Constraint Implementation
回答済みHi. I am working on my thesis relating to the sports league scheduling issue and came across this constraint.
Any idea on how can I implement this? I am using Python for my development.
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Gurobi Staff
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You should be able to model these constraints with the quicksum function.
It would look something like
[...]
model.addConstrs(
gp.quicksum(x[i,j,l] for j in T2[c] for l in range(k,k+intp[c]-1)) <= max[c]
for c in CA3HH for i in T1[c] for k in P if k <= abs(k) + 1 - intp[c]))Note that this is more a pseudo code, because I don't know any of your data structures. Also note that \(\texttt{range(k,k+intp[c]-1}\) does not contain the last entry \(\texttt{k+intp[c]-1}\), so if you need it, you should go for \(\texttt{range(k,k+intp[c]}\).
Best regards,
Jaromił0 -
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Hi.
Thanks. It worked well. Furthermore, I came across this constraint:
How can you incorporate a quicksum with a GenConstrMax?
Thanks in advance
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You can work in a similar way as above. However, when working with general constraints, you have to introduce auxiliary variables. This is because general constraints accept only single Var objects as input and require a Var object to define its output. In your case what you will have to model is similar to
\[\begin{align*}
z_{\min,l} &= k_{\min} - \sum_{j \in T_2} \sum_{s=l}^{l+k+1} x_{i,j,s}\\
z_{\max,l} &= \sum_{j \in T_2} \sum_{s=l}^{l+k+1} x_{i,j,s} - k_{\max}\\
w_l &= \max \{z_{\min,l}, z_{\max,l}, 0\} \\
d_i &= \sum_{l=1}^{|P|-k+1}w_l
\end{align*}\]
where \(z,w\) are auxiliary optimization variables (Var objects). I am not 100% sure about all the indices so you will have to figure this one out. You can model the \(\max\) functions by using the addGenConstrMax method.Best regards,
Jaromił0 -
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Hi.
Thanks for this. I came across this constraint:
How can I implement this?
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It is very similar to the first constraint you posted. Thus, you can use the quicksum function as discussed above.
Best regards,
Jaromił0 -
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Thanks for your response. Furthermore, I have the following constraint:
How can I implement the k not using Gurobi?
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What exactly do you mean by
How can I implement the k not using Gurobi?
You can define \(\bar{k}\) and use it in your constraints.
k_bar = ...
Are you sure that the sum you posted is correct? You don't use the \(k\) index used for \(k=\bar{k}\) but you use \(k\) for the constraint index \(k \in P\).
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That is how it is defined, but it does not make sense now that I think of it. Thanks for your help
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Hi.
How would this be implemented in Gurobi with python? Cause I got stuck while implementing
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This has been already discussed above. You can use the quicksum function and the addGenConstrMax method.
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