Integrality tolerance

[remi-garcia]

Default value for integrality tolerance is 10e-5 for Gurobi or CPLEX. It would be nice to have a unique parameter for this. Is adding this parameter an option?

[odow]

So this has been discussed before: #61

We're also considering a GSOC project to verify feasibility of models, which would require standardizing how "infeasibilility" is measured on a constraint-by-constraint basis.

To date, we've avoided adding tolerance attributes for a few reasons:

• we'd want to generalize "integrality" tolerance, potentially to a per constraint-type basis. For example:

  struct Tolerance{F, S} <: MOI.AbstractOptimizerAttribute

• differences in how solvers may interpret the tolerance (absolute or relative? pre-solve or final solution (Yes, for some solvers, e.g., Gurobi, these can differ)?)
• differences in valid min/max values.

So, I'd say that the answer is a qualified yes for if adding tolerance parameters is an option. But we'd need to think hard about what and how to go about it.

[mlubin]

I think it's an exception rather than a rule when two solvers have consistent sets of tolerances. Differences in whether the tolerances are applied to the pre-solved problem or the original problem and before or after scaling are extremely common, as @odow mentioned.

Integrality might be simple enough that we can safely define a solver-independent version, but I'd want to see more evidence that this is true for most of the MIP solvers accessible through MOI, not just Gurobi and CPLEX.

[odow]

I'm also not sure how this would tie in with the bridging system. If you define a tolerance for a constraint, but it gets bridged, what does that mean?

[remi-garcia]

I understand why this is much more complex than I though. Thanks.

If that's of any help I found the parameters for a few solver for this integrality tolerance:
Artelys Knitro: KN_PARAM_MIP_INTEGERTOL (default: 10e-8)
BARON: AbsIntFeasTol (default: 10e-5)
CBC: bool setIntegerTolerance(double value) (no default?)
GLPK: no parameter for integrality tolerance. Unless it is tol_int (default 10e-5) - Absolute tolerance used to check if optimal solution to the current LP relaxation is integer feasible.
MOSEK: might be MSK_DPAR_MIO_TOL_ABS_RELAX_INT (default 10e-5)
SCIP: no parameter for integrality tolerance (but feasibility tolerance for constraints available)

[odow]

Closing because I don't think there are good ways to abstract this. We should instead make sure that the solvers thoroughly document their options.

See this discussion in HiGHS for more details as well: ERGO-Code/HiGHS#560 (comment)