问题
I'm using gekko for the first time to do optimization with python. I don't have a lot of experience with python, but I know the basics. I get error code -13 when I run the optimization:
#import Gekko optimization package
from gekko import gekko
import math
#create gekko model
m = gekko()
#constants
pi = math.pi
#initialize needed variables
frictionLoss = m.Var()
empirical = m.Var(value=1)
widthInlet = m.Var(value=1) #in meters
heightInlet = m.Var(value=1) #in meters
diameterOutlet = m.Var(value=1) #in meters
diameterCut = m.Var()
viscosity = m.Var(value=1) #kg/m*s
turns = m.Var()
velocityInlet = m.Var(value=1) #m/s
densityParticle = 10000 #kg/m**3
densityGas = 1.225 #kg/m**3
lengthCone = m.Var(value=1) #in meters
lengthCylinder = m.Var(value=1) #in meters
gravity = 9.806 #m/s^2
separation = m.Var()
#define box equations
m.Equation(frictionLoss==empirical*widthInlet*heightInlet/diameterOutlet**2)
m.Equation(turns==((pi*(2*lengthCylinder - lengthCone))/heightInlet))
m.Equation(diameterCut==((9*viscosity*widthInlet)/(2*pi*turns*velocityInlet*(densityParticle-densityGas)))**.5)
m.Equation(separation==((velocityInlet**2)/((diameterCut/2 )+ gravity)))
#add constraint on surface area
#m.Equation(separation<=.9)
#define object function (negative to maximize instead of minimize)
m.Obj(-separation)
#set mode to steady state optimization (solution does not change with time)
m.options.IMODE = 3
m.solve()
#print results
print('the optimized friction loss is: ' + str(frictionLoss.value))
print('the optimized empirical constant is: ' + str(empirical.value))
print('the optimized inlet width is: ' + str(widthInlet.value))
print('the optimized inlet height is: ' + str(heightInlet.value))
print('the optimized outlet diameter is: ' + str(diameterOutlet.value))
print('the optimized cut diameter is: ' + str(diameterCut.value))
print('the optimized viscosity is: ' + str(viscosity.value))
print('the optimized number of turns is: ' + str(turns.value))
print('the optimized inlet velocity is: ' + str(velocityInlet.value))
print('the optimized particle density is: ' + str(densityParticle.value))
print('the optimized gas density is: ' + str(densityGas.value))
print('the optimized cone length is: ' + str(lengthCone.value))
print('the optimized cylinder length is: ' + str(lengthCylinder.value))
The error returned is:
File "/Users/username/Documents/me 46200/optimization/cyclone optimization/cyclone_optimization.py", line 45, in <module>
m.solve()
File "/Users/username/opt/anaconda3/lib/python3.8/site-packages/gekko/gekko.py", line 2174, in solve
raise Exception(response)
Exception: @error: Solution Not Found
I'm sure this is another rookie fudge up of mine. Any assistance would be appreciated :)
回答1:
The IPOPT solver error is:
EXIT: Invalid number in NLP function or derivative detected.
An error occured.
The error code is -13
This typically occurs when there is a NaN evaluated because of divide by zero. You can either reformulate equations such as x==1/y to x*y==1 or else put a lower bound on y to avoid divide by zero. Here is a modified version of your problem that solves successfully.
#import Gekko optimization package
from gekko import gekko
import math
#create gekko model
m = gekko()
m.options.SOLVER=1
#constants
pi = math.pi
densityParticle = 10000 #kg/m**3
densityGas = 1.225 #kg/m**3
gravity = 9.806 #m/s^2
#initialize needed variables
lower = 1e-3
empirical = m.Var(value=1,lb=lower)
widthInlet = m.Var(value=1,lb=lower) #in meters
heightInlet = m.Var(value=1,lb=lower) #in meters
diameterOutlet = m.Var(value=1,lb=lower) #in meters
viscosity = m.Var(value=1,lb=lower) #kg/m*s
velocityInlet = m.Var(value=1,lb=lower) #m/s
lengthCone = m.Var(value=1,lb=lower) #in meters
lengthCylinder = m.Var(value=1,lb=lower) #in meters
frictionLoss = m.Var(lb=lower)
diameterCut = m.Var(lb=lower)
turns = m.Var(lb=lower)
separation = m.Var(lb=lower)
#define box equations
m.Equation(frictionLoss==empirical*widthInlet*heightInlet/diameterOutlet**2)
m.Equation(turns==((pi*(2*lengthCylinder - lengthCone))/heightInlet))
m.Equation(diameterCut==((9*viscosity*widthInlet)/(2*pi*turns*velocityInlet*(densityParticle-densityGas)))**.5)
m.Equation(separation==((velocityInlet**2)/((diameterCut/2 )+ gravity)))
#add constraint on surface area
m.Equation(separation<=.9)
#define object function (negative to maximize instead of minimize)
m.Maximize(separation)
#set mode to steady state optimization (solution does not change with time)
m.options.IMODE = 3
m.solve()
#print results
print('the optimized friction loss is: ' + str(frictionLoss.value[0]))
print('the optimized empirical constant is: ' + str(empirical.value[0]))
print('the optimized inlet width is: ' + str(widthInlet.value[0]))
print('the optimized inlet height is: ' + str(heightInlet.value[0]))
print('the optimized outlet diameter is: ' + str(diameterOutlet.value[0]))
print('the optimized cut diameter is: ' + str(diameterCut.value[0]))
print('the optimized viscosity is: ' + str(viscosity.value[0]))
print('the optimized number of turns is: ' + str(turns.value[0]))
print('the optimized inlet velocity is: ' + str(velocityInlet.value[0]))
print('the optimized particle density is: ' + str(densityParticle))
print('the optimized gas density is: ' + str(densityGas))
print('the optimized cone length is: ' + str(lengthCone.value[0]))
print('the optimized cylinder length is: ' + str(lengthCylinder.value[0]))
The solution is:
apm 136.36.211.159_gk_model0 <br><pre> ----------------------------------------------------------------
APMonitor, Version 0.9.2
APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------
Each time step contains
Objects : 0
Constants : 0
Variables : 13
Intermediates: 0
Connections : 0
Equations : 6
Residuals : 6
Number of state variables: 13
Number of total equations: - 5
Number of slack variables: - 1
---------------------------------------
Degrees of freedom : 7
----------------------------------------------
Steady State Optimization with APOPT Solver
----------------------------------------------
Iter Objective Convergence
0 2.16410E-01 8.99000E-01
1 -4.04256E-01 2.98848E-01
2 -9.00000E-01 7.23825E-02
3 -8.89266E-01 9.38042E-02
4 -8.90825E-01 2.39141E-01
5 -8.96687E-01 4.43769E-02
6 -8.99389E-01 1.59439E-02
7 -9.00000E-01 5.84573E-03
8 -9.00000E-01 2.35805E-10
9 -9.00000E-01 2.35805E-10
Successful solution
---------------------------------------------------
Solver : APOPT (v1.0)
Solution time : 1.410000000032596E-002 sec
Objective : -0.900000000000000
Successful solution
---------------------------------------------------
the optimized friction loss is: 0.21599357118
the optimized empirical constant is: 0.97878134972
the optimized inlet width is: 0.84720656046
the optimized inlet height is: 0.32475560886
the optimized outlet diameter is: 1.1165943231
the optimized cut diameter is: 0.05806387037
the optimized viscosity is: 0.99182260906
the optimized number of turns is: 0.012001017114
the optimized inlet velocity is: 2.9751518855
the optimized particle density is: 10000
the optimized gas density is: 1.225
the optimized cone length is: 1.2088239788
the optimized cylinder length is: 0.60503227947
There is additional information in the Design Optimization course such as the two bar truss problem that is related to your problem.
来源：https://stackoverflow.com/questions/64491175/python-optimization-using-gekko