Set parameter TokenServer to value "gurobi.cc.ic.ac.uk"

********************************
*** COLUMN GENERATION SCHEME ***
********************************

*** OUTER ITERATION 0 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.8955 seconds.
    local lower bound updated to 0.220088
    local upper bound updated to 0.437241

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.45922 seconds.
    local lower bound updated to 0.42612
    local upper bound updated to 0.42612
The Primal step takes 3.35739 (S)
lower bound updated to 0.42612

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.488434
    local lower bound updated to 0.485318

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.485318
    local lower bound updated to 0.485318
The Dual step takes 0.149543 (S)
upper bound updated to 0.485318
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.11087 seconds.
    local lower bound updated to 0.286472
    local upper bound updated to 0.436231

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 7.65666 seconds.
    local lower bound updated to 0.429224
    local upper bound updated to 0.429648

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.92162 seconds.
    local lower bound updated to 0.429224
    local upper bound updated to 0.429393

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.02539 seconds.
    local lower bound updated to 0.429393
    local upper bound updated to 0.429393
The Primal step takes 27.7224 (S)
lower bound updated to 0.429393

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.476539
    local lower bound updated to 0.45133

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.476539
    local lower bound updated to 0.468708

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.468708
    local lower bound updated to 0.468708
The Dual step takes 0.580964 (S)
upper bound updated to 0.468708
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 38.4579 seconds.
    local lower bound updated to 0.347198
    local upper bound updated to 0.445562

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 24.4814 seconds.
    local lower bound updated to 0.440529
    local upper bound updated to 0.444636

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 20.4145 seconds.
    local lower bound updated to 0.440529
    local upper bound updated to 0.443832

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 48.6288 seconds.
    local lower bound updated to 0.440529
    local upper bound updated to 0.443788

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 34.2851 seconds.
    local lower bound updated to 0.44174
    local upper bound updated to 0.443204

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 38.6073 seconds.
    local lower bound updated to 0.44174
    local upper bound updated to 0.442912

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 29.8877 seconds.
    local lower bound updated to 0.442452
    local upper bound updated to 0.442901

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 53.9353 seconds.
    local lower bound updated to 0.44254
    local upper bound updated to 0.442784

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 55.8605 seconds.
    local lower bound updated to 0.442769
    local upper bound updated to 0.442781

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 51.782 seconds.
    local lower bound updated to 0.442781
    local upper bound updated to 0.442781
The Primal step takes 396.368 (S)
lower bound updated to 0.442781

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.462411
    local lower bound updated to 0.444464

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.462034
    local lower bound updated to 0.446156

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.459255
    local lower bound updated to 0.447794

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.453696
    local lower bound updated to 0.449255

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.450584
    local lower bound updated to 0.449525

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.449525
    local lower bound updated to 0.449525
The Dual step takes 7.64057 (S)
upper bound updated to 0.449525
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 110.527 seconds.
    local lower bound updated to 0.393653
    local upper bound updated to 0.448433

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 70.7113 seconds.
    local lower bound updated to 0.43931
    local upper bound updated to 0.448155

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 136.565 seconds.
    local lower bound updated to 0.444871
    local upper bound updated to 0.447954

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 150.581 seconds.
    local lower bound updated to 0.445667
    local upper bound updated to 0.447744

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 145.407 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.446739

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 117.141 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.446597

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 124.042 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.446558

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 96.8446 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.446532

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 123.706 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.446458

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.446049
    local upper bound updated to 0.446438

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 130.72 seconds.
    local lower bound updated to 0.446049
    local upper bound updated to 0.446403

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 148.096 seconds.
    local lower bound updated to 0.446049
    local upper bound updated to 0.44632

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.446087
    local upper bound updated to 0.446317

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.446271
    local upper bound updated to 0.446316

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 200.024 seconds.
    local lower bound updated to 0.446313
    local upper bound updated to 0.446315
The Primal step takes 2154.52 (S)
lower bound updated to 0.446313

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.455728
    local lower bound updated to 0.446315

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.45402
    local lower bound updated to 0.446468

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.448046
    local lower bound updated to 0.446627

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.446627
    local lower bound updated to 0.446627
The Dual step takes 17.4967 (S)
upper bound updated to 0.446627
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.402868
    local upper bound updated to 0.446627

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.445417
    local upper bound updated to 0.446433

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.446182
    local upper bound updated to 0.446408

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.44628
    local upper bound updated to 0.446408

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.446392
    local upper bound updated to 0.446407

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.446407
    local upper bound updated to 0.446407
The Primal step takes 1200.24 (S)
lower bound updated to 0.446407

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.454239
    local lower bound updated to 0.446407

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.446407
    local lower bound updated to 0.446407
The Dual step takes 7.69397 (S)
upper bound updated to 0.446407
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.402868
    local upper bound updated to 0.446407

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.446407
    local upper bound updated to 0.446407
The time obtain the optimal randomized assortment is 4215.86 (S)
Now, the randomization optimization has been finished. We are checking the lower bound ....
Set parameter OutputFlag to value 1
Set parameter LogFile to value "/rds/general/user/zw1819/home/RAO/RAO_MC/FinalRun/RecFMResult/logFile_19_4_200.000000_204820.log"
The computation time limit for a lower bound is 81778
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 128 physical cores, 256 logical processors, using up to 4 threads
Optimize a model with 3048 rows, 2232 columns and 10290 nonzeros
Model fingerprint: 0x4bde9c24
Variable types: 2159 continuous, 73 integer (73 binary)
Coefficient statistics:
  Matrix range     [9e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 624 rows and 1122 columns
Presolve time: 0.04s
Presolved: 2424 rows, 1110 columns, 9638 nonzeros
Variable types: 1039 continuous, 71 integer (71 binary)
Found heuristic solution: objective 0.5229400

Root relaxation: objective 3.237674e-01, 267 iterations, 0.00 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.32377    0   24    0.52294    0.32377  38.1%     -    0s
H    0     0                       0.4976278    0.32377  34.9%     -    0s
     0     0    0.33590    0   25    0.49763    0.33590  32.5%     -    0s
     0     0    0.38402    0   37    0.49763    0.38402  22.8%     -    0s
H    0     0                       0.4746856    0.38402  19.1%     -    0s
     0     0    0.38405    0   37    0.47469    0.38405  19.1%     -    0s
     0     0    0.38989    0   34    0.47469    0.38989  17.9%     -    0s
H    0     0                       0.4723995    0.39048  17.3%     -    0s
     0     0    0.39048    0   34    0.47240    0.39048  17.3%     -    0s
H    0     0                       0.4471011    0.39591  11.5%     -    0s
     0     0    0.39591    0   35    0.44710    0.39591  11.5%     -    0s
     0     0    0.39612    0   35    0.44710    0.39612  11.4%     -    0s
     0     0    0.39779    0   33    0.44710    0.39779  11.0%     -    0s
H    0     0                       0.4464069    0.39779  10.9%     -    3s
     0     2    0.39779    0   33    0.44641    0.39779  10.9%     -    3s
   296   182    0.41909   12   17    0.44641    0.40472  9.34%  37.6    5s
   687   359    0.41687    9   24    0.44641    0.41191  7.73%  34.2   10s
  1466   732    0.42541   11   20    0.44641    0.41451  7.15%  32.3   15s
  1881   885    0.42440   10   25    0.44641    0.41614  6.78%  32.9   21s
  2054   908    0.43425   12   32    0.44641    0.41645  6.71%  32.4   26s
H 2412   931                       0.4464069    0.41645  6.71%  34.5   27s
  2694   971     cutoff   22         0.44641    0.41803  6.36%  34.5   30s
  3497   973    0.44418   22   18    0.44641    0.42141  5.60%  34.5   36s
  4295   931    0.44454   31    8    0.44641    0.42351  5.13%  33.8   40s
  5093   973    0.43185   21   14    0.44641    0.42469  4.87%  33.4   45s
  5661  1115     cutoff   27         0.44641    0.42537  4.71%  33.5   50s
H 6228  1201                       0.4464069    0.42584  4.61%  33.0   51s
  6666  1269    0.43836   24   11    0.44641    0.42613  4.54%  32.8   56s
  7178  1406    0.44426   20   20    0.44641    0.42674  4.41%  32.7   60s
  8065  1633    0.43017   20   18    0.44641    0.42733  4.27%  32.5   65s
  8922  1803    0.43048   25   20    0.44641    0.42805  4.11%  32.4   71s
  9560  1903    0.44523   26   12    0.44641    0.42847  4.02%  32.3   75s
 10324  2023    0.44342   23   17    0.44641    0.42876  3.95%  32.3   80s
 11907  2229    0.44011   29   12    0.44641    0.42953  3.78%  32.4   87s
 13053  2360    0.44531   30    4    0.44641    0.43008  3.66%  32.2   91s
 14087  2442    0.44371   29   10    0.44641    0.43049  3.56%  32.1   95s
 15330  2597     cutoff   26         0.44641    0.43094  3.47%  31.9  100s
 16101  2680    0.43485   28   15    0.44641    0.43129  3.39%  31.8  106s
 17322  2720     cutoff   29         0.44641    0.43183  3.27%  31.7  110s
 18433  2753    0.43880   27   12    0.44641    0.43220  3.18%  31.6  116s
 19161  2795     cutoff   27         0.44641    0.43241  3.14%  31.5  121s
 20213  2873    0.43947   26   14    0.44641    0.43271  3.07%  31.5  126s
 21952  2917     cutoff   31         0.44641    0.43321  2.96%  31.3  131s
 22759  2949    0.43777   20   23    0.44641    0.43335  2.93%  31.3  135s
 23841  2976    0.44255   23   12    0.44641    0.43373  2.84%  31.1  140s
 25872  2958    0.44307   24   14    0.44641    0.43428  2.72%  31.0  148s
 26144  2966     cutoff   28         0.44641    0.43442  2.69%  31.0  150s
 27219  2972    0.43780   26   21    0.44641    0.43459  2.65%  30.9  155s
H27751  2972                       0.4464069    0.43485  2.59%  30.9  155s
 28269  2959    0.44406   32   14    0.44641    0.43494  2.57%  30.8  161s
 28838  2949     cutoff   29         0.44641    0.43499  2.56%  30.7  165s
 30511  2925    0.44055   29    8    0.44641    0.43536  2.47%  30.6  170s
 32000  2868    0.44327   25   19    0.44641    0.43576  2.38%  30.5  176s
 32975  2817     cutoff   24         0.44641    0.43607  2.31%  30.4  180s
 33840  2751    0.44445   27   12    0.44641    0.43626  2.27%  30.4  186s
 36289  2607    0.44244   27   14    0.44641    0.43682  2.15%  30.1  192s
 37086  2504    0.44352   24   10    0.44641    0.43709  2.09%  30.0  196s
 38046  2371 infeasible   25         0.44641    0.43726  2.05%  30.0  200s
 40147  2164     cutoff   28         0.44641    0.43784  1.92%  29.8  206s
 40815  2025    0.44127   23   16    0.44641    0.43815  1.85%  29.8  210s
 42509  1723     cutoff   24         0.44641    0.43860  1.75%  29.7  217s
 43787  1523    0.44564   27   18    0.44641    0.43914  1.63%  29.6  221s
 45388  1042     cutoff   30         0.44641    0.43999  1.44%  29.5  226s
 46218   774     cutoff   28         0.44641    0.44056  1.31%  29.4  231s
 47993    64    0.44428   24   17    0.44641    0.44242  0.89%  29.2  235s

Cutting planes:
  Gomory: 1
  Implied bound: 299
  MIR: 168
  Flow cover: 495
  RLT: 52
  Relax-and-lift: 137

Explored 48351 nodes (1407169 simplex iterations) in 235.91 seconds (231.12 work units)
Thread count was 4 (of 256 available processors)

Solution count 7: 0.446407 0.446407 0.447101 ... 0.52294

Optimal solution found (tolerance 1.00e-04)
Best objective 4.464069167091e-01, best bound 4.464068963220e-01, gap 0.0000%
The objective bound is 0.446407 while the objective upper bound is 0.446407

============================================

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.75 (ave)

============================================
