Different solutions for different modelling approaches

回答済み

Paul-Niklas Kandora

2024年04月25日 10:00

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• 
• 

Hey,

I obtain different solutions for different modelling approaches:

1.) Approach 

factor_obj_c = {
    c: m.addVar(name=f"factor_obj_{c}") for c in C
}
quad_expr_c = {
    c: m.addVar(name=f"quad_expr_{c}") for c in C
}
sum_binary_c = {
    c: m.addVar(name=f"sum_bin_{c}") for c in C
}

m.setObjective((1 / C) * gp.quicksum(factor_obj_c[c] for c in C), GRB.MINIMIZE)

for c in C:
    m.addConstr(
        sum_binary_c[c] == gp.quicksum(z_c_r[c, r] for r in R_c[c])
    )
    m.addQConstr(
        quad_expr_c[c] == gp.quicksum(z_c_r[c, r] * mu_c_r[c, r] for r in R_c[c])
    )
    m.addQConstr(
        quad_expr_c[c] == sum_binary_c[c] * factor_obj_c[c]
    )

Please note here that C is some set and R_c some dict which can be accessed through key c. Also one this I should mention is that for my example C = {1} so that we can formulate quad_expr_c in the following as a one-dimensional decision variable (in the example below we refer to quad_expr). The solution approach above returns the wrong solution compared to the situation where I make the following change:

2.) Approach (correct solution)

factor_obj = {
    c: m.addVar(name=f"factor_obj_{c}") for c in C
}
quad_expr = m.addVar(1)

m.setObjective((1 / C) * gp.quicksum(factor_obj[c]
                                     for c in C), GRB.MINIMIZE)

for c in C:
    m.addConstr(
        quad_expr == gp.quicksum(z_c_r[c, r] * mu_c_r[c, r]
                                    for r in R_c[c])
    )
    m.addConstr(
        gp.quicksum(z_c_r[c, r] for r in R_c[c]) * factor_obj[c] ==
        quad_expr
    )

Very grateful for support here!

Best 

Paul

0

• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:25

  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.
• 

  Jaromił Najman

  • Gurobi Staff

  2024年04月25日 14:36

  Hi Paul,

  Could you please provide a minimal reproducible example of both formulations? You can use the write method to generate human-readable LP files by calling

  model.write("myModel.lp")

  You can open the file \(\texttt{myModel.lp}\) in any standard text editor to analyze whether the formulations who are comparing are indeed equivalent.

  Best regards, 
  Jaromił

  0
• 

  Paul-Niklas Kandora

  2024年04月25日 15:02

  • 
  • 
  • 

  Jaromił Najman thanks for the response! I was actually able to solve the problem by myself with introducing a support variable (support_quad_expr):
  
  

  factor_obj = {
      c: m.addVar(name=f"factor_obj_{c}") for c in C
  }
  support_quad_expr = m.addVar(1)
  quad_expr_c = {
      c: m.addVar(name=f"quad_expr_{c}") for c in C
  }
  
  

  m.setObjective((1 / C) * gp.quicksum(factor_obj[c]
                                       for c in C), GRB.MINIMIZE)
  
  for c in C:
      m.addConstr(
          quad_expr_c[c] == gp.quicksum(z_c_r[c, r] * mu_c_r[c, r] for r in R_c[c])
      )
      m.addConstr(
          quad_expr_c[c] == support_quad_expr
      )
      m.addConstr(
          gp.quicksum(z_c_r[c, r] for r in R_c[c]) * factor_obj[c]
          == support_quad_expr
      )

  I assume that gurobi had difficulties to understand the following:
  
  

  quad_expr_c[c] == gp.quicksum(z_c_r[c, r] * mu_c_r[c, r] for r in R_c[c])

  Best
  
  Paul

  0

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