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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Using SOS1 was not my idea. There is a post by Tobias Achterberg somewhere in the gurobi forum [1] about modelling indicator constraints mentioning that trick - I doubt it was first
used/published there.<br>
<br>
There are also several posts about SOS1 vs Big-M in that forum, although I doubt that all details apply to CBC. In short they say if the M is suffient small, than Big-M is better due to the better relaxation. If M is to large, it will cause numerical issues
and SOS1 is better. Note that gurobi rewrites SOS to Big-M if it can derive a sufficient small M during presolve. I have no idea whether CBC does that.<br>
<br>
[1] https://groups.google.com/forum/#!forum/gurobi<br>
<br>
<br>
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<div id="divRpF137218" style="direction: ltr;"><font face="Tahoma" size="2" color="#000000"><b>Von:</b> Rhavar [rhavar@protonmail.com]<br>
<b>Gesendet:</b> Freitag, 29. Dezember 2017 23:26<br>
<b>An:</b> Bjørn Sigurd Johansen<br>
<b>Cc:</b> Tobias Stengel; cbc@list.coin-or.org<br>
<b>Betreff:</b> RE: [Cbc] Suboptimal solution as optimal?<br>
</font><br>
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<div>@<span lang="EN-US">Tobias Stengel Wow! Thanks, you're a genius. That works fantastically.</span><br>
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<div><br>
</div>
<div>@Bjørn Sigurd Johansen<br>
</div>
<div><br>
</div>
<div>I'm no expert (i learnt about them an hour ago). But adding a section:<br>
</div>
<div><br>
</div>
<div>SOS<br>
</div>
<div> set1: S1:: no_change:1 change_amount:2<br>
</div>
<div><br>
</div>
<div>at the end (before "end") works for me.<br>
</div>
<div><br>
</div>
<div>Also I don't think your constraint makes sense, as it would force everything to always be 0. </div>
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<div class="protonmail_signature_block">
<div class="protonmail_signature_block-user">
<div>-Ryan<br>
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<div class="protonmail_signature_block-proton protonmail_signature_block-empty"><br>
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<blockquote class="protonmail_quote" type="cite">
<div>-------- Original Message --------<br>
</div>
<div>Subject: RE: [Cbc] Suboptimal solution as optimal?<br>
</div>
<div>Local Time: December 29, 2017 3:29 PM<br>
</div>
<div>UTC Time: December 29, 2017 9:29 PM<br>
</div>
<div>From: bjorn.sigurd.johansen@spidersolutions.no<br>
</div>
<div>To: Tobias Stengel <Tobias.Stengel@locom.de>, Rhavar <rhavar@protonmail.com><br>
</div>
<div>cbc@list.coin-or.org <cbc@list.coin-or.org><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div class="WordSection1">
<p class="MsoNormal"><span style="" lang="EN-US">Hi!</span><br>
</p>
<p class="MsoNormal"><span style="" lang="EN-US"> </span><br>
</p>
<ol start="1" style="margin-top:0cm" type="1">
<li class="MsoListParagraph" style="margin-left:0cm"><span style="" lang="EN-US">How can a SOS1 constraint be defined in the model/lp text file?</span><br>
</li><li class="MsoListParagraph" style="margin-left:0cm"><span style="" lang="EN-US">Is a SOS1 constraint handled more efficiently than a constraint of type</span><br>
</li></ol>
<p class="MsoNormal" style="margin-left:54.0pt"><span style="" lang="EN-US">MyBinaryVariable1 + MyBinaryVariable2 + … + MyBinaryVariableN <=0 ?</span><br>
</p>
<p class="MsoNormal" style="margin-left:35.4pt"><span style="" lang="EN-US"> </span><br>
</p>
<p class="MsoNormal" style="margin-left:54.0pt"><span style="" lang="EN-US"> </span><br>
</p>
<p class="MsoNormal"><span style="" lang="EN-US"> </span><br>
</p>
<p class="MsoNormal"><span style="" lang="EN-US"> </span><br>
</p>
<div>
<p class="MsoNormal"><span class="colour" style="color:green">Best regards,</span><br>
</p>
<p class="MsoNormal"><span class="colour" style="color:green">Bjørn Sigurd</span><br>
</p>
</div>
<p class="MsoNormal"><span style="" lang="EN-US"> </span><br>
</p>
<p class="MsoNormal"><span style="" lang="EN-US"> </span><br>
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<div style="border:none; border-top:solid #E1E1E1 1.0pt; padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span lang="EN-US"> Cbc [mailto:cbc-bounces@coin-or.org]
<b>On Behalf Of </b>Tobias Stengel<br>
<b>Sent:</b> fredag 29. desember 2017 21:49<br>
<b>To:</b> Rhavar <rhavar@protonmail.com><br>
<b>Cc:</b> cbc@list.coin-or.org<br>
<b>Subject:</b> Re: [Cbc] Suboptimal solution as optimal?</span></p>
</div>
</div>
<p class="MsoNormal"><span lang="EN-US"> </span><br>
</p>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span class="colour" style="color:black"><span class="font" style="font-family:Tahoma,sans-serif"><span class="size" style="font-size:10pt">You can use a SOS1:<br>
First add a binary variable "has_no_change" and add the constraint<br>
has_no_change + has_change = 1<br>
Then your c1 can be replaced with a SOS1 containing change_amount and has_no_change.<br>
<br>
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></span></p>
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</span></span></span><br>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span class="colour" style="color:black"><span class="font" style="font-family:Tahoma,sans-serif"><span class="size" style="font-size:10pt">Von:</span></span></span></b><span class="colour" style="color:black"><span class="font" style="font-family:Tahoma,sans-serif"><span class="size" style="font-size:10pt">
Cbc [cbc-bounces@coin-or.org]" im Auftrag von "Rhavar [rhavar@protonmail.com]<br>
<b>Gesendet:</b> Freitag, 29. Dezember 2017 16:04<br>
<b>An:</b> John Forrest<br>
<b>Cc:</b> <a href="mailto:cbc@list.coin-or.org" target="_blank">cbc@list.coin-or.org</a><br>
<b>Betreff:</b> Re: [Cbc] Suboptimal solution as optimal?</span></span></span><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"></span></span></span></p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">A bit of a tangent, but the reason the model is "not well scaled" is because I have two variables:</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">change_amount (a number saying how much change will be created)</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">has_change (a binary 0 or 1, saying if there's change)</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">and I need to constrain these two things together. The only way I could think of was by creating
two different constraints:</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">c0: + change_amount - has_change >= 0</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">c1: + 2100000000000000 has_change - change_amount >= 0</span></span></span><br>
</p>
</div>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Which in a high level language would be:</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">let has_change = change_amount > 0</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">(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></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Is there a smarter way of doing what I'm trying to do?</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">---</span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">-Ryan</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<blockquote style="margin-top:5.0pt; margin-bottom:5.0pt">
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">-------- Original Message --------</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Subject: Re: [Cbc] Suboptimal solution as optimal?</span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Local Time: December 29, 2017 4:39 AM</span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">UTC Time: December 29, 2017 10:39 AM</span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">From:
<a href="mailto:john.forrest@fastercoin.com" target="_blank">john.forrest@fastercoin.com</a></span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">To:
<a href="mailto:cbc@list.coin-or.org" target="_blank">cbc@list.coin-or.org</a></span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Fixed hopefully - stable and trunk.</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">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></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">John Forrest</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">On 28/12/17 18:30, John Forrest wrote:</span></span></span><br>
</p>
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<blockquote style="margin-top:5.0pt; margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Ryan,</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">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></span><br>
</p>
</div>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">If you add -depth -100 (which means only go into this simpler version at depth 100) then all
looked fine.</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">John Forrest</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">On 27/12/17 18:37, Rhavar wrote:</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">I have a problem:</span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"><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=" target="_blank">https://gist.github.com/RHavar/dfb9de631363ecb9e1c326fff5ebd09b</a></span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">(lp file and solution file attached)</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">In the solution it says: "Optimal - objective value" but I think I have found a superior
solution by hand:</span></span></span><br>
</p>
</div>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
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<p class="MsoNormal"><span class="apple-converted-space"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span></span><span class="s1"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">o6
= 1</span></span></span></span><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"></span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">i22 = 1</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">Which gives a better objective (<span class="s1">70 instead of </span>825)</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">--</span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">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></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt">-Ryan</span></span></span><br>
</p>
</div>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</div>
</div>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
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<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</div>
<pre><span class="colour" style="color:black">_______________________________________________</span><br></pre>
<pre><span class="colour" style="color:black">Cbc mailing list</span><br></pre>
<pre><span class="colour" style="color:black"><a href="mailto:Cbc@list.coin-or.org" target="_blank">Cbc@list.coin-or.org</a></span><br></pre>
<pre><span class="colour" 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=" target="_blank">https://list.coin-or.org/mailman/listinfo/cbc</a></span><br></pre>
<pre><span class="colour" style="color:black"> </span><br></pre>
</blockquote>
<p><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</div>
<div>
<p class="MsoNormal"><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</div>
<pre><span class="colour" style="color:black">_______________________________________________</span><br></pre>
<pre><span class="colour" style="color:black">Cbc mailing list</span><br></pre>
<pre><span class="colour" style="color:black"><a href="mailto:Cbc@list.coin-or.org" target="_blank">Cbc@list.coin-or.org</a></span><br></pre>
<pre><span class="colour" 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=" target="_blank">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><br></pre>
<pre><span class="colour" style="color:black"> </span><br></pre>
</blockquote>
<p><span class="colour" style="color:black"><span class="font" style="font-family:"Times New Roman",serif"><span class="size" style="font-size:12pt"> </span></span></span><br>
</p>
</blockquote>
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</blockquote>
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