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<body class='hmmessage'><div dir='ltr'>Dear Ambros,<div><br></div><div>Yes, thank's for the link,</div><div><br></div><div>I juste want to know if there is special constraint handler in SCIP that do the job,</div><div>as an answer, for my question :</div><div><br></div><div>we want to : lhs <= |c1x1-c2x2| <= rhs</div><div>that can be expressed as : y= |c1x1-c2x2| , lhs <= y <= rhs, y >=0</div><div>and use binary method to transform : <span style="font-size: 12pt;"> y= </span><span style="font-size: 12pt;">|c1x1-c2x2|, by adding binary variable b and two constraints :</span></div><div><span style="font-size: 12pt;">0<= y - (c1x1 - c2x2) <= upperbound * b</span></div><div><span style="font-size: 12pt;">0<= y - (c2x2 - c1x1) <= </span><span style="font-size: 12pt;">upperbound *(1-b)</span></div><div>lhs <= y <= rhs</div><div><span style="font-size: 12pt;">b \in {0,1}</span></div><div><span style="font-size: 12pt;"><br></span></div><div><span style="font-size: 12pt;">here is LP to check it out : the upper bound is 10000, you can exchange the value of u and v, for both cases y = 1 </span></div><div><span style="font-size: 12pt;"><br></span></div><div><div><b>Minimize</b></div><div><b> Obj: </b></div><div><b>Subject to</b></div><div><b> c1: + y - v + u >= 0 </b></div><div><b> c2: + y - v + u -10000 b <= 0 </b></div><div><b> c3: + y - u + v >= 0 </b></div><div><b> c4: + y - u + v +10000 b <= 10000</b></div><div><b>Bounds</b></div><div><b> 2 <= u <= 2</b></div><div><b> 3 <= v <= 3</b></div><div><b> 0 <= b <= 1</b></div><div><b> y >= 0</b></div><div><b>General</b></div><div><b> y</b></div><div><b>Binary</b></div><div><b> b</b></div><div><b>End</b></div></div><div><span style="font-size: 12pt;"><br></span></div><div><span style="font-size: 12pt;">But it is not effecient to me, because i have lot of pair xi and xj to consider,</span></div><div><span style="font-size: 12pt;">in the master problem, doing this will kill branch&price </span></div><div><br></div><div>Thank's and regards </div><div><br></div><div>---</div><div>Abdelkader Ouali</div><div><br><br><div>> Date: Tue, 15 Jul 2014 11:28:08 +0200<br>> From: gleixner@zib.de<br>> To: scip@zib.de<br>> Subject: Re: [Scip] help : expressing absolute in linear constraint<br>> <br>> Dear Abdelkader Ouali,<br>> <br>> this is a standard reformulation question in mixed-integer linear <br>> programming and what is best depends a bit on your problem. A bit of <br>> googling will help, see, e.g.,<br>> <br>> http://orinanobworld.blogspot.de/2012/07/modeling-absolute-values.html<br>> <br>> Best regards,<br>> ambros<br>> <br>> <br>> <br>> Am 15.07.2014 11:19, schrieb Abdelkader Ouali:<br>> > Dear SCIP users,<br>> ><br>> > Is there a way to express absolute in linear constraint<br>> > like*lhs <= |c1x1 - c2x2| <= rhs*<br>> ><br>> > Kind regards<br>> ><br>> > ---<br>> > Abdelkader Ouali<br>> ><br>> ><br>> > _______________________________________________<br>> > Scip mailing list<br>> > Scip@zib.de<br>> > http://listserv.zib.de/mailman/listinfo/scip<br>> ><br>> <br>> -- <br>> ____________________________________________________________<br>> Ambros M. Gleixner<br>> Zuse Institute Berlin - Matheon - Berlin Mathematical School<br>> http://www.zib.de/gleixner<br>> _______________________________________________<br>> Scip mailing list<br>> Scip@zib.de<br>> http://listserv.zib.de/mailman/listinfo/scip<br></div></div> </div></body>
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