[Bonmin] Issues when dealing with linear constraints involving integer variables

[Filippo Pecci]

Dear all,

We have been using BONMIN to solve some MINLP problems with binary 
integers that represent  ON/OFF type elements in our optimization. One 
of the linear constraints we have is a that the sum of integer variables 
is a fixed positive integer N (i.e. \sum{i\in I}v_i=N)

  * We use bonmin through OPTI's mex interface. As a result, we
    implement this linear constraint on the integer variable as N \leq
    \sum{i\in I}v_i \leq N. This has some convergence issues, often
    failing to find a feasible solution.

  * We  relaxed the above constraints using small delta to N-\delta \leq
    \sum{i\in I}v_i \leq N+\delta. Although this solved the issue for
    some small N, the same problem was faced for larger N values.

  * We also replaced this constraint with \sum{i\in I}v_i \leq N, which
    is equivalent to the original constraint in our problem since the
    objective function cannot be improved with less ON elements (i.e.
    with less v_i that are equal to 1). This formulation always works
    with good convergence properties.


What is it about bonmin that causes this behaviour? Pseudocosts? How 
bonmin passes equality constraints in integer variables to ipopt? Can it 
be related to the branching rules?

Thank you for your time and consideration.

Best regards,

Filippo Pecci
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