[SCIP] column generation while cutting?

[James Cussens]

I have an application where I generate cuts which include variables which
do not exist yet. At present, I follow the normal two-stage approach: the
cut is generated without the missing variables, and later a pricer deduces
that they are worth adding and my application ensures they are added to the
previously generated cuts.

My pricer only ever generates variables which appear in the cuts I
generate, so I suspect it will be more efficient to generate the missing
variables *as soon as my cutting plane algorithm (CPA) has generated the
cut*. That is, the idea is to create them just before adding the cut (which
would then contain all its variables). My CPA generates (a representation
of) the cut with all its variables, including those not already created (so
it does a sort of pricing), so we have these variables immediately to hand
at the point of adding the cut. It is true that, since we are generating
variables unconditionally, we may end up with more variables than if we
priced them in, but my guess is that we won't get too many unnecessary
variables created.

The CPA is implemented as the separator for a certain constraint handler.
So presumably I could just add suitable calls to SCIPaddPricedVar in the
separator callback, just before creating and adding the row (ie cut).

Does anyone see a problem with doing this? It just seems an odd approach
....

James

-- 
James Cussens
Dept of Computer Science &
York Centre for Complex Systems Analysis
Room 326, The Hub, Deramore Lane            Tel    +44 (0)1904 325371
University of York                                        Fax  +44 (0)1904
500159
York YO10 5GE, UK                               http://www.cs.york.ac.uk/~jc
http://www.york.ac.uk/docs/disclaimer/email.htm
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