L1 distance

回答済み

Lorenzo Steccanella

2021年06月10日 14:11 編集済み

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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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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 02:53 編集済み

  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

  2021年06月10日 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

  2021年06月10日 14:48

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  Amazing!... thanks a lot Jaromił!

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