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 0.530154 seconds.
    local lower bound updated to 0.301067
    local upper bound updated to 0.51133

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.685845 seconds.
    local lower bound updated to 0.502636
    local upper bound updated to 0.502636
The Primal step takes 1.21826 (S)
lower bound updated to 0.502636

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.625435
    local lower bound updated to 0.594797

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.594797
    local lower bound updated to 0.594797
The Dual step takes 0.0522188 (S)
upper bound updated to 0.594797
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.57611 seconds.
    local lower bound updated to 0.38852
    local upper bound updated to 0.534699

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.382347 seconds.
    local lower bound updated to 0.424425
    local upper bound updated to 0.526117

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.88902 seconds.
    local lower bound updated to 0.51115
    local upper bound updated to 0.522456

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.97177 seconds.
    local lower bound updated to 0.521596
    local upper bound updated to 0.522154

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.83086 seconds.
    local lower bound updated to 0.521596
    local upper bound updated to 0.521653

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.80066 seconds.
    local lower bound updated to 0.521653
    local upper bound updated to 0.521653
The Primal step takes 13.4628 (S)
lower bound updated to 0.521653

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.58632
    local lower bound updated to 0.564999

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.564999
    local lower bound updated to 0.564999
The Dual step takes 0.346788 (S)
upper bound updated to 0.564999
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.78892 seconds.
    local lower bound updated to 0.431079
    local upper bound updated to 0.55413

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.463187 seconds.
    local lower bound updated to 0.474992
    local upper bound updated to 0.536899

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.61967 seconds.
    local lower bound updated to 0.519888
    local upper bound updated to 0.534579

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.88777 seconds.
    local lower bound updated to 0.528597
    local upper bound updated to 0.531027

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.61066 seconds.
    local lower bound updated to 0.528597
    local upper bound updated to 0.53051

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.0578 seconds.
    local lower bound updated to 0.528597
    local upper bound updated to 0.529787

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 5.3089 seconds.
    local lower bound updated to 0.52915
    local upper bound updated to 0.529691

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 4.57547 seconds.
    local lower bound updated to 0.529691
    local upper bound updated to 0.529691
The Primal step takes 29.3313 (S)
lower bound updated to 0.529691

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.56096
    local lower bound updated to 0.530914

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.545901
    local lower bound updated to 0.538998

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.545901
    local lower bound updated to 0.539688

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.545901
    local lower bound updated to 0.542809

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.545901
    local lower bound updated to 0.544274

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.544907
    local lower bound updated to 0.544276

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.544276
    local lower bound updated to 0.544276
The Dual step takes 4.80828 (S)
upper bound updated to 0.544276
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.9306 seconds.
    local lower bound updated to 0.468474
    local upper bound updated to 0.543131

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 14.8878 seconds.
    local lower bound updated to 0.51819
    local upper bound updated to 0.538329

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 31.0852 seconds.
    local lower bound updated to 0.533273
    local upper bound updated to 0.538213

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 13.053 seconds.
    local lower bound updated to 0.533273
    local upper bound updated to 0.538007

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.0576 seconds.
    local lower bound updated to 0.533273
    local upper bound updated to 0.537196

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 21.8347 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.536463

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 26.6133 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.536292

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 14.9471 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.536217

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 30.7738 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.536087

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 26.0553 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.536035

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 12.9044 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.535985

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 24.3448 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.535933

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 15.9625 seconds.
    local lower bound updated to 0.535424
    local upper bound updated to 0.535921

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 20.1444 seconds.
    local lower bound updated to 0.535551
    local upper bound updated to 0.535913

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 23.3928 seconds.
    local lower bound updated to 0.535698
    local upper bound updated to 0.535862

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 34.1961 seconds.
    local lower bound updated to 0.535721
    local upper bound updated to 0.535856

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 26.4745 seconds.
    local lower bound updated to 0.53578
    local upper bound updated to 0.535851

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 25.4871 seconds.
    local lower bound updated to 0.535851
    local upper bound updated to 0.535851
The Primal step takes 389.225 (S)
lower bound updated to 0.535851

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.558314
    local lower bound updated to 0.536084

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.558314
    local lower bound updated to 0.536737

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.542654
    local lower bound updated to 0.537602

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.542654
    local lower bound updated to 0.537932

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.539352
    local lower bound updated to 0.537949

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.537949
    local lower bound updated to 0.537949
The Dual step takes 10.8188 (S)
upper bound updated to 0.537949
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 8.49201 seconds.
    local lower bound updated to 0.482878
    local upper bound updated to 0.537949

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 31.248 seconds.
    local lower bound updated to 0.52845
    local upper bound updated to 0.537033

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 35.8739 seconds.
    local lower bound updated to 0.535476
    local upper bound updated to 0.536572

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 33.7176 seconds.
    local lower bound updated to 0.535476
    local upper bound updated to 0.536271

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 33.7 seconds.
    local lower bound updated to 0.535841
    local upper bound updated to 0.53622

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 31.3644 seconds.
    local lower bound updated to 0.536065
    local upper bound updated to 0.536189

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 34.5991 seconds.
    local lower bound updated to 0.536065
    local upper bound updated to 0.53616

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 30.7774 seconds.
    local lower bound updated to 0.536065
    local upper bound updated to 0.53615

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 27.8311 seconds.
    local lower bound updated to 0.53615
    local upper bound updated to 0.53615
The Primal step takes 267.657 (S)
lower bound updated to 0.53615

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.55267
    local lower bound updated to 0.53615

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.536184
    local lower bound updated to 0.536151

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.536151
    local lower bound updated to 0.536151
The Dual step takes 9.50744 (S)
upper bound updated to 0.536151
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.1375 seconds.
    local lower bound updated to 0.485619
    local upper bound updated to 0.536151

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 44.5751 seconds.
    local lower bound updated to 0.536028
    local upper bound updated to 0.536151

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 46.2285 seconds.
    local lower bound updated to 0.536151
    local upper bound updated to 0.536151
The time obtain the optimal randomized assortment is 831.388 (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_15_4_200.000000_206316.log"
The computation time limit for a lower bound is 85164
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 24 physical cores, 48 logical processors, using up to 4 threads
Optimize a model with 2640 rows, 2138 columns and 8470 nonzeros
Model fingerprint: 0x3d1271ee
Variable types: 2081 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 742 rows and 1312 columns
Presolve time: 0.02s
Presolved: 1898 rows, 826 columns, 7423 nonzeros
Variable types: 771 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6495295
Found heuristic solution: objective 0.6360094

Root relaxation: objective 2.483167e-01, 273 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    0.24832    0   24    0.63601    0.24832  61.0%     -    0s
H    0     0                       0.6061657    0.24832  59.0%     -    0s
     0     0    0.26505    0   26    0.60617    0.26505  56.3%     -    0s
     0     0    0.26505    0   26    0.60617    0.26505  56.3%     -    0s
H    0     0                       0.6015925    0.38952  35.3%     -    0s
     0     0    0.38952    0   27    0.60159    0.38952  35.3%     -    0s
H    0     0                       0.5926126    0.38952  34.3%     -    0s
     0     0    0.39111    0   27    0.59261    0.39111  34.0%     -    0s
H    0     0                       0.5613544    0.43073  23.3%     -    0s
     0     0    0.43073    0   24    0.56135    0.43073  23.3%     -    0s
     0     0    0.43233    0   25    0.56135    0.43233  23.0%     -    0s
H    0     0                       0.5450764    0.44107  19.1%     -    0s
     0     0    0.44107    0   24    0.54508    0.44107  19.1%     -    0s
H    0     0                       0.5428881    0.44193  18.6%     -    0s
     0     0    0.44193    0   26    0.54289    0.44193  18.6%     -    0s
     0     0    0.44619    0   29    0.54289    0.44619  17.8%     -    0s
H    0     0                       0.5423251    0.44619  17.7%     -    0s
H    0     0                       0.5385701    0.44619  17.2%     -    2s
     0     2    0.44619    0   29    0.53857    0.44619  17.2%     -    2s
H  488   172                       0.5365664    0.48434  9.73%  31.5    4s
   489   186    0.51665    8   19    0.53657    0.48434  9.73%  31.8    5s
H  508   186                       0.5361506    0.48434  9.66%  31.2    5s
  1171   327     cutoff   11         0.53615    0.49678  7.34%  29.6   10s
  2261   507    0.52292   15    9    0.53615    0.50362  6.07%  25.7   15s
H 2563   523                       0.5361506    0.50459  5.89%  24.8   15s
  4283   698    0.51400   12   29    0.53615    0.50945  4.98%  22.3   21s
  4399   730     cutoff   22         0.53615    0.50945  4.98%  23.5   25s
H 4425   690                       0.5361506    0.50945  4.98%  23.7   25s
H 4629   649                       0.5361505    0.50945  4.98%  24.5   26s
  5750   488     cutoff   24         0.53615    0.50945  4.98%  25.5   30s
  6854   453     cutoff   28         0.53615    0.51413  4.11%  25.1   35s
  9468   523     cutoff   24         0.53615    0.52020  2.98%  24.3   40s
 11964   311 infeasible   29         0.53615    0.52492  2.10%  23.6   45s

Cutting planes:
  Implied bound: 180
  MIR: 116
  Flow cover: 394
  RLT: 53
  Relax-and-lift: 52

Explored 13537 nodes (314315 simplex iterations) in 46.04 seconds (37.61 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.536151 0.536151 0.536151 ... 0.592613

Optimal solution found (tolerance 1.00e-04)
Best objective 5.361505456477e-01, best bound 5.361505456477e-01, gap 0.0000%
The objective bound is 0.536151 while the objective upper bound is 0.536151

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.51 (ave)

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