Sum of subset of binary variables == 1 in Gurobipy

Question

I am writing a very simple optimization model in Gurobipy but am struggling with the binary variable constraints.

I have 5 materials in 3 groups. The decision variables are whether or not to use one of the materials and are binary. Each decision variable has a cost coefficient and I am minimizing total cost in the objective. The first group has 3 of the materials and the latter 2 groups have just one material in each.

I would like to write a constraint so that the sum of the decision variables in group 1 == 1 and so on... meaning you can only pick one material from each group.

The constraints would look something like this:

x[0] + x[3] + x[4] == 1
x[1] == 1
x[2] == 1

Is there a way to iterate through a list of components by group and to match those against the variable names?

Thank you!

In your model, how are you associating the decision variables to the groups? Do you have one large set of all materials and subsets of that set for the groups? Or do you have a double-indexed variable of some kind? It looks like from your example, you have subsets associated with the groups, so you can just sum across each of the the subsets and sum <= 1 for each ... Is that what you intend? — AirSquid, Nov 07 '22 at 22:58
@AirSquid Thank you for the reply! I have one large set of materials as the decision variables. I created 3 lists of materials representing the groups and are all within the larger set. I don't think I can iterate over the d.v.'s by index with the lists, correct? If that is not possible, then I think I'll need to define a multi-variable problem like I think you're suggesting. — TroyE219, Nov 08 '22 at 14:16

score 1 · Accepted Answer · answered Nov 08 '22 at 16:08

You certainly can use subsets to form constraints, and here it is the best idea. As long as you provide a valid list or set of indices within the larger set, you should be fine.

Here is an example in gurobipy. CAUTION: My gurobi license is not current so I cannot execute this code, but I think it is correct and should be close enough to demonstrate the concept.

import gurobipy as gp
from gurobipy import GRB

materials = list(range(8))

# groups of materials
groups = {1: {0,2,3},
          2: {1},
          3: {4,5,6,7}}

# a little sanity check for non-duplication and full coverage... OPTIONAL
assert set.union(*groups.values()) == set(materials)               # full coverage
assert sum(len(grp) for grp in groups.values()) == len(materials)  # no duplicates

m = gp.Model('example')

m.select = m.addVars(materials, name='select', vtype=GRB.BINARY)

# sum up over each group to limit selection to one...
# this will make one constraint for each group.
for grp in groups.values():
    m.addConstr(sum(select[m] for m in grp) <= 1)

Sum of subset of binary variables == 1 in Gurobipy

1 Answers1