How can I use addVars for indexes that are dependant? (in Python)

Answered

Eduardo Praça

May 05, 2022 00:14

Hello. I have a code with a binary variable that has 3 indexes: 'x[i,j,k]'

I understand that for instance, if

I = [1,2,3]

J=[1,2]

K=[1,2,3,4]

x = m.addVars(I,J,K,vtype = GRB.BINARY,name = 'X') would create 4*3*2 = 24 variables no problem.

What if I had not J bui J(i), such as:

I = [1,2,3]

Ji=[[1,2],[1],[2]]

K = [1,2,3,4]

How can I create the 1*2*4 + 1*1*4 + 1*1*4 = 16 variables?

This code doesn't seem to respond properly, why so?

 for i in I:
    J = J[i-1]
    x = m.addVars(I,J,K,vtype = GRB.BINARY,name = 'X')

Thank you in advance.

0

Comments

3 comments

Official comment
Simranjit Kaur

Gurobi Staff

November 16, 2025 23:38
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Simon Bowly

Gurobi Staff

May 05, 2022 03:22 Edited
Hi Eduardo,

You can build sparse indexes like this, but you'll need to create a list of index tuples explicitly first and pass it to addVars. One way to do this is the following:
```
I = [1, 2, 3]
Ji = [[1, 2], [1], [2]]
K = [1, 2, 3, 4]

indices = [(i, j, k) for i, J in zip(I, Ji) for j in J for k in K]
x = m.addVars(indices, name='X')
```
(Your original code was close to what you needed, but you wind up creating separate subsets of variables and overwriting 'x' on each pass in the loop)
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Eduardo Praça

May 05, 2022 11:57
Thank you! It works properly now!

Another way would be to create with a dictionary, but I've no idea if it would work when putting constrains. Anyway, the one above is faster.

Best Regards,

Eduardo.
```
x={}
for i in I:
    J = Ji[i-1]
    for j in J:
        for k in K:
            x[i,j,k] = m.addVar(vtype = GRB.BINARY, name=f'X[{i},{j},{k}]')
```
0

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