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<p>Hi James,<br>
</p>
SCIP provides the possibility to define an objective limit, i.e.,
SCIPsetObjlimit(scip, objlimit). Afterwards, SCIP only declares
solution as feasible if they are strictly better than objlimit. To
avoid numerical issues I would recommend that you use this method
instead of adding a constraint that is parallel to the objective
function.<br>
<br>
Just a side remark: SCIP provides two interesting parameters if a
constraint is parallel to the objective function (e.g., an objective
limit)<br>
1) constraints/linear/detectcutoffbound<br>
2) constraints/linear/detectlowerbound<br>
if one is set to TRUE, SCIP will prevent that this constraints will
enter the LP. Both are set to TRUE per default.<br>
<br>
Nevertheless, SCIP will propagate this constraint which may cause
numerical issues unless you have set the 'propagate' flag to FALSE.<br>
<br>
Cheers,<br>
Jakob<br>
<br>
<br>
<div class="moz-cite-prefix">On 12.11.2016 15:44, James Cussens
wrote:<br>
</div>
<blockquote
cite="mid:CALQgqO12Bfx8qaDA+ODo1zFEWUtru2JsgsB=y9OQFE0PebhS6g@mail.gmail.com"
type="cite">
<div dir="ltr">I have written a "relaxator" which is called after
the LP relaxation (for the current node) has been solved.
<div><br>
</div>
<div>It works (well, should work) by solving a combinatorial
relaxation of the current problem: a subscip is created by
copying some but not all of the main problem's constraints. An
extra constraint is then added to this subscip which says that
the objective value of any solution cannot be better (which
means lower since we are working with the transformed problem)
than that of the LP solution which has just been found: call
this the "objlimit constraint". This subscip is then solved.</div>
<div><br>
</div>
<div>A problem I am having is that the objective value of the
solution to this subscip is almost always slightly better than
is allowed by the "objlimit" constraint. In some cases it is
equal. Here is an example of that:</div>
<div><br>
</div>
<div>Here is an "objlimit" constraint (the LHS is the objective,
the RHS the current lower bound):</div>
<div>....<br>
</div>
<div>
<div>+2233.687538<t_I#36#24>[B]
+3470.976165<t_I#36#22#23#25>[B]
+3514.739589<t_I#36#22#25#34>[B]
+3600.517959<t_I#36#22#25#26>[B]
+3602.888251<t_I#36#22#25>[B]
+4315.968312<t_I#36#23#25#26>[B]
+4353.360389<t_I#36#25#26#34>[B]
+4364.720055<t_I#36#25#26>[B] </div>
<div>....</div>
<div>+7696.24707<t_I#36#19#27>[B]
+7755.844738<t_I#36#27#32>[B]
+7767.597019<t_I#36#21#27>[B]
+7769.766551<t_I#36#27>[B]
+8160.498138<t_I#36#17#28>[B]
+8232.30374<t_I#36#28>[B]
+8344.946419<t_I#36>[B] >= 97290.4565854556;</div>
<div><br>
</div>
</div>
<div>
<div>And here is a solution to my relaxed problem, containing
the above objlimit constraint:<br>
</div>
<div><br>
</div>
<div>objective value: 97290.443308</div>
<div>t_I#0#13 1 <span class="gmail-Apple-tab-span" style="white-space:pre"> </span>(obj:575.319346)</div>
<div>t_I#2 1 <span class="gmail-Apple-tab-span" style="white-space:pre"> </span>(obj:1558.283114)</div>
<div>t_I#3#8#15#33 1 <span class="gmail-Apple-tab-span" style="white-space:pre"> </span>(obj:708.049421)</div>
<div>....</div>
<div>
<div>t_I#36#24 1 <span class="gmail-Apple-tab-span" style="white-space:pre"> </span>(obj:2233.687538)</div>
</div>
<div><br>
</div>
<div>Clearly, we illegally have a solution with obj value
97290.443308 which is strictly lower than 97290.4565854556</div>
<div><br>
</div>
<div>Am I right in thinking that this is some sort of rounding
error? Is there perhaps a better way of indicating that only
solutions which are no better than some value are allowed?
The objlimit constraint contains every variable (!) so
perhaps it should be no surprise that there are problems.</div>
<div><br>
</div>
<div>I suspect that this particular relaxator approach may not
be a great idea, but I would still like to get to the bottom
of this phenomenon.</div>
<div><br>
</div>
<div>James</div>
<div><br>
</div>
<div><br>
</div>
-- <br>
<div class="gmail_signature">James Cussens<br>
Dept of Computer Science &<br>
York Centre for Complex Systems Analysis<br>
Room 326, The Hub, Deramore Lane Tel +44
(0)1904 325371<br>
University of York
Fax +44 (0)1904 500159<br>
York YO10 5GE, UK <a
moz-do-not-send="true"
href="http://www.cs.york.ac.uk/%7Ejc" target="_blank">http://www.cs.york.ac.uk/~jc</a><br>
<a moz-do-not-send="true"
href="http://www.york.ac.uk/docs/disclaimer/email.htm"
target="_blank">http://www.york.ac.uk/docs/disclaimer/email.htm</a></div>
</div>
</div>
<br>
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<br>
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</pre>
</blockquote>
<br>
<pre class="moz-signature" cols="72">--
Jakob Witzig
Zuse Institute Berlin (ZIB)
Division Mathematical Optimization and Scientific Information
Research Group Mathematical Optimization Methods
Takustrasse 7
14195 Berlin
Tel. : +49 (0)30 84185-416
Fax : +49 (0)30 84185-269
email: <a class="moz-txt-link-abbreviated" href="mailto:witzig@zib.de">witzig@zib.de</a></pre>
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