[Scip] Design choices

[Martin Bergner]

Hi Marc,

just to throw in my 2 cents and in order to support Stefans intuition,
we recently spent some time thinking about just this objective limit
issue and also considered that a bug.

In a branch-and-price context, we often provide the dual bound of the
convexity constraint as an objective limit since we only want to find
solutions with a strictly better objective value. Nonetheless, if the
problem is feasible, we know that there exists a solution with exactly
the given objective function limit without precisely knowing how it
looks like (yes it's probably one of the columns already priced before,
but I don't want to find that particular column and transfer it back to
a pricing solution). There, an apparently infeasible pricing problem is
highly disturbing and not intuitive at all. Actually, you usually
suspect some issues in your model and I wonder how many hours we have
actually spent trying to trace down a bug in our code. In any case, I
don't want to put a number on that, it might be less than I thought.

In our GCG context, we further are able to propagate bound changes on
original variables to the pricing problem in certain cases. If a pricing
problem is infeasible after a branching decision and some bound changes,
I considered the node to be infeasible. That is not true, if we add the
solution limit and I have multiple pricing problems. I was planning to
trace down this issue next week because we encountered it just recently.

Thank you very much for clarifying this, I was planning to submit a bug
report to SCIP about this behavior because I also considered it broken.
But, according to your explanation, it's not a bug, it's a feature and
your reasoning behind that is perfectly logical. I don't like the status
to be SCIP_INFEASIBLE but I don't see how you could change that, given
how the whole behavior is implemented. Please mention that in at least
in the documentation.

What is the canonical workaround in my case? Forget the objective limit
or add 10*feas_epsilon to it in case of a MIN Problem?

Regards,
Martin

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