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Seeking Guidance on Binary Variable Behavior in Benders Decomposition

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  • Jaromił Najman
    Gurobi Staff Gurobi Staff

    Hello Abdalrahman,

    Do I understand correctly that you have a model where a binary variable \(u\) does not impact the optimal objective value but you would still like to have it set to \(1\) in the optimal solution? Is this correct?

    If yes, then you could try the following:

    • If you know a priori that this is a model where the binary variable has no effect, then just fix the variable to \(1\).
    • If you know after solving the model that the specific binary variable has no effect, then you can fix the binary variable to \(1\), use the rest of the solution vector as MIP start, and re-solve the model. If you are sure that the binary has no effect on the optimal solution vector, then you don't have to re-solve.
    • If the binary variable has any impact on other variables, maybe you could use those in the objective function to favor when the respective binary is \(1\).

    Best regards, 
    Jaromił

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