hs43.x[3]': [2.0000000018], \ 
 'hs43.x[4]': [-0.99999999967], 'hs43.obj': [-44.00000003], \
 'hs43.slk_1': [0.0], 'hs43.slk_2': [0.99999999287], \
 'hs43.slk_3': [0.0]}