Re: [Help-glpk] Phase II numerical instability

[Andrew Makhorin]

> I have a problem with the new version of GLPK. I tried solving a
> LP with
> version 4.1 and had no errors with the standalone solver and
> --nopresol
> setting. Using --std I get an error message numerical
> instability primal
> simplex phase I, but glpsol produces a result. If I use version
> 4.5 and
> higher glpsol is not able to produce results. I just get
> hundreds of primal
> simplex phase II numercal instabilities and the solver is stuck
> in a loop.
> 
> I will attach the .mps-file.

Using `--nopresol' option I managed to solve your instance (see
the log below). Most probably the instance is not well conditioned
due to extra round-off errors introduced by the lp presolver.

Andrew Makhorin


lpx_read_mps: reading problem data from `UnstableLP.mps'...
lpx_read_mps: problem eSimGene
lpx_read_mps: 622 rows, 373 columns, 1460 non-zeros
lpx_read_mps: 23 integer columns, 22 of which are binary
lpx_read_mps: 1933 cards were read
lpx_adv_basis: size of triangular part = 598
      0:   objval = -1.500000000e+000   infeas =  1.000000000e+000 (23)
     44:   objval = -1.484875533e+000   infeas =  3.391932213e-001 (22)
spx_simplex: numerical instability (primal simplex, phase I)
     44:   objval = -1.484875533e+000   infeas =  1.000000000e+000 (21)
     57:   objval = -9.999999954e-001   infeas =  8.487112738e-001 (22)
spx_simplex: numerical instability (primal simplex, phase I)
     57:   objval = -9.999999954e-001   infeas =  1.000000000e+000 (21)
    111:   objval =  1.373978193e+001   infeas =  7.632769432e-015 (21)
*   111:   objval =  1.373978193e+001   infeas =  1.136868377e-013 (21)
*   116:   objval =  1.363848093e+001   infeas =  1.136868377e-013 (21)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
+   116: mip =     not found yet >=              -inf        (1; 0)
+   136: mip =  1.597152145e+001 >=  1.363848093e+001  14.6% (11; 0)
+   178: mip =  1.597152145e+001 >=     tree is empty   0.0% (0; 43)
INTEGER OPTIMAL SOLUTION FOUND
Time used:   3.0 secs
Memory used: 0.8M (882064 bytes)