Modeling conditional constraints with products of variables inside

回答済み

Krypt

2023年11月19日 19:10 編集済み

• 
• 
• 

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.

関連

• Python
• General Constraints
• Indicator Constraints

0

• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:34

  This post is more than two 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 try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  Simranjit Kaur

  • Gurobi Staff

  2023年11月19日 22:52 編集済み

  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

  2023年11月21日 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

  2023年11月22日 06:29

  • 
  • 
  • 

  Thank you!

  0

投稿コメントは受け付けていません。