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<tt>Dear Myroslav,<br>
<br>
branching on a generated variable introduces a constraint whose
dual multiplier needs to be considered in the objective function
of the following pricing problems (when the added constraint is
active). This might change the nature of the pricing problems
completely. Imagine a branch-and-price example where the pricing
problem is a classical shortest path problem. Let z_P the variable
corresponding to a path P that has been generated. In the branch
z_P = 0 you need to ensure that your pricing problem doesn't
generate P again. This changes your pricing problem to a
k-shortest path problem.<br>
<br>
I left out most of the details, but there is plenty of literature
about branching rules in branch-and-price. An example of how a
branching rule interacts nicely with the pricing problem is shown
in the Binpacking example of SCIP, see <a moz-do-not-send="true"
href="http://scip.zib.de/doc-6.0.0/html/BINPACKING_MAIN.php">here</a>
for more details.<br>
<br>
Best,<br>
Benny<br>
</tt><br>
<div class="moz-cite-prefix">On 08/29/2018 12:17 PM, myroslav wrote:<br>
</div>
<blockquote type="cite"
cite="mid:40939517-8370-c916-06f5-0495257e6782@uni-wuerzburg.de">Dear
SCIP community,
<br>
<br>
<br>
I wanted to ask about how branching affects pricing and how it is
managed in SCIP. If I understand how variables are added in
SCIP, I can't think of a scenario when branching decisions really
affect pricing. A branching decision is made on variables known
to SCIP (those that have been already generated/ present in SCIP),
so a branching constraint involving these variables is not taken
into account when we price new variables. I would appreciate if
someone could clear that out.
<br>
<br>
<br>
Thanks,
<br>
<br>
Myroslav
<br>
<br>
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</blockquote>
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