Gurobi Python: fail to call the decision variable outside ".addConstr" function
回答済みHi there, I am using the Gurobi Python and trying to solve an ILP optimization problem as shown below:
where x_{s,n} is the decision variable, and R is a function of x_{s,n}.
In this problem, since the expressions for R is very complicated (i.e., it is hard to implement R in a single line in model.addConstr(...)). Thus, we want to define R first, then construct the constraints. A simplified version of the code that reflects our idea is as follows：
!pip install gurobipy
import gurobipy as gp
from gurobipy import GRB
import math
import numpy as np
# Create a new model
m = gp.Model("mip1")
# define the fixed number
C_exp_c = 111
S = 20 # total service number (number of VNF chains)
N = 8 # VNF blocks 【Notice, we only consider the clocks in the cloud!】
shape = (S, N)
# Create variables
x_vars = m.addVars(shape, vtype=GRB.BINARY, name = 'X')
#
R_c = np.zeros(shape)
R_e = np.zeros(shape)
# define R
for s in range(S):
for n in range(N):
R_c[s, n] = max(1 - x_vars[s, n], 0)
R_e[s, n] = max(1 - x_vars[s, n], 0)
# <= Constraint: Equation (8b)
m.addConstr((GRB.quicksum(R_c[s, n] for n in range(N) for s in range(S))) <= C_exp_c)
# set objective func
objective = GRB.quicksum((R_c[s, n] + R_e[s, n]) for n in range(N) for s in range(S))
m.ModelSense = GRB.MINIMIZE
m.setObjective(objective)
m.optimize()
solution = m.getAttr('x', x_vars )
when we excecute, there is an error shows up as
I search for many Gurobi examples in Github, and find that there is no example shows they do the similar thing -- other than call the decision variables outside ".addConstr" function, all of them call the decision variables directly in the function of ".addConstr".
The first question is: could I call the decision variables outside ".addConstr" function shown in my codes?
second is, if yes, could you please help me figure out what is wrong with my code? Since I am new to Python, maybe there are many silly mistakes.....anyways, Thank you very much!
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Gurobi Staff
There are 2 issues with your code.
1. You are not creating a 20x3 variable called x_vars but rather you are creating 2 variables x[20] and x[8] accessible via \(\texttt{x[20]}\) and \(\texttt{x[8]}\). Thus, you get the KeyError. Constructing your x variables via
x_vars = m.addVars(S,N, vtype=GRB.BINARY, name = 'X')
solves this issue.
2. You are taking the max value of a LinExpr object. This is not defined. Gurobi has its own max function to handle this. You can use the addGenConstrMax method to formulate the expressions you need. For this, you will have to introduce auxiliary variables for each term \(1-x_{s,n}\) because the addGenConstrMax method accepts only single optimization variables. Moreover, you will have to define \(\texttt{R_c}\) as optimization variables.
The best thing is that you don't even need the max expression because your x variables are Binary. This means that
\[R_c = \max {1-x,0} = 1-x.\]
I don't fully understand why you need \(\texttt{R_c}\) and \(\texttt{R_e}\), since both equal the same value.
So what should work for you is
x_vars = m.addVars(S, N, vtype=GRB.BINARY, name='X')
R_c = m.addVars(S, N, vtype=GRB.BINARY, name='R_c')
for s in range(S):
for n in range(N):
m.addConstr(R_c[s,n] == 1 - x_vars[s,n], name="max_%d%d"%(s,n))
[...]Best regards,
Jaromił0 -
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Dear Jaromił,
Thank you so much for your warm and professional answer, It does help a lot!
To answer your question: In fact, R_c and R_e are different functions with respect to x. This program is a simplified version, and I'm sorry to confuse you by writing R_c and R_e in the same form due to our negligence. But I believe this did not affect the accuracy of your reply, you answered the question we wanted to ask, thank you very much!
We will modify our Python program according to your suggestions. If we encounter a new problem, we will try to solve it ourselves first. If it does not work, we will continue to follow up under this problem.
Finally, this forum is really awesome! Thank you for providing such a platform!
Best,
Han
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