A few tips:
- Use the Python power operator
** instead of ^
- Every equation must have an equality
== or inequality >, <, >=, <=.
- Define multiple variables with one line using
m.Array() such as for slk and add that have dimension 3.
- See the solver result with
disp=True, especially if the problem is not solvable or has an error.
Here is a modified version of your script:
from gekko import GEKKO
import math
m = GEKKO ()
#Parameters
a = 131.078
b = 1.48477
c = 0.90798
d0 = 1.47588
e0 = 1.47588
d = math.cos(d0)
e = math.sin(e0)
lim1 = 300
lim2 = 100
lim3 = 200
rate1 = 30
rate2 = 31
rate3 = 28
rate4 = 29
rate5 = 30
add = m.Array(m.Var,3,lb=0)
slk = m.Array(m.Var,3,lb=0)
x1 = m.Var(value = 390,lb=0,ub=400)
x2 = m.Var(value = 1000,lb=0,ub=1000)
x3 = m.Var(value = 419.5,lb=340,ub=420)
x4 = m.Var(value = 340.5,lb=340,ub=420)
x5 = m.Var(value = 198.175,lb=-1000,ub=1000)
x6 = m.Var(value = 0.5,lb=0,ub=0.5236)
m.Equation(add[0] == x1 - lim1 + slk[0])
m.Equation(add[1] == x2 - lim2 + slk[1])
m.Equation(add[2] == x2 - lim3 + slk[2])
m.Equation(300 - x3*x4*m.cos(b - x6)/a + c*x3**2*d/a == 0)
m.Equation(-x3*x4*m.cos(b + x6)/a + c*x4**2*d/a == 0)
m.Equation(-x3*x4*m.sin(b + x6)/a + c*x4**2*e/a == 0)
m.Equation(200 - x3*x4*m.sin(b - x6)/a + c*x3**2*e/a == 0)
m.Minimize(rate1*x1 + (rate2-rate1)*add[0])
m.Minimize(rate3*x2 + (rate4-rate3)*add[1] + (rate5-rate4)*add[2])
m.solve(disp=True)
print(x1.value)
print(x2.value)
print(x3.value)
print(x4.value)
print(x5.value)
print(x6.value)
The solver correctly produces the result that the problem is infeasible.
EXIT: Converged to a point of local infeasibility. Problem may be infeasible.
An error occured.
The error code is 2
---------------------------------------------------
Solver : IPOPT (v3.12)
Solution time : 4.060000000026776E-002 sec
Objective : 5159.30673181783
Unsuccessful with error code 0
---------------------------------------------------
Creating file: infeasibilities.txt
Use command apm_get(server,app,'infeasibilities.txt') to retrieve file
@error: Solution Not Found
The Hock & Schitkowski benchmark 87 that you likely found on the APMonitor website is:
! Nonlinear electrical network
! The problem is corrected to conform to the problem as stated in
! D. M. Himmelblau, Applied Nonlinear Programming,
! McGraw-Hill, 1972, pp. 413-414
! except that jump-discontinuities in the objective function are
! omitted by stating it as the sum of two piecewise-linear terms
Model hs87
Parameters
a = 131.078
b = 1.48477 ! Hock & Schittkowski say 1.48577
c = 0.90798
d0 = 1.47588
e0 = 1.47588
d = cos(d0)
e = sin(e0)
lim[1] = 300
lim[2] = 100
lim[3] = 200
rate[1] = 30
rate[2] = 31
rate[3] = 28
rate[4] = 29
rate[5] = 30
End Parameters
Variables
add[1:3] > 0
slk[1:3]
x[1] = 390, >= 0, <= 400
x[2] = 1000, >= 0, <= 1000
x[3] = 419.5, >= 340, <= 420
x[4] = 340.5, >= 340, <= 420
x[5] = 198.175, >= -1000, <= 1000 ! Hock & Schittkowski say <= 10000
x[6] = 0.5, >= 0, <= 0.5236
obj[1:2]
End Variables
Equations
! piecewise linear
add[1] = x[1] - lim[1] + slk[1]
add[2] = x[2] - lim[2] + slk[2]
add[3] = x[2] - lim[3] + slk[3]
x[1] = 300 - x[3]*x[4]*cos(b - x[6])/a + c*x[3]^2*d/a
x[2] = -x[3]*x[4]*cos(b + x[6])/a + c*x[4]^2*d/a
x[5] = -x[3]*x[4]*sin(b + x[6])/a + c*x[4]^2*e/a
200 - x[3]*x[4]*sin(b - x[6])/a + c*x[3]^2*e/a = 0
! best known objective = 8827.5977
obj[1] = rate[1]*x[1] + (rate[2]-rate[1])*add[1]
obj[2] = rate[3]*x[2] + (rate[4]-rate[3])*add[2] + (rate[5]-rate[4])*add[3]
End Equations
End Model
You can solve this through the online interface. It looks like your equations aren't quite correct, but they are close. You can use the online interface to compare answers.
