Gurobi implementing a constraint with the sum of the multiplication of sums with python [closed]

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I am using gurobi with gurobipy to implement a linear programm.

While implementing the following constraint, I get a failur.

$\forall i \in I: \forall j \in J: y_\text{i,j} \left [ \sum\limits_{a \in A} \left ( \sum\limits_{b \in B} x_\text{i,a,b} * \sum\limits_{b \in B} x_\text{j,a,b} \right ) +1 \right ] = c_\text{i,j}$

With $x,y \in \left \{ 0,1 \right \}$ and $a$ and $b$ as indices sets.

My minimal example looks like

import gurobipy as grb

m = grb.Model()

set_I = range(2)
set_J = range(2)
set_A = range(2)
set_B = range(2)

x_vars = {(i,a,b):m.addVar(vtype=grb.GRB.BINARY, name="x_{}_{}_{}".format(i,a,b)) for i in set_I for a in set_A for b in set_B}
y_vars = {(i,j): m.addVar(vtype=grb.GRB.BINARY, name="y_{}_{}".format(i,j)) for i in set_I for j in set_J}
c_vars = {(i,j): m.addVar(vtype=grb.GRB.CONTINUOUS, name="c_{}_{}".format(i,j)) for i in set_I for j in set_J}

for i in set_I:
    for j in set_J:
        m.addConstr(
            lhs=y_vars[i,j] * (grb.quicksum(grb.quicksum(x_vars[i,a,b] for a in set_A for b in set_B) * grb.quicksum(x_vars[j,a,b] for a in set_A for b in set_B))+1),
            sense=grb.GRB.GREATER_EQUAL,
            rhs=c_vars[i,j]
        )

and creates

Traceback (most recent call last):
  File ".\stackoverflow.py", line 17, in <module>
    lhs=y_vars[i,j] * (grb.quicksum(grb.quicksum(x_vars[i,a,b] for a in set_A for b in set_B) * grb.quicksum(x_vars[j,a,b] for a in set_A for b in set_B))+1),
  File "src\gurobipy\gurobi.pxi", line 3627, in gurobipy.quicksum
TypeError: 'gurobipy.QuadExpr' object is not iterable

Does anyone can help me to fix this problem and implement this constraint correctly?

I’m voting to close this question because optimization modeling questions belong on or.stackexchange.com. — Greg Glockner
– Greg Glockner, Commented Jun 22, 2022 at 22:51
@Greg Glockner: Does questions about the implementation belong to or.stackexchange.com as well? I thought that this is about the implementation with gurobi and python. Therefore it belongs to stackoverflow. — Mike
– Mike, Commented Jun 23, 2022 at 12:32
This isn't an implementation question, it's a modeling one. Products of binary variables should be linearized. — Greg Glockner
– Greg Glockner, Commented Jun 24, 2022 at 16:43

Erwin Kalvelagen · Accepted Answer · 2022-06-23 09:58:46Z

0

You'll have to rework this. You can't do y*x*x as that is no longer quadratic. You can reformulate using extra variables and equations:

z = x*x
y*z

I suspect you also have to rewrite the quicksum(quicksum*quicksum) using loops.

I agree that the error message is not very informative.

edited Jun 23, 2022 at 9:58

answered Jun 23, 2022 at 9:47

Erwin Kalvelagen

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2 Comments

Greg Glockner Over a year ago

It should be linearized since x and y are binary variables. That's why I flagged it as a modeling question, not a programming one.

Erwin Kalvelagen Over a year ago

@GregGlockner Gurobi will linearize this for you.

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