Variate Piece-wise Linear Function

Answered

Natalie Tam

• August 03, 2023 15:27

My modelling problem consists of finding a minimized cost for the model, and finding xij the decision variable. I want to apply a piece-wise linear function on it like so: 

But I can only find examples when the functions in the linear functions are constant. Even then, I tried putting dummy values for the y points

 

y = model.addVar(name='y')
xpts = [0, 4800, 15000, 30000 ]
ypts = [50000, 345000, 444000]

model.addGenConstrPWL(x, y, xpts, ypts)
K = 46.35
objective_expr = gp.LinExpr()
for i in I:
  for j in J:
    objective_expr += K*((x[i, j])) + (shipping_cost_matrix[i][j] * dist_matrix[i][j] - cost_per_state[j]) * x[i, j]

model.setObjective(objective_expr, gp.GRB.MINIMIZE)
model.optimize()

 

 

But I get a type error TypeError: {(0, 0): <gurobi.Var *Awaiting Model Update*>, (0, 1), ... (2, 4): <gurobi.Var *Awaiting Model Update*>} is not a variable

 

 

 

Related to

• Piecewise Linear

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• 

  w sj

  • August 05, 2023 16:12

  

  

  

  If your function is continuous, perhaps you can first convert it into a linear function and then use addconstr

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• 

  Jaromił Najman

  Gurobi Staff

  • August 07, 2023 06:54

  Hi Natalie,

  In your code snippet, the definition of \(x\) variables is missing.

  Note that the size of the \(\texttt{xpts}\) and \(\texttt{ypts}\) lists has to be the same, see addGenConstrPWL and the documentation on PWL.

  In your case, you want the \(\texttt{ypts}\) to hold the values at break points of you function, i.e.,

  xpts = [0, 4800, 15000, 30000 ]
  ypts = [0, 24960, 75960, 144960]

  With the \(x\) points and \(y\) points Gurobi is able to compute the PWL segments that you define via linear terms in your function.

  Best regards, 
  Jaromił

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