How do I model if elif else conditional statements in Gurobi?

Answered

Lenard Ruede

• January 31, 2022 14:04

Hi Gurobi Team,

I have an existing energy grid which I want to optimize. My decision variable is binary delta_k[i][j][k]. delta_k is 1 if I adjust a power line from vertex i to vertex j with the capacity k in the grid and 0 if there is no change. I want to minimize the cost. My objective function is delta_k[i][j][k]*t[ij]*(c_fix+c_mat*capacity[k])

t=length from vertex i to vertex j

c_fix and c_mat are fixed parameters and capacity[k] is a capacity value

Now I need to connect the decision variable with my constraints. 

y[i][j][k] (binary) is 1 if there is a power line from i to j with a capacity k in the adjusted grid. y[i][j][k] is 0 if there is no power line.

y[i][j][k] is in all my constraints so far but not in the objective function and delta_k is in my objective function but not in my constraints. So I need to connect them.

y_old[i][j][k] is 1 if there is a power line from i to j with a capacity k in the original energy grid, and y_old[i][j][k] is 0 if there is no power line in the original energy grid. 

The if else statement is:

if delta_k[i][j][k] >0:     

       y[i][j][k]=1

elif delta_k[i][j][k] =0 and y_old[i][j][k]=1:

         y[i][j][k]=1

else:

          y[i][j][k]=0

I have tried to solve it with the big-M approach and indicator constraints. However, I failed because I have an elif statement and thus do not have binary auxiliary variables which I can use. 

How can I convert these conditions into Gurobi constraints form in the python platform?

Kind regards and thank you very much for your support,

Lenard

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• 

  Jaromił Najman

  Gurobi Staff

  • January 31, 2022 15:03
  • Edited

  Hi Lenard,

  Note that your \(\texttt{if-else}\)-clause states that

  if delta_k == 1 or y_old == 1 then y = 1 else y = 0. I omitted the indices for better readability.

  Since all of your variables are binary, you could use Gurobi's or constraint to model your \(\texttt{if-else}\)-clause. 

  model.addConstr(y == or_(delta_k, y_old))

  Again, I omitted the indices for readability.

  Best regards, 
  Jaromił

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• 

  Lenard Ruede

  • January 31, 2022 16:18

  

  

  

  Hi Jaromil,

  thank you very much!

  Best regards,

  Lenard

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