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 0.204759 seconds.
    local lower bound updated to 0.254449
    local upper bound updated to 0.414236

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.244596 seconds.
    local lower bound updated to 0.414236
    local upper bound updated to 0.414236
The Primal step takes 0.450685 (S)
lower bound updated to 0.414236

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.526912
    local lower bound updated to 0.526912
The Dual step takes 0.0123393 (S)
upper bound updated to 0.526912
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.22753 seconds.
    local lower bound updated to 0.285979
    local upper bound updated to 0.419149

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.1077 seconds.
    local lower bound updated to 0.415411
    local upper bound updated to 0.416139

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.90539 seconds.
    local lower bound updated to 0.415411
    local upper bound updated to 0.415808

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.33799 seconds.
    local lower bound updated to 0.415644
    local upper bound updated to 0.415675

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.64225 seconds.
    local lower bound updated to 0.415675
    local upper bound updated to 0.415675
The Primal step takes 15.2275 (S)
lower bound updated to 0.415675

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.467185
    local lower bound updated to 0.428573

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.456443
    local lower bound updated to 0.437966

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.451322
    local lower bound updated to 0.44447

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.44447
    local lower bound updated to 0.44447
The Dual step takes 0.50161 (S)
upper bound updated to 0.44447
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 30.2472 seconds.
    local lower bound updated to 0.351576
    local upper bound updated to 0.425613

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.7183 seconds.
    local lower bound updated to 0.418135
    local upper bound updated to 0.422535

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.7017 seconds.
    local lower bound updated to 0.418135
    local upper bound updated to 0.42191

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 31.5787 seconds.
    local lower bound updated to 0.418135
    local upper bound updated to 0.419994

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 35.9001 seconds.
    local lower bound updated to 0.418812
    local upper bound updated to 0.419109

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 20.6315 seconds.
    local lower bound updated to 0.418812
    local upper bound updated to 0.419082

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 34.3585 seconds.
    local lower bound updated to 0.418812
    local upper bound updated to 0.418955

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 33.4491 seconds.
    local lower bound updated to 0.418812
    local upper bound updated to 0.418923

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 40.5401 seconds.
    local lower bound updated to 0.418916
    local upper bound updated to 0.418921
The Primal step takes 250.147 (S)
lower bound updated to 0.418916

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.452861
    local lower bound updated to 0.419603

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.435489
    local lower bound updated to 0.429023

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.435489
    local lower bound updated to 0.429616

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.433132
    local lower bound updated to 0.42993

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.431262
    local lower bound updated to 0.429983

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.431262
    local lower bound updated to 0.430363

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.431262
    local lower bound updated to 0.430485

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.430485
    local lower bound updated to 0.430485
The Dual step takes 7.76542 (S)
upper bound updated to 0.430485
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 48.4922 seconds.
    local lower bound updated to 0.383967
    local upper bound updated to 0.427003

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.40221 seconds.
    local lower bound updated to 0.405831
    local upper bound updated to 0.42497

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.8438 seconds.
    local lower bound updated to 0.411888
    local upper bound updated to 0.423456

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 70.002 seconds.
    local lower bound updated to 0.421673
    local upper bound updated to 0.423188

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 50.5368 seconds.
    local lower bound updated to 0.421673
    local upper bound updated to 0.422437

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.421673
    local upper bound updated to 0.42242

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.421673
    local upper bound updated to 0.422257

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 63.8377 seconds.
    local lower bound updated to 0.421685
    local upper bound updated to 0.422256

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.7853 seconds.
    local lower bound updated to 0.421698
    local upper bound updated to 0.422217

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 79.6812 seconds.
    local lower bound updated to 0.421698
    local upper bound updated to 0.422187

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.421909
    local upper bound updated to 0.422162

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.421909
    local upper bound updated to 0.422139

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 27.5078 seconds.
    local lower bound updated to 0.421909
    local upper bound updated to 0.422122

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.422047
    local upper bound updated to 0.422115

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 67.211 seconds.
    local lower bound updated to 0.422095
    local upper bound updated to 0.422115

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.422095
    local upper bound updated to 0.422111

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 68.9003 seconds.
    local lower bound updated to 0.422111
    local upper bound updated to 0.422111
The Primal step takes 1151.39 (S)
lower bound updated to 0.422111

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.439255
    local lower bound updated to 0.422111

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.431852
    local lower bound updated to 0.422119

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.428128
    local lower bound updated to 0.422401

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.428128
    local lower bound updated to 0.422431

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.425237
    local lower bound updated to 0.422565

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.425237
    local lower bound updated to 0.42261

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.42279
    local lower bound updated to 0.42261

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.42261
    local lower bound updated to 0.42261
The Dual step takes 25.4917 (S)
upper bound updated to 0.42261
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.387189
    local upper bound updated to 0.422528

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.035 seconds.
    local lower bound updated to 0.421852
    local upper bound updated to 0.422482

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.422174
    local upper bound updated to 0.422434

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.025 seconds.
    local lower bound updated to 0.422341
    local upper bound updated to 0.422432

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.422432
    local upper bound updated to 0.422432
The Primal step takes 500.168 (S)
lower bound updated to 0.422432

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.437304
    local lower bound updated to 0.422432

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.422432
    local lower bound updated to 0.422432
The Dual step takes 9.55491 (S)
upper bound updated to 0.422432
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.387189
    local upper bound updated to 0.422432

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.422432
    local upper bound updated to 0.422432
The time obtain the optimal randomized assortment is 2160.78 (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_17_4_100.000000_107318.log"
The computation time limit for a lower bound is 83837
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 3768 rows, 2878 columns and 12483 nonzeros
Model fingerprint: 0x99d4577a
Variable types: 2813 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [4e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 824 rows and 1556 columns
Presolve time: 0.03s
Presolved: 2944 rows, 1322 columns, 11308 nonzeros
Variable types: 1259 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.4970875
Found heuristic solution: objective 0.4782829
Found heuristic solution: objective 0.4745801

Root relaxation: objective 3.695305e-01, 311 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    0.36953    0   22    0.47458    0.36953  22.1%     -    0s
H    0     0                       0.4633253    0.36953  20.2%     -    0s
H    0     0                       0.4538264    0.36953  18.6%     -    0s
H    0     0                       0.4414867    0.36953  16.3%     -    0s
H    0     0                       0.4342849    0.37029  14.7%     -    0s
     0     0    0.37029    0   30    0.43428    0.37029  14.7%     -    0s
H    0     0                       0.4279771    0.37029  13.5%     -    0s
     0     0    0.37162    0   30    0.42798    0.37162  13.2%     -    0s
     0     0    0.38681    0   32    0.42798    0.38681  9.62%     -    0s
     0     0    0.38714    0   32    0.42798    0.38714  9.54%     -    0s
     0     0    0.39297    0   29    0.42798    0.39297  8.18%     -    0s
     0     0    0.39311    0   29    0.42798    0.39311  8.15%     -    0s
H    0     0                       0.4247790    0.39443  7.14%     -    0s
     0     0    0.39443    0   35    0.42478    0.39443  7.14%     -    0s
     0     0    0.39477    0   34    0.42478    0.39477  7.06%     -    0s
     0     0    0.39553    0   30    0.42478    0.39553  6.88%     -    0s
H    0     0                       0.4224318    0.39553  6.37%     -    3s
     0     2    0.39553    0   30    0.42243    0.39553  6.37%     -    3s
   396   247    0.41151    8   18    0.42243    0.40005  5.30%  54.0    6s
H  528   277                       0.4224318    0.40156  4.94%  52.4    7s
   800   378    0.41574   18    6    0.42243    0.40278  4.65%  47.5   11s
  1101   540    0.40921   14   10    0.42243    0.40354  4.47%  43.9   15s
  1621   736    0.40850    7   19    0.42243    0.40467  4.20%  42.1   20s
  2142   842    0.41202    8   31    0.42243    0.40511  4.10%  39.5   25s
  3034   964    0.41618   17   12    0.42243    0.40579  3.94%  44.0   30s
  3474   966     cutoff   24         0.42243    0.40683  3.69%  44.6   35s
  5737  1076 infeasible   31         0.42243    0.40858  3.28%  42.5   40s
  6645  1307    0.42239   28    2    0.42243    0.40934  3.10%  42.3   45s
  7655  1456    0.41948   26    8    0.42243    0.40968  3.02%  41.9   50s
  8726  1592 infeasible   24         0.42243    0.41033  2.87%  41.7   56s
  9393  1638     cutoff   30         0.42243    0.41061  2.80%  41.4   61s
  9661  1738    0.41787   24    6    0.42243    0.41078  2.76%  41.4   65s
 10527  1875    0.41154   23   14    0.42243    0.41110  2.68%  40.9   70s
 12205  2017     cutoff   22         0.42243    0.41156  2.57%  40.5   76s
 13728  2110    0.41422   21   16    0.42243    0.41217  2.43%  40.2   81s
 14185  2142    0.41668   19   10    0.42243    0.41233  2.39%  40.2   85s
 15860  2259     cutoff   27         0.42243    0.41266  2.31%  40.0   90s
 17547  2332    0.41709   23   10    0.42243    0.41324  2.18%  39.4   95s
 19822  2340    0.41962   26    6    0.42243    0.41372  2.06%  39.1  100s
 22025  2293     cutoff   21         0.42243    0.41444  1.89%  38.9  105s
 25026  2117    0.42169   25    6    0.42243    0.41522  1.71%  38.5  112s
H25553  2117                       0.4224318    0.41538  1.67%  38.5  112s
 25813  2050    0.41932   24    8    0.42243    0.41545  1.65%  38.5  115s
 27260  1945    0.42203   23   10    0.42243    0.41572  1.59%  38.4  120s
 28747  1700    0.41875   22    8    0.42243    0.41639  1.43%  38.4  125s
 30243  1438    0.42003   23   14    0.42243    0.41675  1.35%  38.3  131s
 31703  1135     cutoff   28         0.42243    0.41757  1.15%  38.2  135s

Cutting planes:
  Implied bound: 404
  MIR: 167
  Flow cover: 546
  RLT: 86
  Relax-and-lift: 163

Explored 34844 nodes (1323147 simplex iterations) in 140.23 seconds (167.59 work units)
Thread count was 4 (of 256 available processors)

Solution count 10: 0.422432 0.422432 0.422432 ... 0.47458

Optimal solution found (tolerance 1.00e-04)
Best objective 4.224318108770e-01, best bound 4.224317907227e-01, gap 0.0000%
The objective bound is 0.422432 while the objective upper bound is 0.422432

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.78 (ave)

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