GEKKO 错误：@error: 不足 Model Model 必须至少包含 1 个变量和 1 个等式 STOPPING

Question

I am currently working on a model Mixed-Integer Non-Linear Programming (Bin Packing problem) for a university project, and I am trying to solve it using GEKKO.

Any piece of advice would be much appreciated.

# ___Initialize model___
m = GEKKO()

# ___Global options_____
m.options.SOLVER = 1  

ni = 4550
nj =6
nk= 35

# variables:
x = m.Array(m.Var, (ni,nk,nj), lb=0, integer=True) #integer variable                                            
y = m.Array(m.Var, (nj,nk), lb=0, ub=1, integer=True) #binary variable 

# Parameters:
w1=m.Const(w)
h1=m.Const(h)

Psum_total=m.Const(value=sum_total) 

P = m.Array(m.Param,ni)
for i in range(ni):
    P[i].value = PPP[i]

V = m.Array(m.Param,ni)
for i in range(ni):
  V[i].value=VV[i]

d= m.Array(m.Param,ni)
for i in range(ni):
    d[i] = 50

Psum_vetor=m.Array(m.Param,nj)
for j in range(nj):
  Psum_vetor[j].value=sumP[j]

#Intermediate
Lkj = [[m.Intermediate(m.sum([P[i]*x[i][k][j] for i in range(ni)])) for j in range(nj)] for k in range(nk)]
xyi = [m.Intermediate(m.sum([ x[i][k][j]*y[j][k] for k in range(nk) for j in range(nj)])) for i in range(ni)]
z= m.Intermediate(m.sum([xyi[i]*V[i] for i in range(ni)]))  

s = Psum_total
for k in range(nk):
    for j in range(nj):
        s += Lkj[k][j]

#  Equations
m.Equation([xyi[i] <= d[i] for i in range(ni)])          
m.Equation([sum([ Lkj[k][j]*y[j][k]   for j in range(nj)])  <= h1*w1 for k in range(nk)])
m.Equation([sum([Lkj[k][j]*y[j][k] for k in range(nk)]) ==  s/7 - P[j] for j in range(nj)]) 

m.Obj(-z)
m.options.IMODE = 3
m.solve()

print(x)

OUTPUT:

apm 35.186.172.229_gk_model1 <br><pre> ----------------------------------------------------------------
 APMonitor, Version 1.0.1
 APMonitor Optimization Suite
 ----------------------------------------------------------------
 
 
 --------- APM Model Size ------------
 Each time step contains
   Objects      :            0
   Constants    :            0
   Variables    :            0
   Intermediates:            0
   Connections  :            0
   Equations    :            0
   Residuals    :            0
 
 
 @error: Insufficient Model
 Model must contain at least 1 variable and 1 equation
 STOPPING...

---------------------------------------------------------------------------

Exception                                 Traceback (most recent call last)

<ipython-input-17-9adce22534dc> in <module>
    101 
    102 # Solve minimization
--> 103 m.solve()
    104 
    105 print(x)

/usr/local/lib/python3.7/dist-packages/gekko/gekko.py in solve(self, disp, debug, GUI, **kwargs)
   2183             #print APM error message and die
   2184             if (debug >= 1) and ('@error' in response):
-> 2185                 raise Exception(response)
   2186 
   2187             #load results

Exception:  @error: Insufficient Model
 Model must contain at least 1 variable and 1 equation
 STOPPING...

According to output, it seems to be that it's not recognizing variables or equations.

Thank you in advance for your help.

Answer 1

Here is a version that solves successfully:

# ___Initialize model___
from gekko import GEKKO
m = GEKKO()

# ___Global options_____
m.options.SOLVER = 1  

ni = 4
nj =6
nk= 3

# variables:
x = m.Array(m.Var, (ni,nk,nj), lb=0, integer=True) #integer variable                                            
y = m.Array(m.Var, (nj,nk), lb=0, ub=1, integer=True) #binary variable 

# Parameters:
w=1; h=1; sum_total=1
PPP=[1]*nj; VV = [1]*ni; sumP = [1]*nj
w1=m.Const(w)
h1=m.Const(h)

Psum_total=m.Const(value=sum_total) 

P = m.Array(m.Param,nj)
for i in range(nj):
    P[i].value = PPP[i]

V = m.Array(m.Param,ni)
for i in range(ni):
  V[i].value=VV[i]

d= m.Array(m.Param,ni)
for i in range(ni):
    d[i] = 50

Psum_vetor=m.Array(m.Param,nj)
for j in range(nj):
  Psum_vetor[j].value=sumP[j]

#Intermediate
Lkj = [[m.Intermediate(m.sum([P[i]*x[i][k][j] for i in range(ni)])) for j in range(nj)] for k in range(nk)]
xyi = [m.Intermediate(m.sum([ x[i][k][j]*y[j][k] for k in range(nk) for j in range(nj)])) for i in range(ni)]
z= m.Intermediate(m.sum([xyi[i]*V[i] for i in range(ni)]))  

s = Psum_total
for k in range(nk):
    for j in range(nj):
        s += Lkj[k][j]

#  Equations
m.Equation([xyi[i] <= d[i] for i in range(ni)])          
m.Equation([sum([ Lkj[k][j]*y[j][k]   for j in range(nj)])  <= h1*w1 for k in range(nk)])
m.Equation([sum([Lkj[k][j]*y[j][k] for k in range(nk)]) ==  s/7 - P[j] for j in range(nj)]) 

m.Maximize(z)
m.options.IMODE = 3
m.solve()

print(x)

with solution:

 Successful solution
 
 ---------------------------------------------------
 Solver         :  APOPT (v1.0)
 Solution time  :    10.8742999999959      sec
 Objective      :  -1.338429367332205E-014
 Successful solution
 ---------------------------------------------------
 
[[[[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]]

 [[[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]]

 [[[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]]

 [[[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [6.0] [0.0] [0.0]]
  [[0.0] [0.0] [0.0] [0.0] [0.0] [0.0]]]]

The original problem size with 4550x6x35 + 6x35 = 955710 binary variables may take a while to solve. The APOPT solver options can be adjusted to improve solution speed.

If there is an error with the example code, try:

pip install gekko --upgrade

to upgrade the gekko version to the latest distribution.

Answer 2

I just see that it was an index error. Thanks @Hedengren