[Help-glpk] Re: Doubt according to glpk feature

[Andrew Makhorin]

Hi Joao,

> I attach a .mod and a .dat file to ask you if there is any strategy
> to adopt in Glpk to solve this real large scale linear programming
> model.

> There are no integer ou binary variables.

Your model looks ill-conditioned, and since the glpk simplex solver is
not perfect, the singular basis error happens. Disabling the lp presolver
(--nopresol) I could solve your instance to optimality on my 32-bit
windows machine:

GLPSOL: GLPK LP/MIP Solver, v4.43
Parameter(s) specified in the command line:
 -m snp_39.mod -d snp_39.dat --nopresol -o snp.sol --log snp.log
Reading model section from snp_39.mod...
639 lines were read
Reading data section from snp_39.dat...
1313 lines were read
Generating POCKET_MARGIN...
[...]
Generating CAPACITY_2...
Model has been successfully generated
Scaling...
 A: min|aij| = 1.001e-003  max|aij| = 1.680e+004  ratio = 1.678e+007
GM: min|aij| = 8.878e-002  max|aij| = 1.126e+001  ratio = 1.269e+002
EQ: min|aij| = 8.298e-003  max|aij| = 1.000e+000  ratio = 1.205e+002
Constructing initial basis...
Size of triangular part = 33506
GLPK Simplex Optimizer, v4.43
36326 rows, 210900 columns, 1391830 non-zeros
      0: obj = -2.384185791e-007  infeas = 8.674e+006 (2820)
    500: obj = -2.384185791e-007  infeas = 2.637e+006 (2820)
[...]
Warning: numerical instability (primal simplex, phase I)
  15539: obj =  5.253990817e+010  infeas = 1.335e+003 (2820)
* 15566: obj =  5.254014357e+010  infeas = 1.512e-007 (2820)
* 15919: obj =  5.255072284e+010  infeas = 1.309e-007 (2820)
OPTIMAL SOLUTION FOUND
Time used:   160.0 secs
Memory used: 219.5 Mb (230199786 bytes)
[...]
Model has been successfully processed
Writing basic solution to `snp.sol'...

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err = 1.62e-003 on row 1
        max.rel.err = 9.36e-015 on row 1
        High quality

KKT.PB: max.abs.err = 3.48e-007 on column 58612
        max.rel.err = 3.48e-007 on column 58612
        Medium quality

KKT.DE: max.abs.err = 4.66e-010 on column 18136
        max.rel.err = 2.27e-013 on column 18013
        High quality

KKT.DB: max.abs.err = 2.07e-005 on row 35809
        max.rel.err = 2.07e-005 on row 35809
        Low quality