[Scip] Numerical troubles with a set partitioning formulation

[Tobias Achterberg]

Hi Sebastian,

in order to analyze what is going on, I would do the following:

First, you can activate the LP solver logging by setting the "display/lpinfo" to TRUE.

Then, use gdb and set a breakpoint at the end of lp.c:lpSolveStable where the message 
about unresolved numerical trouble is printed (or, alternatively, where the first "solve 
again" message is displayed).

Then save the CPLEX LP into a *.sav file by calling
    CPXwriteprob(lp->lpi->cpxenv, lp->lpi->cpxlp, "nodelp.sav", 0)
and save the current CPLEX parameters with
    CPXwriteparam(lp->lpi->cpxenv, "nodelp.prm")

Now, if you load in these parameters and this *.sav file into the CPLEX interactive, you 
should be able to generate exactly the same log output as the one displayed from SCIP due 
to the "display/lpinfo" parameter. And you should get the same numerical trouble...

Finally, you can use CPLEX to analyze the source of the numerical issue. For example, use 
"display solution quality" inthe CPLEX interactive to print statistics about the primal 
and dual feasibility and the condition number of the final LP basis.


Tobias


Sebastian Ruther wrote:
> 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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