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Why Barrier report numerical trouble encountered even the ranges are not large?

Ongoing
Hongyu Zhang
  • Gurobi-versary
  • First Comment
  • First Question

Hello!

I am using Barrier with persovle on to solve an LP. So I rescaled the model to make the matrix and objective range relatively small. And this model is solved with dual simplex without an issue. But when I switched to Barrier, it reported the numerical issue encountered. I need to scale the model up to a much larger one so I am going to need Barrier to solve it fast. In such case, do I need to further rescale the model to have even smaller ranges? Or is there any other solution that doesn't sacrifice too much performance while using Barrier? Because it is hard to rescale further.

The output log is attached. Thanks in advance.

Kind regards,

Hongyu.

Model fingerprint: 0xcd057ed6
Coefficient statistics:
  Matrix range     [1e-04, 2e+04]
  Objective range  [6e-01, 2e+03]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e-01, 1e+03]
Presolve removed 81660 rows and 49380 columns
Presolve time: 1.41s
Presolved: 289712 rows, 712740 columns, 2402574 nonzeros
Ordering time: 2.30s

Barrier statistics:
 Dense cols : 12
 Free vars  : 15693
 AA' NZ     : 3.543e+06
 Factor NZ  : 3.045e+07 (roughly 700 MB of memory)
 Factor Ops : 5.356e+09 (less than 1 second per iteration)
 Threads    : 8

                  Objective                Residual
Iter       Primal          Dual         Primal    Dual     Compl     Time
   0  -2.40240648e+11  3.07930172e+09  2.00e+07 6.08e+02  2.29e+08     5s
   1  -1.36091287e+11  3.85190263e+09  4.34e+06 7.34e+03  5.49e+07     5s
   2  -9.94340058e+11  3.80477961e+09  5.25e+05 6.83e+03  4.72e+07     6s
   3  -1.00415108e+12  3.72550505e+09  3.97e+04 1.59e+03  1.09e+07     6s
   4  -7.04851902e+11  3.77142622e+09  1.49e+03 5.71e+02  3.82e+06     7s
   5  -5.56735775e+11  1.64940111e+09  5.90e+02 1.40e+02  1.24e+06     7s
   6  -2.88873336e+11  9.36792842e+08  1.50e+02 5.40e+01  4.56e+05     7s
   7  -1.24067611e+11  3.56691582e+08  4.94e+01 1.50e+01  1.51e+05     8s
   8  -1.32706878e+10  8.44224669e+07  1.83e+00 1.09e+00  1.39e+04     8s
   9  -2.40871126e+09  4.37418704e+07  2.97e-01 2.14e-01  2.53e+03     8s
  10  -1.01176831e+09  3.26167380e+07  1.18e-01 2.74e-03  1.08e+03     9s
  11  -4.36085869e+08  2.83322506e+07  4.97e-02 1.09e-03  4.78e+02     9s
  12  -2.53251522e+08  2.70390427e+07  2.86e-02 8.79e-04  2.87e+02     9s
  13  -1.95481903e+08  2.67258768e+07  2.26e-02 8.24e-04  2.27e+02    10s
  14  -1.06350144e+08  2.18199844e+07  1.35e-02 3.46e-04  1.30e+02    10s
  15  -6.30170224e+07  1.75846458e+07  9.37e-03 2.00e-04  8.08e+01    11s
  16  -4.64458196e+07  1.59399899e+07  1.02e-02 1.96e-04  6.19e+01    11s
  17  -2.66310906e+07  1.47716529e+07  8.88e-03 1.66e-04  4.00e+01    11s
  18  -1.62282081e+07  1.11351346e+07  6.54e-03 9.46e-05  2.56e+01    12s
  19  -7.79618594e+06  8.79672104e+06  4.14e-03 6.39e-05  1.44e+01    13s
  20  -4.54682358e+06  6.51967196e+06  1.82e-03 4.11e-05  8.78e+00    14s
  21  -2.47458445e+06  5.81273095e+06  1.16e-03 3.68e-05  5.89e+00    15s
  22  -1.71121304e+06  4.76636789e+06  8.53e-04 3.07e-05  4.17e+00    16s
  23  -1.12940502e+06  4.07611454e+06  7.24e-04 2.35e-05  2.96e+00    17s
  24  -6.71295365e+05  3.67587326e+06  7.79e-04 2.19e-05  2.18e+00    18s
  25  -5.79110461e+05  3.12282829e+06  7.71e-04 1.54e-05  1.66e+00    19s
  26  -4.86900476e+05  2.92241576e+06  6.97e-04 1.32e-05  1.43e+00    20s
  27  -3.77397571e+05  2.61630268e+06  5.71e-04 9.90e-06  1.12e+00    21s
  28  -2.57051548e+05  2.51645979e+06  5.48e-04 8.93e-06  9.43e-01    22s
  29  -2.25011914e+05  2.34475003e+06  5.28e-04 7.32e-06  7.90e-01    23s
  30  -1.58183597e+05  2.22735569e+06  5.04e-04 6.07e-06  6.42e-01    24s
  31  -1.34910590e+05  2.06902562e+06  5.42e-04 4.77e-06  5.20e-01    25s
  32  -1.03972417e+05  1.92662111e+06  6.48e-04 3.68e-06  4.00e-01    26s
  33  -9.39748246e+04  1.86464122e+06  6.84e-04 3.27e-06  3.58e-01    27s
  34  -8.53082273e+04  1.82496627e+06  6.96e-04 2.98e-06  3.30e-01    28s
  35  -7.81117691e+04  1.81045075e+06  6.88e-04 2.89e-06  3.15e-01    29s
  36  -6.39140087e+04  1.78891560e+06  6.29e-04 2.76e-06  2.90e-01    30s
  37  -5.12439772e+04  1.70326883e+06  5.74e-04 2.25e-06  2.36e-01    31s
  38  -4.77224372e+04  1.68249785e+06  5.78e-04 2.13e-06  2.23e-01    33s
  39  -4.58244633e+04  1.65519466e+06  5.80e-04 1.98e-06  2.10e-01    34s
  40  -4.33535630e+04  1.65088222e+06  5.81e-04 1.96e-06  2.06e-01    35s
  41  -3.95033021e+04  1.63406341e+06  5.82e-04 1.87e-06  1.95e-01    36s
  42  -3.43303048e+04  1.61121508e+06  5.85e-04 1.75e-06  1.81e-01    37s
  43  -2.97486695e+04  1.58871948e+06  5.87e-04 1.64e-06  1.68e-01    38s
  44  -2.08445761e+04  1.56342789e+06  5.91e-04 1.51e-06  1.50e-01    39s
  45  -1.71339053e+04  1.53953533e+06  5.89e-04 1.58e-06  1.37e-01    40s
  46  -1.19754765e+04  1.52094748e+06  5.49e-04 1.40e-06  1.26e-01    41s
  47  -8.90823963e+03  1.49609844e+06  5.44e-04 1.21e-06  1.14e-01    42s
  48  -5.12804609e+03  1.47367706e+06  5.49e-04 1.09e-06  1.04e-01    43s
  49  -4.62606798e+02  1.44807637e+06  5.67e-04 9.80e-07  9.18e-02    44s
  50   3.77400518e+03  1.43018953e+06  5.82e-04 8.96e-07  8.23e-02    45s
  51   6.04970567e+03  1.40998930e+06  5.81e-04 8.05e-07  7.45e-02    46s
  52   6.05042474e+03  1.40997994e+06  5.81e-04 8.05e-07  7.45e-02    47s
  53   8.89551921e+03  1.40381639e+06  5.77e-04 7.78e-07  7.03e-02    48s
  54   1.02836076e+04  1.38166776e+06  5.76e-04 6.66e-07  6.26e-02    49s
  55   1.21481826e+04  1.36979845e+06  5.65e-04 6.29e-07  5.85e-02    50s
  56   1.28725765e+04  1.36411085e+06  5.67e-04 6.12e-07  5.68e-02    51s
  57   1.38629564e+04  1.35836931e+06  5.58e-04 5.95e-07  5.50e-02    53s
  58   1.47269535e+04  1.35427493e+06  5.51e-04 5.88e-07  5.33e-02    54s
  59   1.58426503e+04  1.35277422e+06  5.41e-04 5.87e-07  5.21e-02    55s
  60   1.73620976e+04  1.33708774e+06  5.27e-04 5.83e-07  4.75e-02    56s
  61   1.77650495e+04  1.33481058e+06  5.30e-04 6.80e-07  4.65e-02    57s
  62   1.89351355e+04  1.32181387e+06  5.35e-04 6.41e-07  4.32e-02    58s
  63   1.97945163e+04  1.31569490e+06  5.39e-04 6.23e-07  4.11e-02    59s
  64   2.02402751e+04  1.31162719e+06  5.40e-04 6.07e-07  4.00e-02    61s
  65   2.04028708e+04  1.31065770e+06  5.41e-04 6.02e-07  3.97e-02    61s
  66   2.16982007e+04  1.30575708e+06  5.47e-04 5.79e-07  3.73e-02    62s
  67   2.17519110e+04  1.30529015e+06  5.47e-04 5.78e-07  3.72e-02    63s
  68   2.19806053e+04  1.30388397e+06  5.47e-04 5.71e-07  3.67e-02    64s
  69   2.25643732e+04  1.29949875e+06  5.48e-04 5.53e-07  3.53e-02    65s
  70   2.26606397e+04  1.29874629e+06  5.48e-04 5.51e-07  3.51e-02    66s
  71   2.26852271e+04  1.29751133e+06  5.48e-04 5.55e-07  3.48e-02    67s
  72   2.26873251e+04  1.29747951e+06  5.48e-04 5.54e-07  3.48e-02    67s
  73   2.28569149e+04  1.29675122e+06  5.50e-04 5.54e-07  3.46e-02    68s
  74   2.31062702e+04  1.29382099e+06  5.63e-04 4.40e-07  3.35e-02    69s
  75   2.31143787e+04  1.29377931e+06  5.63e-04 4.39e-07  3.34e-02    70s
  76   2.35342858e+04  1.29231701e+06  5.92e-04 4.87e-07  3.26e-02    72s
  77   2.35967005e+04  1.29197673e+06  5.93e-04 4.86e-07  3.25e-02    73s
  78   2.41037914e+04  1.28813427e+06  6.05e-04 8.03e-07  3.10e-02    74s
  79   2.41058897e+04  1.28808930e+06  6.05e-04 8.06e-07  3.10e-02    75s
  80   2.42526096e+04  1.28648220e+06  6.06e-04 8.01e-07  3.08e-02    75s
  81   2.44698084e+04  1.28599927e+06  6.11e-04 7.99e-07  3.05e-02    76s
  82   2.44775184e+04  1.28595332e+06  6.11e-04 8.02e-07  3.05e-02    77s
  83   2.44790756e+04  1.28590058e+06  6.12e-04 8.05e-07  3.05e-02    78s
  84   2.47964601e+04  1.28537509e+06  6.12e-04 8.02e-07  3.02e-02    79s

Barrier performed 84 iterations in 78.69 seconds (88.53 work units)
Numerical trouble encountered

Model may be infeasible or unbounded.  Consider using the
homogeneous algorithm (through parameter 'BarHomogeneous')


User-callback calls 5706, time in user-callback 0.01 sec
done in 88.9s 
0

Comments

3 comments

Date Votes
  • Official comment
    Simranjit Kaur
    • Gurobi Staff
    This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
  • David Torres Sanchez
    • Gurobi Staff
    Edited

    Hi Hongyu,

    Have you tried the parameters suggested in Solver parameters to manage numerical issues?
    e.g. Aggregate = 0 or Presolve = 0.

    Also, as mentioned the article linked, you could try changing the solution method, unless you specifically need barrier. If you do need barrier, as indicated at the bottom of the log, try BarHomogeneous = 1.

    Cheers, 
    David

    0
  • Hongyu Zhang
    • Gurobi-versary
    • First Comment
    • First Question

    Hi David,

    Thanks for your answers. The problem attached is a smaller example, but the real problem I am going to solve is a scale-up version of this problem, so I do need to use barrier to yield better performance. 

    I indeed tried with presolve off but it didn't help, and i didn't try aggregate. BarHomogeneous didn't help as well. But mysteriously, setting crossover to 1 solve all the problems. I tried to understand why crossover can help numerical issues. Could you help me understand why?

    Kind regards,

    Hongyu.

    0

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