Originally posted by: fracarz

Dear all,
I am trying to solve an huge MIP model but Cplex stucks during the computation of the "dual objective".
In the following there is a log file in which it is evident that Cplex spends a lot of time computing very very close solutions.
 

Default row names c1, c2 ... being created.
Tried aggregator 2 times.
MIP Presolve eliminated 361 rows and 1 columns.
Aggregator did 84 substitutions.
Reduced MIP has 215467 rows, 209867 columns, and 837956 nonzeros.
Reduced MIP has 116 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.81 sec. (590.90 ticks)
Probing time = 0.36 sec. (69.54 ticks)
Tried aggregator 1 time.
Reduced MIP has 215467 rows, 209867 columns, and 837956 nonzeros.
Reduced MIP has 116 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 1.56 sec. (403.05 ticks)
Probing time = 0.22 sec. (64.58 ticks)
Clique table members: 16.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Initializing dual steep norms . . .
Iteration log . . .
Iteration:     1   Dual objective     =             0.000000
Perturbation started.
Iteration:   303   Dual objective     =             0.238884
Iteration:   788   Dual objective     =             0.238887
Iteration:  1712   Dual objective     =             0.238889
Iteration:  2312   Dual objective     =             0.238890
Iteration:  2827   Dual objective     =             0.238891
Iteration:  3264   Dual objective     =             0.238892
Iteration:  3706   Dual objective     =             0.238893
Iteration:  4120   Dual objective     =             0.238894
Iteration:  4578   Dual objective     =             0.238895
Iteration:  4970   Dual objective     =             0.238896
Elapsed time = 19.44 sec. (10002.49 ticks, 5067 iterations)
Iteration:  5385   Dual objective     =             0.238896
Iteration:  5815   Dual objective     =             0.238897
Iteration:  6233   Dual objective     =             0.238898
Iteration:  6620   Dual objective     =             0.238899
Iteration:  7033   Dual objective     =             0.238900
Elapsed time = 39.79 sec. (20004.87 ticks, 7267 iterations)
Iteration:  7438   Dual objective     =             0.238901
Iteration:  7882   Dual objective     =             0.238902
Iteration:  8253   Dual objective     =             0.238903
Iteration:  8641   Dual objective     =             0.238904
Iteration:  9056   Dual objective     =             0.238905
Elapsed time = 60.54 sec. (30009.36 ticks, 9214 iterations)
Iteration:  9441   Dual objective     =             0.238906
Iteration:  9822   Dual objective     =             0.238906
Iteration: 10186   Dual objective     =             0.238907
Iteration: 10552   Dual objective     =             0.238908
Iteration: 10942   Dual objective     =             0.238909
Elapsed time = 81.69 sec. (40013.96 ticks, 11043 iterations)
Iteration: 11309   Dual objective     =             0.238910
Iteration: 11692   Dual objective     =             0.238911
Iteration: 12057   Dual objective     =             0.238912
Iteration: 12416   Dual objective     =             0.238913
Iteration: 12770   Dual objective     =             0.238914
Elapsed time = 102.89 sec. (50014.43 ticks, 12780 iterations)
Iteration: 13121   Dual objective     =             0.238915
Iteration: 13464   Dual objective     =             0.238916
Iteration: 13820   Dual objective     =             0.238916
Iteration: 14203   Dual objective     =             0.238918
Elapsed time = 124.58 sec. (60017.13 ticks, 14519 iterations)
Iteration: 14537   Dual objective     =             0.238919
Iteration: 14904   Dual objective     =             0.238920
Iteration: 15289   Dual objective     =             0.238921
Iteration: 15678   Dual objective     =             0.238923
Iteration: 16030   Dual objective     =             0.238923
Elapsed time = 145.94 sec. (70022.44 ticks, 16243 iterations)
Iteration: 16368   Dual objective     =             0.238924
Iteration: 16704   Dual objective     =             0.238925
Iteration: 17038   Dual objective     =             0.238926
Iteration: 17373   Dual objective     =             0.238926
Iteration: 17743   Dual objective     =             0.238927
Elapsed time = 167.42 sec. (80029.25 ticks, 17774 iterations)
Iteration: 18107   Dual objective     =             0.238928
Iteration: 18462   Dual objective     =             0.238929
Iteration: 18811   Dual objective     =             0.238930
Iteration: 19149   Dual objective     =             0.238931
Elapsed time = 189.07 sec. (90030.26 ticks, 19442 iterations)
Iteration: 19496   Dual objective     =             0.238932
Iteration: 19843   Dual objective     =             0.238933
Iteration: 20197   Dual objective     =             0.238933
Iteration: 20541   Dual objective     =             0.238934
Iteration: 20902   Dual objective     =             0.238935
Elapsed time = 210.99 sec. (100032.41 ticks, 21127 iterations)
Iteration: 21253   Dual objective     =             0.238936
Iteration: 21594   Dual objective     =             0.238937
Iteration: 21949   Dual objective     =             0.238937
Iteration: 22330   Dual objective     =             0.238938
Iteration: 22702   Dual objective     =             0.238939
Elapsed time = 233.23 sec. (110037.84 ticks, 22909 iterations)
Iteration: 23050   Dual objective     =             0.238939
Iteration: 23393   Dual objective     =             0.238940
Iteration: 23750   Dual objective     =             0.238940
Iteration: 24102   Dual objective     =             0.238941
Iteration: 24452   Dual objective     =             0.238941
Elapsed time = 255.52 sec. (120038.08 ticks, 24599 iterations)
Iteration: 24807   Dual objective     =             0.238942
Iteration: 25168   Dual objective     =             0.238943
Iteration: 25529   Dual objective     =             0.238944
Iteration: 25874   Dual objective     =             0.238944
Iteration: 26224   Dual objective     =             0.238946
Elapsed time = 278.06 sec. (130044.28 ticks, 26255 iterations)
Iteration: 26574   Dual objective     =             0.238946
Iteration: 26917   Dual objective     =             0.238947
Iteration: 27265   Dual objective     =             0.238948
Iteration: 27612   Dual objective     =             0.238948
Elapsed time = 300.75 sec. (140044.80 ticks, 27917 iterations)
Iteration: 27948   Dual objective     =             0.238949
Iteration: 28306   Dual objective     =             0.238949
Iteration: 28644   Dual objective     =             0.238950
Iteration: 29006   Dual objective     =             0.238950
Iteration: 29365   Dual objective     =             0.238951
Elapsed time = 323.88 sec. (150047.15 ticks, 29682 iterations)
Iteration: 29704   Dual objective     =             0.238951
Iteration: 30041   Dual objective     =             0.238951
Iteration: 30380   Dual objective     =             0.238952
Iteration: 30736   Dual objective     =             0.238952
Iteration: 31091   Dual objective     =             0.238953
Elapsed time = 347.60 sec. (160071.82 ticks, 31445 iterations)
Iteration: 31445   Dual objective     =             0.238954
Iteration: 31792   Dual objective     =             0.238954
Iteration: 32137   Dual objective     =             0.238955
Iteration: 32470   Dual objective     =             0.238955
Iteration: 32793   Dual objective     =             0.238956
Elapsed time = 370.94 sec. (170077.10 ticks, 33085 iterations)
Iteration: 33130   Dual objective     =             0.238957
Iteration: 33454   Dual objective     =             0.238957
Iteration: 33832   Dual objective     =             0.238957
Iteration: 34179   Dual objective     =             0.238958
Iteration: 34523   Dual objective     =             0.238959
Elapsed time = 394.27 sec. (180084.74 ticks, 34718 iterations)
Iteration: 34846   Dual objective     =             0.238959
Iteration: 35203   Dual objective     =             0.238959
Iteration: 35540   Dual objective     =             0.238961
Iteration: 35888   Dual objective     =             0.238961
Iteration: 36241   Dual objective     =             0.238962
Elapsed time = 418.34 sec. (190085.13 ticks, 36382 iterations)
Iteration: 36590   Dual objective     =             0.238962
Iteration: 36947   Dual objective     =             0.238963
Iteration: 37286   Dual objective     =             0.238964
Iteration: 37621   Dual objective     =             0.238965
Iteration: 37936   Dual objective     =             0.238965
Elapsed time = 442.74 sec. (200089.36 ticks, 38057 iterations)
Iteration: 38272   Dual objective     =             0.238965
Iteration: 38637   Dual objective     =             0.238966
Iteration: 38990   Dual objective     =             0.238966
Iteration: 39327   Dual objective     =             0.238966
Iteration: 39644   Dual objective     =             0.238967
Elapsed time = 467.85 sec. (210094.97 ticks, 39768 iterations)
Iteration: 39983   Dual objective     =             0.238967
Iteration: 40322   Dual objective     =             0.238967
Iteration: 40696   Dual objective     =             0.238967
Iteration: 41038   Dual objective     =             0.238968
Iteration: 41351   Dual objective     =             0.238969
Elapsed time = 492.22 sec. (220101.76 ticks, 41384 iterations)
Iteration: 41678   Dual objective     =             0.238969
Iteration: 42011   Dual objective     =             0.238970
Iteration: 42332   Dual objective     =             0.238970
Iteration: 42653   Dual objective     =             0.238971
Iteration: 42982   Dual objective     =             0.238971
Elapsed time = 517.02 sec. (230104.66 ticks, 43080 iterations)
Iteration: 43338   Dual objective     =             0.238971
Iteration: 43652   Dual objective     =             0.238971
Iteration: 44021   Dual objective     =             0.238971
Iteration: 44336   Dual objective     =             0.238971
Iteration: 44669   Dual objective     =             0.238972
Elapsed time = 541.98 sec. (240109.11 ticks, 44752 iterations)
Iteration: 44998   Dual objective     =             0.238972
Iteration: 45320   Dual objective     =             0.238972
Iteration: 45660   Dual objective     =             0.238972
Iteration: 46007   Dual objective     =             0.238972
Iteration: 46356   Dual objective     =             0.238973
Elapsed time = 568.40 sec. (250113.85 ticks, 46489 iterations)
Iteration: 46680   Dual objective     =             0.238973
Iteration: 47008   Dual objective     =             0.238973
Iteration: 47370   Dual objective     =             0.238973
Iteration: 47734   Dual objective     =             0.238973
Elapsed time = 587.33 sec. (260116.37 ticks, 47986 iterations)
Iteration: 48052   Dual objective     =             0.238973
Iteration: 48382   Dual objective     =             0.238973
Iteration: 48738   Dual objective     =             0.238973
Iteration: 49080   Dual objective     =             0.238974
Iteration: 49420   Dual objective     =             0.238974
Elapsed time = 606.87 sec. (270121.42 ticks, 49596 iterations)
Iteration: 49768   Dual objective     =             0.238974
Iteration: 50156   Dual objective     =             0.238974
Iteration: 50483   Dual objective     =             0.238974
Iteration: 50835   Dual objective     =             0.238974
Elapsed time = 623.25 sec. (280128.34 ticks, 51061 iterations)
Iteration: 51177   Dual objective     =             0.238975
Iteration: 51503   Dual objective     =             0.238975
Iteration: 51837   Dual objective     =             0.238976
Iteration: 52166   Dual objective     =             0.238976
Iteration: 52506   Dual objective     =             0.238976
Elapsed time = 640.12 sec. (290132.38 ticks, 52514 iterations)
Iteration: 52822   Dual objective     =             0.238976
Iteration: 53132   Dual objective     =             0.238976
Iteration: 53458   Dual objective     =             0.238977
Iteration: 53793   Dual objective     =             0.238977
Elapsed time = 657.25 sec. (300134.34 ticks, 53883 iterations)
Iteration: 54116   Dual objective     =             0.238978
Iteration: 54437   Dual objective     =             0.238978
Iteration: 54790   Dual objective     =             0.238978
Iteration: 55140   Dual objective     =             0.238978
Elapsed time = 674.38 sec. (310141.43 ticks, 55379 iterations)
Iteration: 55507   Dual objective     =             0.238978
Iteration: 55852   Dual objective     =             0.238978
Iteration: 56200   Dual objective     =             0.238978
Iteration: 56515   Dual objective     =             0.238978
Elapsed time = 691.65 sec. (320143.35 ticks, 56842 iterations)
Iteration: 56847   Dual objective     =             0.238978
Iteration: 57207   Dual objective     =             0.238979
Iteration: 57550   Dual objective     =             0.238979
Iteration: 57901   Dual objective     =             0.238979
Iteration: 58224   Dual objective     =             0.238979
Elapsed time = 708.04 sec. (330147.41 ticks, 58258 iterations)
Iteration: 58601   Dual objective     =             0.238979
Iteration: 58926   Dual objective     =             0.238979
Iteration: 59330   Dual objective     =             0.238979
Iteration: 59690   Dual objective     =             0.238979
Elapsed time = 724.09 sec. (340151.90 ticks, 59720 iterations)
Iteration: 60122   Dual objective     =             0.238979
Iteration: 60469   Dual objective     =             0.238979
Iteration: 60866   Dual objective     =             0.238980
Iteration: 61288   Dual objective     =             0.238980
Elapsed time = 740.48 sec. (350152.01 ticks, 61294 iterations)
Iteration: 61722   Dual objective     =             0.238980
Iteration: 62140   Dual objective     =             0.238980
Removing perturbation.
Root relaxation solution time = 752.44 sec. (357455.64 ticks)
        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap
      0     0        0.2389    83                      0.2389    62538        
*     0+    0                            0.2389        0.2389             0.00%
Found incumbent of value 0.238884 after 774.12 sec. (366532.45 ticks)
      0     0        cutoff              0.2389        0.2389    62538    0.00%
Elapsed time = 774.13 sec. (366533.69 ticks, tree = 0.01 MB, solutions = 1)
Root node processing (before b&c):
  Real time             =  774.20 sec. (366540.93 ticks)
Sequential b&c:
  Real time             =    0.00 sec. (0.00 ticks)
                          ------------
Total (root+branch&cut) =  774.20 sec. (366540.93 ticks)
Optimal    Optimal
 

This is one of few cases in which I found an optimal solution but often the computation reaches the time limit of 1 hour without leaving the "Dual Objective" phase.

1. Is there a way to reduce the computational time dedicated to this phase and proceed with the exploration of the search tree?
2. Is the "Dual objective" phase so long because of the huge size of problem (~250.000 variables and constraints?)

The problem dimensions are not overly large by the standards of what CPLEX can handle, and the matrix is very sparse. Have you tried changing the root node algorithm to the barrier algorithm?

When trying the barrier algorithm, maybe also consider using more than only a single thread in case you have more than one core on your machine.

Originally posted by: fracarz

Thank you so much for yours answers.

PaulRubin I often read your blog, it is very interesting. I found on it very useful topic like "User Cuts versus Lazy Constraints".

Coming back to my problem. I rerun the code with the barrier method and, as both of you expended, there are improvements. Now CPLEX start to visit the search tree but "only" the root node of the search tree. In the following the new (cutted) logfile is reported:

Tried aggregator 1 time.
MIP Presolve eliminated 1 rows and 1 columns.
Reduced MIP has 215031 rows, 209231 columns, and 1044484 nonzeros.
Reduced MIP has 200 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.44 sec. (293.36 ticks)
Probing time = 0.35 sec. (84.92 ticks)
Tried aggregator 1 time.
Reduced MIP has 215031 rows, 209231 columns, and 1044484 nonzeros.
Reduced MIP has 200 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 1.32 sec. (446.54 ticks)
Probing time = 0.24 sec. (83.20 ticks)
Clique table members: 100.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Tried aggregator 0 times.
No LP presolve or aggregator reductions.
Presolve time = 0.17 sec. (83.04 ticks)
Symmetry aggregator did 49013 additional substitutions.
Tried aggregator 0 times.
Reduced presolve eliminated 3 rows and 0 columns.
Reduced LP has 190293 rows, 184953 columns, and 922563 nonzeros.
Presolve time = 0.19 sec. (108.28 ticks)
Parallel mode: none, using 1 thread for barrier

***NOTE: Found 174 dense columns.

Number of nonzeros in lower triangle of A*A' = 1238748
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.21 sec. (191.65 ticks)
Summary statistics for Cholesky factor:
  Rows in Factor            = 190293
  Integer space required    = 813878
  Total non-zeros in factor = 5327524
  Total FP ops to factor    = 6813310148
 Itn      Primal Obj        Dual Obj  Prim Inf Upper Inf  Dual Inf          
   0   4.7950797e+00  -1.8459150e+05  3.94e+05  1.85e+05  1.85e+05
   1   4.9389309e+00  -1.0842783e+05  2.23e+05  1.04e+05  9.51e+04
   2   4.3679541e+00  -1.2242800e+05  1.93e+05  9.03e+04  8.26e+04
   3   4.1917711e+00  -9.8515166e+04  1.77e+05  8.31e+04  6.06e+04
   4   3.9472919e+00  -7.4750536e+04  1.53e+05  7.17e+04  4.12e+04
   5   3.6621262e+00  -4.3433533e+04  1.25e+05  5.88e+04  1.95e+04
   6   2.3700154e+00  -9.3136650e+03  4.69e+03  2.20e+03  2.15e+02
   7   2.3164581e+00  -1.5466704e+02  5.97e-06  5.08e-12  3.23e+00
   8   2.2924633e+00  -6.2674829e+01  6.30e-06  4.90e-12  1.34e+00
   9   2.1153110e+00  -3.7715207e+01  6.08e-06  6.93e-12  8.15e-01
  10   1.7500152e+00  -2.0695076e+01  5.88e-06  5.41e-12  4.63e-01
  11   1.1506156e+00  -7.2189818e+00  5.75e-06  5.34e-12  1.73e-01
  12   9.6082980e-01  -5.5178392e+00  5.52e-06  5.59e-12  1.36e-01
  13   6.3939402e-01  -2.4657315e+00  5.14e-06  5.16e-12  6.53e-02
  14   3.6817963e-01  -2.0235292e-01  5.07e-06  4.99e-12  1.04e-02
  15   2.6178114e-01   2.1917759e-01  4.73e-06  5.28e-12  3.56e-04
  16   2.3989951e-01   2.3867067e-01  3.67e-06  5.74e-12  3.77e-06
  17   2.3889373e-01   2.3888143e-01  3.89e-06  5.88e-12  3.77e-08
  18   2.3888367e-01   2.3888354e-01  3.22e-06  5.89e-12  3.86e-10
  19   2.3888357e-01   2.3888357e-01  2.90e-06  5.94e-12  1.28e-11
  20   2.3888357e-01   2.3888357e-01  2.66e-06  5.89e-12  8.95e-12
Barrier time = 218.25 sec. (159310.38 ticks)

Total time on 1 threads = 219.55 sec. (159591.91 ticks)
Barrier time = 219.42 sec. (159525.25 ticks)

Primal crossover.
  Primal:  Fixing 140492 variables.
   140491 PMoves:  Infeasibility  1.86499760e-09  Objective  2.38883565e-01
   139246 PMoves:  Infeasibility  1.09680487e-09  Objective  2.38883565e-01
   137824 PMoves:  Infeasibility  1.04716344e-09  Objective  2.38883565e-01
   136305 PMoves:  Infeasibility  9.14382098e-10  Objective  2.38883565e-01
   134773 PMoves:  Infeasibility  4.47775067e-10  Objective  2.38883565e-01
   ........................................................................
   ........................................................................
   ........................................................................
   ........................................................................
        0 DMoves:  Infeasibility  2.23104406e-10  Objective  2.38883565e-01
  Dual:  Pushed 6359, exchanged 27742.
Using devex.
Total crossover time = 37.64 sec. (19083.76 ticks)

Total time on 1 threads = 257.22 sec. (178692.05 ticks)
Root relaxation solution time = 257.26 sec. (178696.95 ticks)

        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap

      0     0        0.2389   168                      0.2389        0         

Implied bound cuts applied:  490
Mixed integer rounding cuts applied:  38

Root node processing (before b&c):
  Real time             = 3608.64 sec. (1665131.87 ticks)
Sequential b&c:
  Real time             =    0.00 sec. (0.00 ticks)
                          ------------
Total (root+branch&cut) = 3608.64 sec. (1665131.87 ticks)

3600 is the time limit. Do you think that the complexity of the problem depends on its size or because of a bad model (actually, I would to show that) or there could be other reasons?

Thanks again for you help.

It looks like CPLEX is stuck in either at cut separation or in some heuristic at the root node. Can you try without cuts (set CPX_PARAM_CUTPASS to -1) and/or without heuristics (set CPX_PARAM_HEURFREQ to -1) and see if that gets you any further?

Also, are you willing to share a SAV file of your model either here or with daniel(dot)junglas(at)de(dot)ibm(dot)com. Then we could check here where the time is burnt.

Originally posted by: fracarz

I cannot access to the computer with the source code until the end of this month. At beginning of September I will try your advises and I wil send you the sav file too. 

Thanks. 

Originally posted by: fracarz

Dear DanielJunglas,
there was a mistake in my previous consideration because, without the barrier algorithm, the problem was solved in 774.20 seconds while, with the barrier 
algorithm, the model starts to visit the search tree nodes but again the time limit is reached without solving the problem. 
For this reason I carried out another test without the barrier method and I disabled both the heuristics (HeurFreq=-1) and the cuts (CUTPASS=-1). However, even 
in this case the time limit is reached. 

In the following there is the new logfile while you can download the sav file from here: 
https://dl.dropboxusercontent.com/u/6741257/model.sav.zip

.... 
Tried aggregator 1 time.
MIP Presolve eliminated 1 rows and 1 columns.
Reduced MIP has 215031 rows, 209231 columns, and 1044484 nonzeros.
Reduced MIP has 200 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 0.40 sec. (293.36 ticks)
Probing time = 0.27 sec. (84.92 ticks)
Tried aggregator 1 time.
Reduced MIP has 215031 rows, 209231 columns, and 1044484 nonzeros.
Reduced MIP has 200 binaries, 0 generals, 0 SOSs, and 0 indicators.
Presolve time = 1.08 sec. (446.54 ticks)
Probing time = 0.17 sec. (83.20 ticks)
Clique table members: 100.
MIP emphasis: balance optimality and feasibility.
MIP search method: dynamic search.
Parallel mode: none, using 1 thread.
Initializing dual steep norms . . .

Iteration log . . .
Iteration:     1   Dual objective     =             0.000000
Perturbation started.
Iteration:   303   Dual objective     =             0.238884
Iteration:   931   Dual objective     =             0.238887
Iteration:  1661   Dual objective     =             0.238889
Iteration:  2226   Dual objective     =             0.238890
Iteration:  2903   Dual objective     =             0.238891
Iteration:  3592   Dual objective     =             0.238892
Iteration:  4401   Dual objective     =             0.238894
Iteration:  5146   Dual objective     =             0.238895
Iteration:  5776   Dual objective     =             0.238896
Iteration:  6143   Dual objective     =             0.238897
Iteration:  6553   Dual objective     =             0.238897
Iteration:  6935   Dual objective     =             0.238898
Iteration:  7303   Dual objective     =             0.238898
Elapsed time = 14.66 sec. (10005.56 ticks, 7329 iterations)
Iteration:  7665   Dual objective     =             0.238899
Iteration:  8016   Dual objective     =             0.238899
Iteration:  8361   Dual objective     =             0.238900
Iteration:  8686   Dual objective     =             0.238900
Elapsed time = 30.31 sec. (20007.08 ticks, 8995 iterations)
Iteration:  9047   Dual objective     =             0.238901
Iteration:  9379   Dual objective     =             0.238901
Iteration:  9737   Dual objective     =             0.238902
Iteration: 10092   Dual objective     =             0.238902
Iteration: 10436   Dual objective     =             0.238903
Elapsed time = 46.13 sec. (30007.90 ticks, 10582 iterations)
Iteration: 10768   Dual objective     =             0.238904
Iteration: 11092   Dual objective     =             0.238905
Iteration: 11408   Dual objective     =             0.238905
Iteration: 11730   Dual objective     =             0.238906
Elapsed time = 62.48 sec. (40020.40 ticks, 12047 iterations)
.............................................................
.............................................................
.............................................................
.............................................................
Elapsed time = 3532.73 sec. (2807114.85 ticks, 217110 iterations)
Iteration: 217250   Dual objective     =             0.239245
Iteration: 217466   Dual objective     =             0.239245
Iteration: 217665   Dual objective     =             0.239245
Elapsed time = 3544.51 sec. (2817124.90 ticks, 217730 iterations)
Iteration: 217879   Dual objective     =             0.239246
Iteration: 218075   Dual objective     =             0.239246
Iteration: 218280   Dual objective     =             0.239246
Elapsed time = 3556.20 sec. (2827130.93 ticks, 218318 iterations)
Iteration: 218489   Dual objective     =             0.239247
Iteration: 218712   Dual objective     =             0.239248
Elapsed time = 3568.06 sec. (2837262.64 ticks, 218937 iterations)
Iteration: 218937   Dual objective     =             0.239248
Iteration: 219148   Dual objective     =             0.239248
Iteration: 219361   Dual objective     =             0.239249
Elapsed time = 3580.40 sec. (2847637.89 ticks, 219594 iterations)
Iteration: 219594   Dual objective     =             0.239249
Iteration: 219811   Dual objective     =             0.239249
Iteration: 220007   Dual objective     =             0.239250
Iteration: 220211   Dual objective     =             0.239250
Elapsed time = 3592.21 sec. (2857640.29 ticks, 220217 iterations)
Iteration: 220416   Dual objective     =             0.239250
Iteration: 220615   Dual objective     =             0.239250
Iteration: 220824   Dual objective     =             0.239251
Elapsed time = 3604.07 sec. (2867648.71 ticks, 220855 iterations)
Removing perturbation.
Root relaxation solution time = 3606.22 sec. (2869672.82 ticks)

        Nodes                                         Cuts/
   Node  Left     Objective  IInf  Best Integer    Best Bound    ItCnt     Gap

      0     0  -1.00000e+37     0                      0.0000   220961         

Root node processing (before b&c):
  Real time             = 3608.72 sec. (2870808.20 ticks)
Sequential b&c:
  Real time             =    0.00 sec. (0.00 ticks)
                          ------------
Total (root+branch&cut) = 3608.72 sec. (2870808.20 ticks)
Unknown    AbortTimeLim

I finally managed to reproduce your problem here. This seems to be one of the cases in which Simplex performs really bad and you should switch to using barrier. The following settings worked for me (cplex 12.6.3):

CPX_PARAM_THREADS                1
CPX_PARAM_CLIQUES                -1
CPX_PARAM_COVERS                 -1
CPX_PARAM_MIPDISPLAY             5
CPX_PARAM_STARTALG               4
CPX_PARAM_SUBALG                 4
CPX_PARAM_FLOWCOVERS             -1
CPX_PARAM_IMPLBD                 -1
CPX_PARAM_GUBCOVERS              -1
CPX_PARAM_FRACCUTS               -1
CPX_PARAM_FLOWPATHS              -1
CPX_PARAM_MIRCUTS                -1
CPX_PARAM_DISJCUTS               -1
CPX_PARAM_CUTPASS                -1
CPX_PARAM_ZEROHALFCUTS           -1
CPX_PARAM_MCFCUTS                -1
CPX_PARAM_LANDPCUTS              -1
CPX_PARAM_LOCALIMPLBD            -1
CPX_PARAM_BQPCUTS                -1

Setting CPX_PARAM_MIPDISPLAY is only optional but it at least gives you additional log output to show that CPLEX is not stuck. The important part is to switch to barrier (startalg and subalg) and to disable cuts.

Originally posted by: fracarz

Dear DanielJunglas,

by using your parameters the problem seems solved. Cplex complete the operations on the root node in 400 seconds and starts to visit the search tree. Thank you so much.