Re: [Help-glpk] glpk

[Andrew Makhorin]

Tomaso,

> Sorry for the error, this file should work.

Thanks.

Most likely excessive round-off errors are introduced by the lp
presolver, since your model looks ill-conditioned (so I don't think
that glpk v4.1 could solve it more reliably). To obtain a more
accurate solution you can either disable the lp presolver at all, or
solve the instance, disable the lp presolver, and re-optimize the
instance with the primal simpelex. The latter allows solving your
instance about 2.5 faster.

With LP presolver enabled:

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err = 3.55e-15 on row 202
        max.rel.err = 2.06e-16 on row 2986
        High quality

KKT.PB: max.abs.err = 1.78e-04 on row 7093
        max.rel.err = 1.15e-04 on row 7093
        Low quality

KKT.DE: max.abs.err = 2.22e-16 on column 1
        max.rel.err = 7.40e-17 on column 1
        High quality

KKT.DB: max.abs.err = 1.27e-32 on row 616
        max.rel.err = 1.27e-32 on row 616
        High quality

With the LP presolver disabled:

Karush-Kuhn-Tucker optimality conditions:

KKT.PE: max.abs.err = 5.33e-15 on row 2121
        max.rel.err = 2.51e-16 on row 1850
        High quality

KKT.PB: max.abs.err = 5.49e-09 on row 5542
        max.rel.err = 8.41e-10 on row 6424
        High quality

KKT.DE: max.abs.err = 2.27e-13 on column 14
        max.rel.err = 1.14e-16 on column 14
        High quality

KKT.DB: max.abs.err = 0.00e+00 on row 0
        max.rel.err = 0.00e+00 on row 0
        High quality

Though you have remove tiny constraint coefficients, some tiny
objective coefficients and rhs'es are still present:

...
 + 1000 x_252 + 1000 x_253 + 1000 x_254 + 1000 x_255 + 1000 x_256
 + 1000 x_257 + 1.02222182124554e-320 x_258 + 1.269748709812e-321 x_260
 + 1.27468936627042e-321 x_261 + 1.27963002272883e-321 x_262
...
 r_12546: - 0.390080337078652 x_141 - 0.000132954060588553 x_140
 - 0.609786708860759 x_124 - x_1 <= 2.12199579145934e-314
 r_12547: - 1.32911392398682e-05 x_173 - 0.483067045939412 x_157
 - 0.516919662921348 x_156 - x_1 <= 4.94065645841247e-324
 r_12548: - 1.32911392398682e-05 x_77 - 0.488017045939413 x_61
 - 0.511969662921347 x_60 - x_1 <= 5.29584241027461e-315


Andrew Makhorin