Modeling conditional constraints with products of variables inside

Answered

Krypt

November 19, 2023 19:10 Edited

• 
• 
• 

Hi, I am trying to model a conditional constraint in Python Gurobi. Here x_e is a binary variable, z and b are continuous variables and r is a parameter.

if b[e,i] >=0.8 then

z[e,j] >= x_e[e,(i,j)]*(z[e,i]+r[i]*2.25*(0.8-b[e,i])*100)

else,

z[e,j] >= x_e[e,(i,j)]*(z[e,i]+r[i]*6*(b[e,i])*100)

 

I tried to model this conditional constraint as follows:

 

ind = mdl.addVars(((item, element) for item in E for element in V), vtype = GRB.BINARY, name = "ind")

mdl.addConstrs((b[e,i] >= 0.8-M*(1-ind[e,i])) for i in V for e in E )

mdl.addConstrs((b[e,i] <= 0.8+M*ind[e,i]) for i in V for e in E )

mdl.addConstrs((ind[e,i] == 1) >> (z[e,j] >= x_e[e,(i,j)]*(z[e,i]+r[i]*2.25*(0.8-b[e,i])*100)) for i in V for j in N for e in E if i!=j)

mdl.addConstrs((ind[e,i] == 0) >> (z[e,j] >= x_e[e,(i,j)]*(z[e,i]+r[i]*6*(b[e,i])*100)) for i in V for j in N for e in E if i!=j)

But this results in a TypeError: must be real number, not gurobipy.QuadExpr error.

 

I guess it is because of multiplying two variables x_e and b (one binary and one continuous). I have regular constraints where Gurobi does not raise such an error for having products of two variables but in the indicator constraint, it throws the error. How do I resolve this issue or model what I am looking for in the simplest possible way?

 

Thank you in advance.

Related to

• Python
• General Constraints
• Indicator Constraints

0

• 

  Simranjit Kaur

  • Gurobi Staff

  November 19, 2023 22:52 Edited

  Indicator constraints, Model.addGenConstrIndicator(), require LinExpr object. You may find this post helpful. It discusses how to use the Big-M method instead of indicator constraints for conditional relations involving quadratic constraints.

  0
• 

  Simranjit Kaur

  • Gurobi Staff

  November 21, 2023 00:59

  We can also work around the LinExpr requirement for Model.addGenConstrIndicator() by introducing auxiliary variables in the model that hold the value of the quadratic expressions and use them in the indicator constraints instead.

  mdl.addConstrs( w[e,i,j] = x_e[e,(i,j)]*(z[e,i]+r[i]*2.25*(0.8-b[e,i])*100) for i in V for j in N for e in E if i!=j )
  mdl.addConstrs( y[e,i,j] = x_e[e,(i,j)]*(z[e,i]+r[i]*6*(b[e,i])*100) for i in V for j in N for e in E if i!=j )
  
  mdl.addConstrs((ind[e,i] == 1) >> (z[e,j] >= w[e,i,j]) for i in V for j in N for e in E if i!=j)
  mdl.addConstrs((ind[e,i] == 0) >> (z[e,j] >= y[e,i,j]) for i in V for j in N for e in E if i!=j)

  Please note the default lower bound for variables in Gurobi is zero. Please update the lower bounds of the auxiliary variables if they can take negative values.

  0
• 

  Krypt

  November 22, 2023 06:29

  • 
  • 
  • 

  Thank you!

  0

Please sign in to leave a comment.