Affect binary value only when continuous variable is negative

Answered

Natalie Pueyo

January 20, 2023 00:27

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Hello,

Is it possible to create a constraint where a continuous variable can only affect a binary variable's value if the continuous variable is negative? I want to replace a hard-coded value and make it into a variable. From hard-coded TW_end:

m.addConstrs(((x[k, l, i] == 0) for i in N for l in L for k in K if TW_end[i][k] <= 0), name="fruitStartPassed")

To calculating tw_e from the variable v_vy (GRB.INTEGER variable between 1 and 5 cm/s) and some parameters :

m.addConstrs(((tw_e[k, i] * (v_vy / 100) == (Y[i] - (self.q_vy + k*self.cell_l))) for i in N for k in K), name="TW_end")

then adding the constraint to cause x[k,l,i] to be 0 if tw_e < 0:

m.addConstrs(((tw_e[k, i] >= -t_move * (1 - x[k, l, i]) + (0.0001 * x[k, l, i])) for i in N for l in L for k in K), name="fruitStartPassed")

where -t_move is the lower bound for tw_e, and t_move is obtained from:

m.addConstr((t_move * (v_vy / 100) == self.travel_l), name="movementTime" )

where v_vy is the same variable described above and travel_l is a parameter. The constraint is based on the answer in https://or.stackexchange.com/questions/5860/link-a-binary-variable-to-continuous-variable-in-java-gurobi by Oguz Toragay. I tried only using the second constraint which I think theoretically forces x[k,l,i] = 0 if tw_e < 0, while avoiding the first constraint because I do not want to force x[k,l,i] = 1 otherwise.

When the constraint with t_move as a variable comes into effect, it results in an infeasible result. If it doesn't have to be used because all tw_e values are positive, the solver runs fine. If I hard-code t_move (to usually be too big), the constraint works fine. Is this because the constraint is the wrong one to use in this setting? If so, is there a constraint I could use?

Thank you,

Natalie

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  Jaromił Najman

  • Gurobi Staff

  January 20, 2023 09:39

  Hi Natalie,

  The constraint looks correct as along as the variable bounds of all constraints are set correctly, i.e., t_move >= 0 and tw_e has a non-default negative lower bound.

  When the constraint with t_move as a variable comes into effect, it results in an infeasible result.

  Did you try to find the cause of infeasibility as described in How do I determine why my model is infeasible?

  Best regards, 
  Jaromił

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  Natalie Pueyo

  January 26, 2023 06:12

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  Hi Jaromil,

  The link you provided helped me determine that the lower bound I was using was wrong. I kept having trouble with that until I found a simpler version of the constraints which work:

  m.addConstrs(((x[k, l, i] == 0) for i in N for l in L for k in K if Y[i] - (self.q_vy + (k + 1)*self.cell_l) >= self.travel_l), name="fruitInHorizon")
  
  m.addConstrs(((x[k, l, i] == 0) for i in N for l in L for k in K if Y[i] - (self.q_vy + k*self.cell_l) <= 0 ), name="fruitStartPassed")

  This removed the need for the problematic lower bounds and the extra auxiliary variable t_move.

  Thank you!

  Natalie

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