[Scip] integer variables get assigned non-integer values
Gregor Hendel
hendel at zib.de
Wed Dec 4 09:55:45 CET 2013
Dear Zhanibev,
1. I try to answer both of your questions at once:
The definition of an integer in SCIP is:
x is integer <=> x \in [ [x] - eps, [x] +eps ].
The standard numeric epsilon is eps=10^-6 which gives you
reasonable integral values on most instances.
If I'm not mistaken, SCIP already solved your integer problem
within an eps of 10^-12.
Just for the sake of completeness: you can change the floating
epsilon from inside the SCIP interactive shell:
set numerics epsilon 0.1
2. Decreasing number of LP iterations
I guess you are the very first to complain about a decrasing number
of LP iterations during the solve ;)
The first reason is that at the first node (the root node), SCIP
solves a lot more LPs than at consecutive
nodes during the cut-separation loop. The second reason is that
during branch-and-bound,
not every node-LP needs to solved from scratch (i.e., by feeding
the node LP into the LP solver as a new
problem).
Basically, the LP relaxation at a node usually differs from its
parent node's LP relaxation by a single
bound change, namely that of the variable branched on. The LP basis
information stays dually
feasible and is quickly reoptimized (made primal feasible) by a
small number of dual simplex interations.
This is called warm starting and should be almost always be faster
(in terms of the LP iteration count)
than resolving the LP from scratch.
SCIP solves the branch-and-bound tree by selecting nodes in a
depth-first-search like fashion (to some extent)
to take advantage of fast warm starting.
Regards
Gregor
Am 04.12.2013 06:55, schrieb Zhanibek Datbayev:
> Hey guys,
>
> I'm trying to tackle a MIP problem using SCIP. All of my variables are
> either integer or binary, but sometimes SCIP produces non-integer
> values. For example below all of the values are integers except of one
> which gets 3491.99999999999.
>
> Is that expected behavior? Should I not worry about this kind of
> values and just convert them to integers (adding 0.1 before doing that)?
>
> Thanks in advance!
>
> -Zhanibek
>
>
> x#2#1 4215 (obj:0)
> x#2#5 56830 (obj:0)
> x#2#7 2688 (obj:0)
> x#2#8 2048 (obj:0)
> x#2#11 20315 (obj:0)
> x#3#10 82685 (obj:0)
> x#3#20 3492 (obj:0)
> x#4#1 4215
> (obj:0.227623824612884)
> x#4#8 2048
> (obj:0.315622376912749)
> x#4#10 82685
> (obj:0.57256205816212)
> x#4#12 31615
> (obj:0.297351147308957)
> x#4#17 5120
> (obj:0.183683178270458)
> x#4#20 3492
> (obj:0.0293412067324434)
> x#5#5 56830
> (obj:0.355742408976591)
> x#5#7 2688
> (obj:0.0281349154730122)
> x#5#11 20315
> (obj:0.275787370980847)
> x#5#13 5540
> (obj:0.0513514245076417)
> x#5#14 20735
> (obj:0.300966021551557)
> x#5#15 20735
> (obj:0.176821089959373)
> x#5#18 2432
> (obj:3.17376668601277e-07)
> x#6#8 2048
> (obj:0.000522082564132327)
> x#6#12 31615
> (obj:0.00409922840858967)
> x#6#14 20735
> (obj:0.00136236177674599)
> x#6#18 2432
> (obj:-0.117098565680789)
> x#7#5 56830
> (obj:0.00617355213116657)
> x#8#1 4215
> (obj:0.000811301308183401)
> x#8#7 2688
> (obj:0.16746227096924)
> x#8#10 82685
> (obj:-0.00863945585761269)
> x#8#11 20315
> (obj:0.0277269751371639)
> x#8#13 5540
> (obj:0.198066307858387)
> x#8#15 20735
> (obj:0.0286204044109112)
> x#8#17 5120
> (obj:0.0021240047761656)
> x#8#20 3492
> (obj:0.0878842690501064)
> x#9#10 82685
> (obj:0.13516549310118)
> x#9#14 20735
> (obj:0.103485318216289)
> x#10#7 2688
> (obj:0.221488641675372)
> x#10#15 20735
> (obj:0.0966569518978526)
> x#10#18 2432
> (obj:0.00821715230798994)
> x#11#1 4215
> (obj:0.0309833140905398)
> x#11#10 82685
> (obj:0.193435054244922)
> x#11#20 3491.99999999999
> (obj:0.272961110760302)
> x#12#5 56830
> (obj:0.170908606920874)
> x#12#8 2048
> (obj:0.0436318450636487)
> x#12#12 31615
> (obj:0.114663635932676)
> x#13#11 20315
> (obj:0.113443166741343)
> x#13#13 5540
> (obj:0.238776163163475)
> x#14#1 4215
> (obj:0.021654717840975)
> x#14#7 2688
> (obj:0.0162037953878893)
> x#14#12 31615
> (obj:0.0780633298974657)
> x#14#13 5540
> (obj:0.0190470353724125)
> x#14#17 5120
> (obj:0.0211936119326756)
> x#14#18 2432
> (obj:0.00580446075062875)
> x#15#8 2048
> (obj:0.0295371902538209)
> x#15#11 20315
> (obj:0.0853453710938286)
> x#15#20 3492
> (obj:0.0192241961849487)
> x#16#5 56830
> (obj:1.08525723231457)
> x#16#17 5120
> (obj:0.252856127702844)
> x#17#14 20735
> (obj:1.07428897058425)
> x#18#15 20735
> (obj:0.624205140104469)
> x#1#12 31615
> (obj:0.294458508903076)
> x#1#13 5540
> (obj:0.0143650582634939)
> x#1#14 20735
> (obj:0.0609253833279164)
> x#1#15 20735
> (obj:0.223615760650029)
> x#1#17 5120
> (obj:0.0466027306419037)
> x#1#18 2432
> (obj:0.0053056051642484)
>
>
>
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