<div>@<span lang="EN-US">Tobias Stengel    Wow! Thanks, you're a genius. That works fantastically.</span><br></div><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><div><br></div><div><br></div><div><br></div><div class="protonmail_signature_block"><div class="protonmail_signature_block-user"><div>-Ryan<br></div></div><div class="protonmail_signature_block-proton protonmail_signature_block-empty"><br></div></div><div><br></div><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="mso-fareast-language:EN-US" lang="EN-US">Hi!</span><br></p><p class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><ol type="1" start="1" style="margin-top:0cm"><li style="margin-left:0cm;mso-list:l0 level1 lfo1" class="MsoListParagraph"><span style="mso-fareast-language:EN-US" lang="EN-US">How can a SOS1 constraint be defined in the model/lp text file?</span><br></li><li style="margin-left:0cm;mso-list:l0 level1 lfo1" class="MsoListParagraph"><span style="mso-fareast-language:EN-US" lang="EN-US">Is a SOS1 constraint handled more efficiently than a constraint of type</span><br></li></ol><p style="margin-left:54.0pt" class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US">MyBinaryVariable1 + MyBinaryVariable2 + … + MyBinaryVariableN <=0                 ?</span><br></p><p style="margin-left:35.4pt" class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><p style="margin-left:54.0pt" class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><p class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><p class="MsoNormal"><span style="mso-fareast-language:EN-US" 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="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><p class="MsoNormal"><span style="mso-fareast-language:EN-US" lang="EN-US"> </span><br></p><div><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 style="margin-bottom:12.0pt" class="MsoNormal"><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><div><div style="text-align:center" align="center" 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"><hr align="center" width="100%" size="2"></span></span></span><br></div><div><p style="margin-bottom:12.0pt" class="MsoNormal"><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">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></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">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></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">change_amount    (a number saying how much change will be created)</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">has_change  (a binary 0 or 1, saying if there's change)</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">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></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">c0: + change_amount - has_change >= 0</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">c1: + 2100000000000000 has_change - change_amount >= 0</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"> </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">Which in a high level language would be:</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">let has_change = change_amount > 0</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">(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></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">---</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"> </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"> </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"> </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"> </span></span></span><br></p></div><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">-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><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><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></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">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">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">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></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><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></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">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></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">John Forrest</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">On 28/12/17 18:30, John Forrest wrote:</span></span></span><br></p></div></div><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></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">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><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">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></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">John Forrest</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">On 27/12/17 18:37, Rhavar wrote:</span></span></span><br></p></div></div><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">I have a problem:</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"><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></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">(lp file and solution file attached)</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">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><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="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></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">i22 = 1</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">Which gives a better objective (<span class="s1">70 instead of </span>825)</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">--</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">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></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><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></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><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><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">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=">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">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=">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><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></div></div></div></blockquote><div><br></div>