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Dear Shahin,<br>
<br>
yes, if you have these constraints in your master problem, you also
need to take these constraints into account in the pricing problem
objective. <br>
But this has nothing to do with SCIP, it is just about the
definition of reduced costs and how branch-and-price works.<br>
<br>
You can image this constraint as x_j = x_j, with the left-hand side
replaced by the \lambda variables. Therefore, a variable will be
added to the constraint if and only if it represents a solution of
the pricing problem in which x_j is set to 1. Thus, you need to
subtract (or add, depending on your objective sense) the dual
solution value of this constraint from the objective of variable x_j
in the pricing problem.<br>
<br>
Best,<br>
Gerald<br>
<br>
<div class="moz-cite-prefix">Am 27.04.2014 00:53, schrieb Shahin
Gelareh:<br>
</div>
<blockquote
cite="mid:CA+r-pT5p41SarAaCE=FT6fKP=Kx86Jm_WQeCX2hgPm1WT0050Q@mail.gmail.com"
type="cite">
<div dir="ltr">
<div>
<div>Dear SCIPers<br>
<br>
</div>
It is clean that one can explicitly express the <span
class="">original</span> <span class="">variables</span>
as combination of the master <span class="">variables</span>.<br>
</div>
<div>My original variables are binary. <br>
</div>
<div>But when one has \sum_i(\lambda_ij_x_ij )= x_j \in {0,1}
there will be dual variables associated to these sets of
constraint.<br>
</div>
<div>How are these constraints which also include the lambdas
would contribute in some way in building the pricing problem
objective?<br>
<br>
</div>
<div>My results show that they cannot be neglected even if they
are equality constraints otherwise it may never converge. So
how we do we actually handle them in SCIP ? <br>
</div>
<div><br>
</div>
<div>Cheers<br>
Shahin<br>
</div>
<div><br>
</div>
<div><br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
</div>
</div>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">On Thu, Jan 10, 2013 at 8:44 AM, Marco
Luebbecke <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:marco.luebbecke@rwth-aachen.de"
target="_blank">marco.luebbecke@rwth-aachen.de</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">Dear
Victor,<br>
<br>
the easiest way is to explicitly express the original
variables as<br>
combination of your master variables. You can then directly
branch on<br>
these original variables, also the elimination of master
variables<br>
that are incompatible to the branching decisions is for free
then (in<br>
the binary case). You only need to tell your pricing problem
about<br>
branching decisions, see<br>
<br>
<a moz-do-not-send="true"
href="http://scip.zib.de/doc/html/FAQ.shtml#Q5.3"
target="_blank">http://scip.zib.de/doc/html/FAQ.shtml#Q5.3</a><br>
<br>
<br>
Best regards,<br>
Marco<br>
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</blockquote>
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