[SCIP] rounding error?

[James Cussens]

I have written a "relaxator" which is called after the LP relaxation (for
the current node) has been solved.

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.

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:

Here is an "objlimit" constraint (the LHS is the objective, the RHS the
current lower bound):
....
+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]
....
+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;

And here is a solution to my relaxed problem, containing the above objlimit
constraint:

objective value:                         97290.443308
t_I#0#13                                            1 (obj:575.319346)
t_I#2                                               1 (obj:1558.283114)
t_I#3#8#15#33                                       1 (obj:708.049421)
....
t_I#36#24                                           1 (obj:2233.687538)

Clearly, we illegally have a solution with obj value 97290.443308 which is
strictly lower than  97290.4565854556

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.

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.

James


-- 
James Cussens
Dept of Computer Science &
York Centre for Complex Systems Analysis
Room 326, The Hub, Deramore Lane            Tel    +44 (0)1904 325371
University of York                                        Fax  +44 (0)1904
500159
York YO10 5GE, UK                               http://www.cs.york.ac.uk/~jc
http://www.york.ac.uk/docs/disclaimer/email.htm
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