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    <div class="moz-cite-prefix">On big M - I was only trying to point
      out why the mini Branch and Bound thought it had a solution (with
      a variable at 1.001) when it didn't.  After preprocessing the
      largest coefficient is about 3e8.<br>
      <br>
      There probably could be more work done on topics such as SOS - I
      was in at the birth of them and first used SOS type 2 in 70's
      (1970's)!  There are papers on branching on general disjunctions
      and SOS are just a particular structured form.<br>
      <br>
      John Forrest<br>
      <br>
      On 30/12/17 18:13, Tobias Stengel wrote:<br>
    </div>
    <blockquote type="cite"
cite="mid:EDC45EE5442B124EBB022ECACBBA5911ED21A8@VM-Exchange2010.intranet.lan">
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      <div>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] <a
href="https://urldefense.proofpoint.com/v2/url?u=https-3A__groups.google.com_forum_-23-21forum_gurobi&d=DwQF-g&c=Ngd-ta5yRYsqeUsEDgxhcqsYYY1Xs5ogLxWPA_2Wlc4&r=js2M0T-3OIMIVDvokcKjokJbk0F8QOCd0mT4FsVFE88&m=yjsiRUN9CzHHh3pEebw2XZCZewn_stfXq8wPhuyltzM&s=pSWe4v5OdzVpIGhv9x2cRKXZs8-WJ--eQZwvvzlGKcw&e="
          moz-do-not-send="true">https://groups.google.com/forum/#!forum/gurobi</a><br>
        <br>
        <br>
        <div>
          <hr tabindex="-1">
          <div id="divRpF137218"><b>Von:</b> Rhavar
            [<a class="moz-txt-link-abbreviated" href="mailto:rhavar@protonmail.com">rhavar@protonmail.com</a>]<br>
            <b>Gesendet:</b> Freitag, 29. Dezember 2017 23:26<br>
            <b>An:</b> Bjørn Sigurd Johansen<br>
            <b>Cc:</b> Tobias Stengel; <a class="moz-txt-link-abbreviated" href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a><br>
            <b>Betreff:</b> RE: [Cbc] Suboptimal solution as optimal?<br>
            <br>
          </div>
          <div>
            <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: <a class="moz-txt-link-abbreviated" href="mailto:bjorn.sigurd.johansen@spidersolutions.no">bjorn.sigurd.johansen@spidersolutions.no</a><br>
              </div>
              <div>To: Tobias Stengel <a class="moz-txt-link-rfc2396E" href="mailto:Tobias.Stengel@locom.de"><Tobias.Stengel@locom.de></a>,
                Rhavar <a class="moz-txt-link-rfc2396E" href="mailto:rhavar@protonmail.com"><rhavar@protonmail.com></a><br>
              </div>
              <div><a class="moz-txt-link-abbreviated" href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a> <a class="moz-txt-link-rfc2396E" href="mailto:cbc@list.coin-or.org"><cbc@list.coin-or.org></a><br>
              </div>
              <div><br>
              </div>
              <div><br>
              </div>
              <div class="WordSection1">
                <p class="MsoNormal"><span lang="EN-US">Hi!</span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <ol start="1" type="1">
                  <li class="MsoListParagraph"><span lang="EN-US">How
                      can a SOS1 constraint be defined in the model/lp
                      text file?</span><br>
                  </li>
                  <li class="MsoListParagraph"><span lang="EN-US">Is a
                      SOS1 constraint handled more efficiently than a
                      constraint of type</span><br>
                  </li>
                </ol>
                <p class="MsoNormal"><span lang="EN-US">MyBinaryVariable1
                    + MyBinaryVariable2 + … + MyBinaryVariableN
                    <=0                 ?</span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <div>
                  <p class="MsoNormal"><span class="colour">Best
                      regards,</span><br>
                  </p>
                  <p class="MsoNormal"><span class="colour">Bjørn Sigurd</span><br>
                  </p>
                </div>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <p class="MsoNormal"><span lang="EN-US"> </span><br>
                </p>
                <div>
                  <div>
                    <p class="MsoNormal"><b><span lang="EN-US">From:</span></b><span
                        lang="EN-US"> Cbc
                        [<a class="moz-txt-link-freetext" 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 class="moz-txt-link-rfc2396E" href="mailto:rhavar@protonmail.com"><rhavar@protonmail.com></a><br>
                        <b>Cc:</b> <a class="moz-txt-link-abbreviated" href="mailto:cbc@list.coin-or.org">cbc@list.coin-or.org</a><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"><span class="colour"><span
                        class="font"><span class="size">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 class="MsoNormal"><span class="colour"><span
                          class="font"><span class="size">
                            <hr width="100%">
                          </span></span></span><br>
                    </div>
                    <div>
                      <p class="MsoNormal"><b><span class="colour"><span
                              class="font"><span class="size">Von:</span></span></span></b><span
                          class="colour"><span class="font"><span
                              class="size"> Cbc
                              [<a class="moz-txt-link-abbreviated" href="mailto:cbc-bounces@coin-or.org">cbc-bounces@coin-or.org</a>]" im Auftrag von
                              "Rhavar [<a class="moz-txt-link-abbreviated" href="mailto:rhavar@protonmail.com">rhavar@protonmail.com</a>]<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" moz-do-not-send="true">cbc@list.coin-or.org</a><br>
                              <b>Betreff:</b> Re: [Cbc] Suboptimal
                              solution as optimal?</span></span></span><span
                          class="colour"><span class="font"><span
                              class="size"></span></span></span></p>
                    </div>
                    <div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">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"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">change_amount 
                                  (a number saying how much change will
                                be created)</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">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"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">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"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">c0: +
                                change_amount - has_change >= 0</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">c1: +
                                2100000000000000 has_change -
                                change_amount >= 0</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">Which in a
                                high level language would be:</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">let
                                has_change = change_amount > 0</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">(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"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">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"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size">---</span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <div>
                        <div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size">-Ryan</span></span></span><br>
                            </p>
                          </div>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size"> </span></span></span><br>
                          </p>
                        </div>
                      </div>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                      <blockquote>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">--------
                                  Original Message --------</span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">Subject:
                                  Re: [Cbc] Suboptimal solution as
                                  optimal?</span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">Local
                                  Time: December 29, 2017 4:39 AM</span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">UTC
                                  Time: December 29, 2017 10:39 AM</span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">From:
                                  <a
                                    href="mailto:john.forrest@fastercoin.com"
                                    target="_blank"
                                    moz-do-not-send="true">john.forrest@fastercoin.com</a></span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size">To:
                                  <a href="mailto:cbc@list.coin-or.org"
                                    target="_blank"
                                    moz-do-not-send="true">cbc@list.coin-or.org</a></span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size"> </span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <p class="MsoNormal"><span class="colour"><span
                                class="font"><span class="size"> </span></span></span><br>
                          </p>
                        </div>
                        <div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size">Fixed
                                    hopefully - stable and trunk.</span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size"> </span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size">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"><span
                                  class="font"><span class="size"> </span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size">John
                                    Forrest</span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size"> </span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size">On
                                    28/12/17 18:30, John Forrest wrote:</span></span></span><br>
                            </p>
                          </div>
                        </div>
                        <blockquote>
                          <div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">Ryan,</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">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"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">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"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">John
                                      Forrest</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">On
                                      27/12/17 18:37, Rhavar wrote:</span></span></span><br>
                              </p>
                            </div>
                          </div>
                          <blockquote>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">I
                                      have a problem:</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"><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"
                                        moz-do-not-send="true">https://gist.github.com/RHavar/dfb9de631363ecb9e1c326fff5ebd09b</a></span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">(lp
                                      file and solution file attached)</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">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"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span
                                  class="apple-converted-space"><span
                                    class="colour"><span class="font"><span
                                        class="size"> </span></span></span></span><span
                                  class="s1"><span class="colour"><span
                                      class="font"><span class="size">o6
                                        = 1</span></span></span></span><span
                                  class="colour"><span class="font"><span
                                      class="size"></span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">i22
                                      = 1</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">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"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">--</span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size">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"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <div>
                                <div>
                                  <p class="MsoNormal"><span
                                      class="colour"><span class="font"><span
                                          class="size">-Ryan</span></span></span><br>
                                  </p>
                                </div>
                              </div>
                              <div>
                                <p class="MsoNormal"><span
                                    class="colour"><span class="font"><span
                                        class="size"> </span></span></span><br>
                                </p>
                              </div>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <div>
                              <p class="MsoNormal"><span class="colour"><span
                                    class="font"><span class="size"> </span></span></span><br>
                              </p>
                            </div>
                            <pre><span class="colour">_______________________________________________</span>
</pre>
                            <pre><span class="colour">Cbc mailing list</span>
</pre>
                            <pre><span class="colour"><a href="mailto:Cbc@list.coin-or.org" target="_blank" moz-do-not-send="true">Cbc@list.coin-or.org</a></span>
</pre>
                            <pre><span class="colour"><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" moz-do-not-send="true">https://list.coin-or.org/mailman/listinfo/cbc</a></span>
</pre>
                            <pre><span class="colour"> </span>
</pre>
                          </blockquote>
                          <p><span class="colour"><span class="font"><span
                                  class="size"> </span></span></span><br>
                          </p>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size"> </span></span></span><br>
                            </p>
                          </div>
                          <div>
                            <p class="MsoNormal"><span class="colour"><span
                                  class="font"><span class="size"> </span></span></span><br>
                            </p>
                          </div>
                          <pre><span class="colour">_______________________________________________</span>
</pre>
                          <pre><span class="colour">Cbc mailing list</span>
</pre>
                          <pre><span class="colour"><a href="mailto:Cbc@list.coin-or.org" target="_blank" moz-do-not-send="true">Cbc@list.coin-or.org</a></span>
</pre>
                          <pre><span class="colour"><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" moz-do-not-send="true">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>
</pre>
                          <pre><span class="colour"> </span>
</pre>
                        </blockquote>
                        <p><span class="colour"><span class="font"><span
                                class="size"> </span></span></span><br>
                        </p>
                      </blockquote>
                      <div>
                        <p class="MsoNormal"><span class="colour"><span
                              class="font"><span class="size"> </span></span></span><br>
                        </p>
                      </div>
                    </div>
                  </div>
                </div>
              </div>
            </blockquote>
            <div><br>
            </div>
          </div>
        </div>
      </div>
      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <br>
      <pre wrap="">_______________________________________________
Cbc mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Cbc@list.coin-or.org">Cbc@list.coin-or.org</a>
<a class="moz-txt-link-freetext" 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=yjsiRUN9CzHHh3pEebw2XZCZewn_stfXq8wPhuyltzM&s=ESRXK7OXcjFgREDPx_Lj3xnHVssB6iquAmm-PCtKT2M&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=yjsiRUN9CzHHh3pEebw2XZCZewn_stfXq8wPhuyltzM&s=ESRXK7OXcjFgREDPx_Lj3xnHVssB6iquAmm-PCtKT2M&e=</a> 
</pre>
    </blockquote>
    <p><br>
    </p>
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