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Using information on feasible solutions in Branch-and-Benders-Cut

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4 comments

  • Mario Ruthmair
    Gurobi Staff Gurobi Staff

    Hi Tjard,

    I have an idea of what could be the reason for this behaviour, but let me first try to understand your Benders model and approach correctly. Please correct me on the following statements:

    • Your model contains binary or general integer variables in the constraints and continuous variables in the objective.
    • The integer and continuous variables are not related (correctly) in the beginning, this is what the Benders optimality cuts are fixing in the lazy constraint callbacks.
    • You provide solution values for all integer variables, and the solver computes the corresponding values for the continuous variables. However, those are incorrect since some Benders cuts are still missing.
    • You add the Benders cuts and would expect that the same integer solution from before with different values for the continuous variables is found by the solver or accepted if you provide it.
    • But what happens is that the integer part of the solution from before is considered as being infeasible and ignored from now on.

    Is this true?

    Best regards,
    Mario

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  • Tjard Bätge
    First Comment
    First Question

    Hi Mario,

    thank you for your quick response.

    All of your statements are correct. However, some notes:

    • First statement: The objective of the primary (master) problem contains both, binary / integer and continuous, variables. The continuous variables are the auxiliary variables that are being restricted by the optimality cuts during the solution process. 
    • Last statement: The integer part is "ignored from now on" implies that it is not found later on. However, a solution of identical value is often found again, but (much) later in the search. Additionally, the infeasibility results from the continuous variable of the before solution "being too good", not from the integer part being infeasible after applying the optimality cut.

    Best regards,

    Tjard

    0
  • Mario Ruthmair
    Gurobi Staff Gurobi Staff

    Thanks, Tjard, for the additional information. There could be an issue with the solver. We are currently trying to reproduce it using a small example.

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  • Tjard Bätge
    First Comment
    First Question

    Thank you again for looking into this issue. Let me know if I can assist in any way. 

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