how to obtain the solution information of sub-problem when using callback

Peng GUO

• June 16, 2020 21:24

Dear all,

Currently, I am trying to implement a Benders Decomposition. I can add a lazy constraint to limint the binary variables of the master problem. I can obtain the optimal solution of the master problem after many iterations.

Actually I can obtain more information from the sub-problem. I know the solution value of the subproblem actually gives a upper bound  UB for the objective function Z of the master problem. I try to reduce the maximum possible value of Z by using the constraint Z<=UB-epsilon where epsilon is a very small value, such as epsilon =1. When adding the constraint, the master problem reports infeasible very soon. I want to know how to add the solution value of the subproblem to limit  the objective function of the master problem.

Thanks very much

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:45

  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?.
• 

  Jaromił Najman

  Gurobi Staff

  • July 30, 2020 08:44

  Hi,
  
  Are you sure that subtracting \(\epsilon=1\) from your upper bound is valid? E.g., the optimal objective value of your master problem is \(Z=2\) and the upper bound you get from one of your subproblems is \(UB=2.5\). Then, adding the constraint \(Z\leq UB-\epsilon\) may make your master problem infeasible. Is there a particular reason why you subtract the \(\epsilon\)? What happens if you don't subtract the \(\epsilon\) but still add the constraint \(Z\leq UB\)?

  Best regards,
  Jaromił

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• 

  Peng GUO

  • August 11, 2020 13:50

  

  

  

  Hi, 

  You are right. But I am trying to tighten the upper bound for speeding up the solution process. If the UB=10 and \(\epsilon=1\), \(Z=9\) for next iteration by using \(Z\leq UB-\epsilon\). But there is a risk to cause the model infeasible. Do you have any good suggestion? If I just add \(Z\le UB\), it is slow to help the model to find a good upper bound sometimes.

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• 

  Jaromił Najman

  Gurobi Staff

  • September 04, 2020 13:46

  Hi,

  We recently added a knowledge base article, which could provide some insight on your problem.

  Best regards,
  Jaromił

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