[Scip] Numerical troubles with a set partitioning formulation

[Sebastian Ruther]

  Hello,

I've had numerical troubles with larger instances for a long time. So 
far I've been able to ignore them because I mostly dealt with smaller 
instances but I now have to resolve this issue.


I'm running SCIP 2.1 with CPLEX 12.3 on Windows 7. I've coded a 
branch-and-price algorithm with a pure set partitioning master LP. All 
coefficients are integral, the objective function coefficients are 
either 5000 (artificial variables) or ranging from 400 to 1000 for some 
columns but most of them have a cost of 0. (I don't think this is the 
issue though - in earlier versions these columns did have non-zero cost 
and I still had numerical troubles). All variables are binary.

The numerical troubles happen throughout the algorithm, but SCIP is 
usually able to recover using different tolerances, methods, etc. This 
can take up a lot of time though. However, at some point it is not able 
to recover and will try for ObjBranchGE::scip_execps. Since I don't give 
it any additional columns there it then will finish the node. Please see 
the output below.
I dumped the Lp using SCIPwriteLP. CPLEX solves this without any issues 
but of course it may use methods that SCIP isn't allowed to use because 
it knows that variables may not have been added yet. I've attached the 
.lp file. This is the Lp at the end of the root node (or I should say it 
aborts the root node at this point).

The output is:

(node 1) numerical troubles in LP 297 -- solve again with primal simplex 
without scaling
(node 1) numerical troubles in LP 298 -- solve again with primal simplex 
without presolving
(node 1) numerical troubles in LP 299 -- solve again with primal simplex 
with tighter feasibility tolerance
(node 1) numerical troubles in LP 300 -- solve again from scratch with 
primal simplex
(node 1) numerical troubles in LP 301 -- solve again from scratch with 
dual simplex
(node 1) numerical troubles in LP 302 -- solve again from scratch with 
dual simplex without scaling
(node 1) numerical troubles in LP 303 -- solve again from scratch with 
dual simplex without presolving
(node 1) numerical troubles in LP 304 -- solve again from scratch with 
dual simplex with tighter feasibility tolerance
(node 1) unresolved numerical troubles in LP 305
(node 1) numerical troubles in LP 306 -- solve again with dual simplex 
without scaling
(node 1) numerical troubles in LP 307 -- solve again with dual simplex 
without presolving
(node 1) numerical troubles in LP 308 -- solve again with dual simplex 
with tighter feasibility tolerance
(node 1) numerical troubles in LP 309 -- solve again from scratch with 
dual simplex
(node 1) numerical troubles in LP 310 -- solve again from scratch with 
primal simplex
(node 1) numerical troubles in LP 311 -- solve again from scratch with 
primal simplex without scaling
(node 1) numerical troubles in LP 312 -- solve again from scratch with 
primal simplex without presolving
(node 1) numerical troubles in LP 313 -- solve again from scratch with 
primal simplex with tighter feasibility tolerance
(node 1) unresolved numerical troubles in LP 314
   256s|     1 |     0 |313683 |     - |  14M|   0 |   - |4373 |1057 
|4373 |1057 |   0 |   0 |   0 |      --      |2.620000e+006 |
   256s|     1 |     0 |313683 |     - |  14M|   0 |   - |4373 |1057 
|4373 |1057 |   0 |   0 |   0 |      --      |2.620000e+006 |
(node 1) unresolved numerical troubles in LP 314 -- using pseudo 
solution instead (loop 1)
it then goes into ObjBranchGE::scip_execps.

I use the following to generate the constraints:

set partitioning constraints
             SCIP_CALL( SCIPcreateConsSetpart(
                 scip,
&cons,
                 namebuf.str().c_str(), //name
                 0,     //nvars
                  0,     //vars
                 InitMPconsInitial,
                 InitMPconsSeparate,
                 InitMPconsEnforce,
                 InitMPconsCheck,
                 InitMPconsPropagate,
                 InitMPconsLocal,
                 InitMPconsModifiable,
                 InitMPconsDynamic ,
                 InitMPconsRemovable,
                 InitMPconsStickingatnode) );

convexity constraints:
             SCIP_CALL( SCIPcreateConsSetpack(
                     scip,
&cons,
                     namebuf.str().c_str(), //name
                     0,     //nvars
                      0,     //vars
                     InitMPconsInitial,
                     InitMPconsSeparate,
                     InitMPconsEnforce,
                     InitMPconsCheck,
                     InitMPconsPropagate,
                     InitMPconsLocal,
                     InitMPconsModifiable,
                     InitMPconsDynamic ,
                     InitMPconsRemovable,
                     InitMPconsStickingatnode) );

with
#define InitMPconsInitial true
#define InitMPconsSeparate false
#define InitMPconsEnforce true
#define InitMPconsCheck true
#define InitMPconsPropagate true
#define InitMPconsLocal false
#define InitMPconsModifiable true
#define InitMPconsDynamic false
#define InitMPconsRemovable false
#define InitMPconsStickingatnode false


Any ideas what I can do? I mean the formulation is very basic and I 
don't think the coefficients are too large.
Thank you!
Sebastian

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