how to use value of a continuous variable as another variable's index?

Answered

Haung Carol

November 13, 2023 17:23

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Hi~

I have a integer variable a_int.

a_int = {(i, k): model.addVar(vtype=gp.GRB.INTEGER, name=f'a_int_{i}_{k}') for i in V for k in K}
And I have another continuous variable X[t,k], which t=a_int[i,k].

when a_int[i,k]!=0, the relationships below will established!!!

That is I hope X[t,d] can be written as X[a_int[i,k],k], but variable can't be an index.

How to written in gurobi python

 

 

P.S.

for example:

a_int[ 5,1]: 0.0
a_int[ 5,2]: 10.0
a_int[ 6,1]: 0.0
a_int[ 6,2]: 13.0

so two constraints will be established:

X[10,2]==customer 5's X coord

X[13,2]==customer 6's X coord

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• 

  Mario Ruthmair

  • Gurobi Staff

  November 14, 2023 20:05

  Hi,

  Yes, variables as indices of other variables are not possible. Maybe you can reformulate your problem in a way to avoid this situation. But without knowing your problem, you might work with binary variables Y[i,k,t] for i in V, k in K, t in the domain of variable a_int[i,k]. Then,

  a_int[i,k] == sum_{t} t * Y[i,k,t]
  sum_{t} Y[i,k,t] == 1

  The continuous coordinate variables might also have another index, i.e., Z[i,k,t]. Together with the Y[i,k,t], you can ensure that only one Z[i,k,t] is non-zero:

  LB * Y[i,k,t] <= Z[i,k,t] <= UB * Y[i,k,t]
  X[t,k] = sum_{i} Z[i,k,t]

  Not sure if that works for your problem. Maybe you need more constraints to limit the number of non-zero 3-index variables.

  Best regards,
  Mario

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