Re: [Bug-glpk] 4.39 fails to produde optimal solution

[Andrew Makhorin]

Looks like large constraint coefficients cause the effect described
in the paper:

A. Neumaier and O. Shcherbina, Safe bounds in linear and mixed-integer
programming, Math. Programming A 99 (2004), 283-296.
http://www.mat.univie.ac.at/~neum/ms/mip.pdf

when tightening the feasible region "improves" the optimum.

In particular, if MIR or Gomory mixed integer cuts are enabled, glpsol
finds the correct solution:

$ glpsol --cpxlp glpkin.txt --mir
GLPSOL: GLPK LP/MIP Solver 4.40
Reading problem data from `glpkin.txt'...
12 rows, 48 columns, 216 non-zeros
48 integer variables, all of which are binary
178 lines were read
ipp_basic_tech:  0 row(s) and 0 column(s) removed
ipp_reduce_bnds: 1 pass(es) made, 0 bound(s) reduced
ipp_basic_tech:  0 row(s) and 0 column(s) removed
ipp_reduce_coef: 1 pass(es) made, 0 coefficient(s) reduced
glp_intopt: presolved MIP has 12 rows, 48 columns, 216 non-zeros
glp_intopt: 48 integer columns, all of which are binary
Scaling...
 A: min|aij| =  1.000e+00  max|aij| =  5.040e+07  ratio =  5.040e+07
GM: min|aij| =  6.708e-01  max|aij| =  1.491e+00  ratio =  2.222e+00
EQ: min|aij| =  4.650e-01  max|aij| =  1.000e+00  ratio =  2.151e+00
2N: min|aij| =  2.500e-01  max|aij| =  1.439e+00  ratio =  5.758e+00
Constructing initial basis...
Size of triangular part = 12
Solving LP relaxation...
*     0: obj =   5.975086563e+04  infeas =  0.000e+00 (0)
*    23: obj =   4.295331243e+04  infeas =  0.000e+00 (0)
OPTIMAL SOLUTION FOUND
Integer optimization begins...
MIR cuts enabled
+    23: mip =     not found yet >=              -inf        (1; 0)
+    63: >>>>>   4.296612894e+04 >=   4.295331243e+04 < 0.1% (7; 0)
+    64: >>>>>   4.295674010e+04 >=   4.295331243e+04 < 0.1% (5; 3)
+    65: >>>>>   4.295528707e+04 >=   4.295331243e+04 < 0.1% (4; 5)
+    80: >>>>>   4.295372226e+04 >=   4.295346307e+04 < 0.1% (2; 8)
+    84: mip =   4.295372226e+04 >=     tree is empty   0.0% (0; 13)
INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.2 Mb (162716 bytes)