Retrieve dual multipliers for each leaf node in a MIP problem

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Montree Jaidee

2023年05月24日 13:13 編集済み

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Hi,

I am trying to implement a code similar to the following paper: Inference-Based Sensitivity Analysis for Mixed Integer/Linear Programming | Operations Research (informs.org).

As an example, assume that I would like to solve the above problem with branch-and-bound and obtained a tree like this

Is it possible to obtain the lower bound and upper bound of x at each leaf node (highlighted node)? If that node is infeasible how can I extract dual multipliers from it? I think I have to use  FarkasDual or Pi attribute to get it.

Thank you in advance,

Montree

関連

• Callbacks
• Infeasible
• Sensitivity

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  Mario Ruthmair

  • Gurobi Staff

  2023年05月25日 13:13

  Hi,

  Gurobi's branch-and-bound algorithm is based on node relaxations (relaxing integrality), and involves a lot of other strategies that deviate from classical textbook branch-and-bound algorithms.
  Your figure shows a combinatorial enumeration tree which is different to what is implemented in Gurobi's solver engine. Additionally, you cannot retrieve branching decisions (e.g., binary variable fixings) in some node of Gurobi's branch-and-bound tree.

  So, if you want to have detailed access to all branch-and-bound node information, you might need to implement your own branch-and-bound algorithm, and for example use Gurobi as a solver for your nodes' problems.
  Then, provided the node problem is a linear program (without integer variables), you can access duals via constraint attribute Pi, or if infeasible via attribute FarkasDual. In the latter case you need to set parameter InfUnbdInfo=1.

  Best regards,
  Mario

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