[SCIP] Question regarding column generation

[Alexander Helber]

Hi Mike and Marc,

if I understand the question correctly, the first option would be to 
register a pricer with SCIP for every arc and the second to have one 
pricer that processes all arcs at once? I think in the first case, SCIP 
will skip the remaining pricers if sufficient new variables have already 
been generated in the current pricing iteration, see settings 
pricing->maxvars and pricing->maxvarsroot. As far as I can tell, these 
settings are only relevant for the SCIPpriceLoop in solve.c. If your 
pricing is cheap and generates many variables, it might be better to 
price variables for all arcs at once and let SCIP select the best 
maxvars(root) many variables depending on the score you give them. If 
you generate less than maxvars(root) many variables, I think both 
options will be the same regarding SCIP.

All the best
Alex


On 12.05.25 07:38, Marc Pfetsch wrote:
>
>
> Hi Mike,
>
> I don't think it matters for SCIP. I guess it will depend on your 
> implementation what is easier or faster.
>
> Best
>
> Marc
>
>
> On 10/05/2025 06:15, Hewitt, Michael wrote:
>> I am using the SCIP framework to implement a column generation 
>> algorithm for a MIP defined on a network in which I generate 
>> variables for each arc in the network by solving a pricing problem. 
>> Does it matter which of the following I do:
>>
>>  1. For each arc, solve the pricing problem and add variables with
>>     negative reduced costs via SCIPcreateVar and SCIPaddPricedVar
>>
>> Or
>>
>>  2. Solve the pricing problem for each arc, then after all arcs have
>>     been priced add the variables with negative reduced costs via
>>     SCIPcreateVar and SCIPaddPricedVar
>>
>> Thanks, Mike
>>
>> Mike Hewitt
>> Professor
>> Quinlan School of Business, Loyola University Chicago
>> mhewitt3 at luc.edu <mailto:mhewitt3 at luc.edu>
>>
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-- 
Alexander Helber
Research and Teaching Assistant

Chair of Operations Research
RWTH Aachen University
Kackertstrasse 7
52072 Aachen
Germany
Web: or.rwth-aachen.de
Mail:helber at or.rwth-aachen.de
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