[SCIP] SOCP subproblems as heurstics

[Benjamin Müller]

Dear Miles,

I guess the answer is a bit more complicated, because it kind of depends 
which heuristics you are actually using in SCIP.

The most important heuristic in SCIP for MINLPs is sub-NLP. Basically, a 
MIP heuristic is proposing an integer feasible solution, which violates 
at least one nonlinear constraint. The sub-NLP heuristic is using the 
proposed point as a starting point and fixes all (!) integer variables 
to the corresponding values, presolves the remaining problem, and 
finally calls a local NLP solver.

But not all heuristics fix all integer variables before solving a 
nonlinear sub-problem. For example, nlpdiving iteratively fixes 
fractional integer variables and resolve the NLP-relaxation. So, it 
might happen that not all integer variables have been fixed, but a 
feasible solution could be already found.

Cheers,
Benny

On 05/29/2017 10:42 PM, Miles Lubin wrote:
> Dear SCIP experts,
>
> I have one more question on SCIP's behavior so that I can accurately
> characterize it in my thesis. From my discussions with Felipe Serrano
> last year, I understood that SCIP when acting as an MISOCP solver will
> occasionally use Ipopt (if available) to solve SOCP subproblems as
> heuristic for feasible solutions. In these subproblems, is it always the
> case that all integer variables are fixed, or are there also subproblems
> solved with a strict subset of the integer variables fixed with the hope
> that the optimal solution will satisfy integrality?
>
> Thanks!
> Miles
>
>
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Benjamin Müller
Zuse Institute Berlin
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benjamin.mueller at zib.de
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