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I have an MILP model, in which I am handling all Big M constraints with add_if_then constraints (following this topic). I generate this model only once (to save time) and solve it iteratively with different coefficients of the objective function (I only update the objective function) - coded via docplex in Python.

After some iterations, the binary/integer variables get real values (the optimality gap is 5%). What would be the reason of this (other than having Big M constraints)? Unfortunately, I am unable to share the entire model with you. However, I can provide you with further information.

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All solution values will be floating-point numbers - independent of the variable types. In an optimal or feasible solution, they will simply be close to an integer value, depending on the specified tolerance. Usually, there is a numeric tolerance for small violations regarding the bounds and right hand sides and another one that is only concerned about the integrality of the solution.

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  • $\begingroup$ Oh, I see. I just set mdlS.parameters.mip.tolerances.integrality = 0. I will report if the problem still exists. $\endgroup$
    – mdslt
    Commented Apr 4, 2022 at 12:44
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    $\begingroup$ Setting the integrality tolerance to zero is not without risk. In a model with tricky numerics (which can easily happen in a "big M" formulation), an integrality tolerance of zero can lead to suboptimal solutions or even a false claim of infeasibility. $\endgroup$
    – prubin ♦
    Commented Apr 4, 2022 at 15:51
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    $\begingroup$ @mdslt It's likely the binary/integer values you are seeing are very close to integers. If you are concerned about feasibility, then re-solving with the almost-integer variable values fixed to their rounded integer values would confirm whether you have actually obtained a feasible solution $\endgroup$
    – holger3000
    Commented Apr 4, 2022 at 16:02

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