L1 distance

Answered

Lorenzo Steccanella

June 10, 2021 14:11 Edited

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Hi, 

I'm having an hard time in formulate the following model in gurobipy:

I added the last constrain just to show that my implementation that follows doesn't return the correct result:

def abs_diff(x_1, x_2, m):
    z = m.addVar()
    y = m.addVar()
    m.addConstr(z == (x_1 - x_2))
    m.addConstr(y == gp.abs_(z))
    return y

def abs_diff_constr(x_1, x_2, d, m):
    z = m.addVar()
    y = m.addVar()
    m.addConstr(z == (x_1 - x_2))
    m.addConstr(y == gp.abs_(z))
    m.addConstr((y - d) <= 0)

m = gp.Model("isoG1D")

# Create variables
x1 = m.addVar(name="x1")
x2 = m.addVar(name="x2")
x3 = m.addVar(name="x3")

# set objective
obj = - (abs_diff(x1, x2, m) + abs_diff(x2, x3, m) + abs_diff(x1, x3, m) + abs_diff(x3, x1, m))
m.setObjective(obj, GRB.MINIMIZE)

# add constraints
abs_diff_constr(x1, x2, 1, m)
abs_diff_constr(x2, x3, 1, m)
abs_diff_constr(x1, x3, 2, m)
abs_diff_constr(x3, x1, 2, m)

m.optimize()

 

I would expect the optimal solution to be -6  but instead I'm getting 0.

Can anyone help me with this?

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:53 Edited

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
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  Jaromił Najman

  • Gurobi Staff

  June 10, 2021 14:37

  Hi Lorenzo,

  The default lower bound of variables is 0. However, you want that your \(\texttt{z}\) variables also attain negative values. Thus, you have to write

  z = m.addVar(lb=-GRB.INFINITY)

  in both \(\texttt{abs_diff}\) functions.

  Best regards,
  Jaromił

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  Lorenzo Steccanella

  June 10, 2021 14:48

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  Amazing!... thanks a lot Jaromił!

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