Error while setting up MILP constraints
回答済みHello all,
I have difficulties to implement constraints for my MILP. The aim is to build a MILP, which schedules jobs on parallel machines m, while having a recipe r. I have the following model notation.
The model formulation is as following:
I defined the data and their ranges and added the decision variables.
X = mo.addVars(numberofJobs, numberofMachines, numberofPositions, vtype =GRB.BINARY, name="X")
Y = mo.addVars(numberofMachines, numberofPositions, numberofRecipes, vtype =GRB.BINARY, name="Y")
Z = mo.addVars(numberofMachines, numberofPositions, numberofRecipes, numberofRecipes, vtype =GRB.BINARY, name="Z")
U = mo.addVars(numberofJobs, vtype =GRB.BINARY, name="U")
S = mo.addVars(numberofMachines, numberofPositions, vtype =GRB.CONTINUOUS, name="S")
C = mo.addVars(numberofMachines, numberofPositions, vtype =GRB.CONTINUOUS, name="C")
The constraint 2.2 shows the error: IndexError: list index out of range.
for m in machines:
for p in positions:
mo.addConstr(S[m,p]+ gp.quicksum([x[j][r][m]*X[j,m,p] for j in jobs]) == C[m,p], "NB1_" + str(m)+str(p))
for m in machines:
for p in positions:
for r in recipes:
for re in recipes:
mo.addConstr(Z[m,p,r,re]>=Y[m,p-1,r]+Y[m,p,re]-1, "NB3_"+str(m)+str(p)+str(r)+str(r))
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Gurobi Staff
Hi Moritz,
It is not possible to reproduce your issue without a minimal reproducible example. You should try to isolate the Index and Key errors.
The IndexError means that an array access to at least one of \(\texttt{S[m,p],x[j][r][m],X[j,m,p],C[m,p]}\) was out of the respective array bounds.
The KeyError means that you tried to access an array at position \(\texttt{0,-1,0}\). Probably all your arrays start at \(\texttt{(0,0,0)}\).
Best regards,
Jaromił0 -
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Hi Jaromil,
thanks for your fast response! I could fix the IndexError: and the KeyError: with your help and advises.
There is one more question I have regarding my model. I want to get the maximum value of a decision variable in my objective and in a set of constraints as shown below. I want to get the maximum value of C[m,p].
I tried the following two methods.
(1) with gurobipy.max_() lookingmo.setObjective(gp.quicksum(H * U[j] for j in jobs) + gp.max_(C[m,p] for m in machines for p in positions) , GRB.MINIMIZE)Failure code: GurobiError: Unsupported type (<class 'gurobipy.GenExprMax'>) for LinExpr addition argument
and with max()
mo.setObjective(gp.quicksum(H * U[j] for j in jobs) + max(C[m,p] for m in machines for p in positions) , GRB.MINIMIZE)
Failure Code: TypeError: '>' not supported between instances of 'Var' and 'Var'
(2) for the constraint
the code looks like:for m in machines:
mo.addConstr(gp.max_(C[m,p] for p in positions)>=C[m,p], "NB10_"+str(m))Failure code: GurobiError: General expressions can only be equal to a single var
For me the gp.max_() function makes the most sense. Maybe you can help me with this issue as well.
Best regards,
Moritz0 -
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Hi Moritz,
When working with general constraints such as the max function, you have to introduce an auxiliary optimization variable to hold the value of the function. This is the \(\texttt{resvar}\) argument in the addGenConstrMax method. To make your code work, you have to model
\[\begin{align*}
z_m &= \max \{C_{m,p}| p \in P\} \quad \forall m \in M\\
w &= \max \{C_{m,p}| p \in P, m \in M\}
\end{align*}\]A possible Python code might be
z = mo.addVars(machines, lb=-GRB.INFINITY)
for m in machines:
mo.addConstr(z[m] == gp.max_(C[m,p] for p in positions))
mo.addConstr(z[m]>=C[m,p], "NB10_"+str(m))
w = mo.addVar(lb=-GRB.INFINITY)
mo.addConstr(w == gp.max_(C[m,p] for p in positions for m in machines))
# use w in your objectiveBest regards,
Jaromił1 -
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Hi Jaromił,
huge thanks for your help. My MILP-model is now working and there are no error messages popping up anymore.
Best regards,
Moritz0 -
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