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<li class="MsoListParagraph" style="margin-left:0in;mso-list:l2 level1 lfo2"><span lang="NO-BOK">SOS1: Thanks.<br>
<br>
<o:p></o:p></span></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l2 level1 lfo2">Yes, certainly I mean to ask if
<br>
<span style="font-family:"Courier New"">MyBinaryVariable1 + MyBinaryVariable2 + … + MyBinaryVariableN <=</span><b><span style="font-size:12.0pt;font-family:"Courier New";background:yellow;mso-highlight:yellow">1</span></b><span style="font-family:"Courier New""><br>
</span>is less efficient than a SOS1 constraint ?<br>
<br>
<o:p></o:p></li></ol>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:-.25in;mso-list:l1 level1 lfo3">Bjorn<o:p></o:p></li></ul>
<p class="MsoListParagraph" style="margin-left:.25in"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><b>From:</b> Rhavar [mailto:rhavar@protonmail.com] <br>
<b>Sent:</b> Friday, December 29, 2017 11:27 PM<br>
<b>To:</b> Bjørn Sigurd Johansen (Spider Solutions AS) <bjorn.sigurd.johansen@spidersolutions.no><br>
<b>Cc:</b> Tobias Stengel <Tobias.Stengel@locom.de>; cbc@list.coin-or.org<br>
<b>Subject:</b> RE: [Cbc] Suboptimal solution as optimal?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">@Tobias Stengel Wow! Thanks, you're a genius. That works fantastically.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">@Bjørn Sigurd Johansen<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I'm no expert (i learnt about them an hour ago). But adding a section:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">SOS<o:p></o:p></p>
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<p class="MsoNormal"> set1: S1:: no_change:1 change_amount:2<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">at the end (before "end") works for me.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Also I don't think your constraint makes sense, as it would force everything to always be 0. <o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-Ryan<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal">-------- Original Message --------<o:p></o:p></p>
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<div>
<p class="MsoNormal">Subject: RE: [Cbc] Suboptimal solution as optimal?<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">Local Time: December 29, 2017 3:29 PM<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">UTC Time: December 29, 2017 9:29 PM<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">From: <a href="mailto:bjorn.sigurd.johansen@spidersolutions.no">
bjorn.sigurd.johansen@spidersolutions.no</a><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal">To: Tobias Stengel <<a href="mailto:Tobias.Stengel@locom.de">Tobias.Stengel@locom.de</a>>, Rhavar <<a href="mailto:rhavar@protonmail.com">rhavar@protonmail.com</a>><o:p></o:p></p>
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<p class="MsoNormal"><a href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a> <<a href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a>><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi!<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<ol start="1" type="1">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
How can a SOS1 constraint be defined in the model/lp text file?<o:p></o:p></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1">
Is a SOS1 constraint handled more efficiently than a constraint of type<o:p></o:p></li></ol>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.75in">
MyBinaryVariable1 + MyBinaryVariable2 + … + MyBinaryVariableN <=0 ?<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:35.4pt">
<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.75in">
<o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="colour"><span style="color:green">Best regards,</span></span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="colour"><span style="color:green">Bjørn Sigurd</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><b>From:</b> Cbc [<a href="mailto:cbc-bounces@coin-or.org">mailto:cbc-bounces@coin-or.org</a>]
<b>On Behalf Of </b>Tobias Stengel<br>
<b>Sent:</b> fredag 29. desember 2017 21:49<br>
<b>To:</b> Rhavar <<a href="mailto:rhavar@protonmail.com">rhavar@protonmail.com</a>><br>
<b>Cc:</b> <a href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a><br>
<b>Subject:</b> Re: [Cbc] Suboptimal solution as optimal?<o:p></o:p></p>
</div>
</div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span class="size"><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black">You can use a SOS1:</span></span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black"><br>
<span class="size">First add a binary variable "has_no_change" and add the constraint</span><br>
<span class="size">has_no_change + has_change = 1</span><br>
<span class="size">Then your c1 can be replaced with a SOS1 containing change_amount and has_no_change.</span><br>
<br>
<span class="size">If you need to force has_change = 0 if change_amount = 0 you still need c0 (or something similar). Often this is not necessary, e.g. if has_change does not show up in any other constraint and has a positive coefficient in the objective (assuming
minimization).</span></span><o:p></o:p></p>
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<div class="MsoNormal" align="center" style="text-align:center"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">
<hr size="2" width="100%" align="center">
</span></span></div>
<p class="MsoNormal" align="center" style="text-align:center"><o:p> </o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"><span class="size"><b><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black">Von:</span></b></span><span class="size"><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black">
Cbc [cbc-bounces@coin-or.org]" im Auftrag von "Rhavar [rhavar@protonmail.com]</span></span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:black"><br>
<span class="size"><b>Gesendet:</b> Freitag, 29. Dezember 2017 16:04</span><br>
<span class="size"><b>An:</b> John Forrest</span><br>
<span class="size"><b>Cc:</b> <a href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a></span><br>
<span class="size"><b>Betreff:</b> Re: [Cbc] Suboptimal solution as optimal?</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">A bit of a tangent, but the reason the model is "not well scaled" is because I
have two variables:</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">change_amount (a number saying how much change will be created)</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">has_change (a binary 0 or 1, saying if there's change)</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">and I need to constrain these two things together. The only way I could think
of was by creating two different constraints:</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">c0: + change_amount - has_change >= 0</span></span><o:p></o:p></p>
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<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">c1: + 2100000000000000 has_change - change_amount >= 0</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Which in a high level language would be:</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">let has_change = change_amount > 0</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">(the reason I use 2.1e14 is because it's a max theoretical amount change could
ever be. Although in practice, it's several orders of magnitude less).</span></span><o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
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<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Is there a smarter way of doing what I'm trying to do?</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">---</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">-Ryan</span></span><o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">-------- Original Message --------</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Subject: Re: [Cbc] Suboptimal solution as optimal?</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Local Time: December 29, 2017 4:39 AM</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">UTC Time: December 29, 2017 10:39 AM</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">From:
<a href="mailto:john.forrest@fastercoin.com">john.forrest@fastercoin.com</a></span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">To:
<a href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a></span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Fixed hopefully - stable and trunk.</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">The original model is not well scaled - one element was 2.1e14 and even after preprocessing
the problem had to be solved applying scaling factors. The small fast branch and bound is deliberately a bit forgiving on this. When the code thinks it has got a solution it double checks. In this case it did that and threw that solution out - but it had
left some variables fixed when they should not have been.</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">John Forrest</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">On 28/12/17 18:30, John Forrest wrote:</span></span><o:p></o:p></p>
</div>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Ryan,</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Bug in Cbc. My first try gave correct result, but I managed to get error. For
small problems, Cbc will do a simpler faster branch and bound on a portion of the tree. This is returning infeasible - I will look into it.</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">If you add -depth -100 (which means only go into this simpler version at depth
100) then all looked fine.</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">John Forrest</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">On 27/12/17 18:37, Rhavar wrote:</span></span><o:p></o:p></p>
</div>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">I have a problem:</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__gist.github.com_RHavar_dfb9de631363ecb9e1c326fff5ebd09b&d=DwMDaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=js2M0T-3OIMIVDvokcKjokJbk0F8QOCd0mT4FsVFE88&m=S4VZrfTJ9vrNsPyEyqDoTZUqb0eG9rdZ8l7-jr8EA9Y&s=dWErV9QjwaNhpQZZkV1ZmdJ_Ofpqgb80lh0-5ORAiSU&e=">https://gist.github.com/RHavar/dfb9de631363ecb9e1c326fff5ebd09b</a></span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">(lp file and solution file attached)</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">In the solution it says: "Optimal - objective value" but I think I have found
a superior solution by hand:</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> o6 = 1</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">i22 = 1</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">Which gives a better objective (</span></span><span class="s1"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">70
instead of </span></span><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">825)</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">--</span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">So I guess my question is, does "Optimal - objective value" mean that it's guaranteed
to be the optimal solution? Or am I doing something wrong? Or is there a bug in cbc? </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black">-Ryan</span></span><o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<pre><span class="colour"><span style="color:black">_______________________________________________</span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black">Cbc mailing list</span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"><a href="mailto:Cbc@list.coin-or.org">Cbc@list.coin-or.org</a></span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__list.coin-2Dor.org_mailman_listinfo_cbc&d=DwMDaQ&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=js2M0T-3OIMIVDvokcKjokJbk0F8QOCd0mT4FsVFE88&m=S4VZrfTJ9vrNsPyEyqDoTZUqb0eG9rdZ8l7-jr8EA9Y&s=SVcz-BvCf0RgvZrRQQxyV89AGoSkVGhfQhv4tx1JKV4&e=">https://list.coin-or.org/mailman/listinfo/cbc</a></span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"> </span></span><o:p></o:p></pre>
</blockquote>
<p><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
<pre><span class="colour"><span style="color:black">_______________________________________________</span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black">Cbc mailing list</span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"><a href="mailto:Cbc@list.coin-or.org">Cbc@list.coin-or.org</a></span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"><a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__list.coin-2Dor.org_mailman_listinfo_cbc&d=DwICAg&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=js2M0T-3OIMIVDvokcKjokJbk0F8QOCd0mT4FsVFE88&m=S4VZrfTJ9vrNsPyEyqDoTZUqb0eG9rdZ8l7-jr8EA9Y&s=SVcz-BvCf0RgvZrRQQxyV89AGoSkVGhfQhv4tx1JKV4&e=">https://urldefense.proofpoint.com/v2/url?u=https-3A__list.coin-2Dor.org_mailman_listinfo_cbc&d=DwICAg&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=js2M0T-3OIMIVDvokcKjokJbk0F8QOCd0mT4FsVFE88&m=S4VZrfTJ9vrNsPyEyqDoTZUqb0eG9rdZ8l7-jr8EA9Y&s=SVcz-BvCf0RgvZrRQQxyV89AGoSkVGhfQhv4tx1JKV4&e=</a> </span></span><o:p></o:p></pre>
<pre><span class="colour"><span style="color:black"> </span></span><o:p></o:p></pre>
</blockquote>
<p><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</blockquote>
<div>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span class="size"><span style="font-size:12.0pt;font-family:"Times New Roman",serif;color:black"> </span></span><o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
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