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 0.669123 seconds.
    local lower bound updated to 0.276439
    local upper bound updated to 0.495716

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.76121 seconds.
    local lower bound updated to 0.493866
    local upper bound updated to 0.493866
The Primal step takes 2.43254 (S)
lower bound updated to 0.493866

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.616858
    local lower bound updated to 0.611585

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.616858
    local lower bound updated to 0.615881

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.616858
    local lower bound updated to 0.616361

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.616361
    local lower bound updated to 0.616361
The Dual step takes 0.311554 (S)
upper bound updated to 0.616361
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.05198 seconds.
    local lower bound updated to 0.347228
    local upper bound updated to 0.51032

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 17.3714 seconds.
    local lower bound updated to 0.500099
    local upper bound updated to 0.500917

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 12.4587 seconds.
    local lower bound updated to 0.500099
    local upper bound updated to 0.500132

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 14.8405 seconds.
    local lower bound updated to 0.500132
    local upper bound updated to 0.500132
The Primal step takes 49.7346 (S)
lower bound updated to 0.500132

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.532208
    local lower bound updated to 0.505504

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.532208
    local lower bound updated to 0.52569

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.532208
    local lower bound updated to 0.526443

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.531923
    local lower bound updated to 0.526802

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.526802
    local lower bound updated to 0.526802
The Dual step takes 2.11622 (S)
upper bound updated to 0.526802
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 35.5944 seconds.
    local lower bound updated to 0.406982
    local upper bound updated to 0.526802

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.07154 seconds.
    local lower bound updated to 0.485678
    local upper bound updated to 0.51481

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 44.5838 seconds.
    local lower bound updated to 0.507302
    local upper bound updated to 0.512287

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 25.1038 seconds.
    local lower bound updated to 0.507302
    local upper bound updated to 0.511262

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 24.9647 seconds.
    local lower bound updated to 0.507302
    local upper bound updated to 0.510829

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 41.4672 seconds.
    local lower bound updated to 0.507375
    local upper bound updated to 0.510434

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.16109 seconds.
    local lower bound updated to 0.507375
    local upper bound updated to 0.510427

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 29.5921 seconds.
    local lower bound updated to 0.50741
    local upper bound updated to 0.510425

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 45.497 seconds.
    local lower bound updated to 0.508509
    local upper bound updated to 0.509943

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 33.3623 seconds.
    local lower bound updated to 0.508509
    local upper bound updated to 0.509834

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 56.1684 seconds.
    local lower bound updated to 0.508509
    local upper bound updated to 0.509747

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 58.9357 seconds.
    local lower bound updated to 0.509094
    local upper bound updated to 0.509688

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 45.1191 seconds.
    local lower bound updated to 0.509548
    local upper bound updated to 0.50967

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 58.9182 seconds.
    local lower bound updated to 0.509548
    local upper bound updated to 0.509664

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 40.8318 seconds.
    local lower bound updated to 0.509659
    local upper bound updated to 0.509664
The Primal step takes 555.433 (S)
lower bound updated to 0.509659

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.534143
    local lower bound updated to 0.510159

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529524
    local lower bound updated to 0.511065

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.525715
    local lower bound updated to 0.514247

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.524483
    local lower bound updated to 0.518323

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.520979
    local lower bound updated to 0.518401

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.518401
    local lower bound updated to 0.518401
The Dual step takes 10.2323 (S)
upper bound updated to 0.518401
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 86.0207 seconds.
    local lower bound updated to 0.437997
    local upper bound updated to 0.518352

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.90379 seconds.
    local lower bound updated to 0.46694
    local upper bound updated to 0.515431

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 87.3505 seconds.
    local lower bound updated to 0.510554
    local upper bound updated to 0.514906

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 94.4055 seconds.
    local lower bound updated to 0.511445
    local upper bound updated to 0.513909

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 110.054 seconds.
    local lower bound updated to 0.511445
    local upper bound updated to 0.513702

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 93.0283 seconds.
    local lower bound updated to 0.511445
    local upper bound updated to 0.51351

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 86.9249 seconds.
    local lower bound updated to 0.511445
    local upper bound updated to 0.513475

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 94.9102 seconds.
    local lower bound updated to 0.512067
    local upper bound updated to 0.513406

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 109.187 seconds.
    local lower bound updated to 0.512083
    local upper bound updated to 0.51331

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 90.8446 seconds.
    local lower bound updated to 0.512291
    local upper bound updated to 0.513122

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 96.0113 seconds.
    local lower bound updated to 0.512291
    local upper bound updated to 0.513088

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 99.2876 seconds.
    local lower bound updated to 0.512613
    local upper bound updated to 0.513037

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 102.472 seconds.
    local lower bound updated to 0.51286
    local upper bound updated to 0.513014

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 108.149 seconds.
    local lower bound updated to 0.513007
    local upper bound updated to 0.513013
The Primal step takes 1264.65 (S)
lower bound updated to 0.513007

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.52348
    local lower bound updated to 0.513013

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.516554
    local lower bound updated to 0.513108

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.516554
    local lower bound updated to 0.51391

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.51391
    local lower bound updated to 0.51391
The Dual step takes 15.9165 (S)
upper bound updated to 0.51391
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 90.3698 seconds.
    local lower bound updated to 0.444934
    local upper bound updated to 0.51391

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 149.272 seconds.
    local lower bound updated to 0.508317
    local upper bound updated to 0.513597

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 145.833 seconds.
    local lower bound updated to 0.511903
    local upper bound updated to 0.513394

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.025 seconds.
    local lower bound updated to 0.511903
    local upper bound updated to 0.513367

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 154.906 seconds.
    local lower bound updated to 0.512198
    local upper bound updated to 0.513367

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 151.978 seconds.
    local lower bound updated to 0.512335
    local upper bound updated to 0.513239

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 118.418 seconds.
    local lower bound updated to 0.512435
    local upper bound updated to 0.513172

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 118.044 seconds.
    local lower bound updated to 0.51307
    local upper bound updated to 0.513171

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 126.951 seconds.
    local lower bound updated to 0.51315
    local upper bound updated to 0.513171

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 106.624 seconds.
    local lower bound updated to 0.513171
    local upper bound updated to 0.513171
The Primal step takes 1362.49 (S)
lower bound updated to 0.513171

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.518969
    local lower bound updated to 0.513171

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.516803
    local lower bound updated to 0.513254

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513254
    local lower bound updated to 0.513254
The Dual step takes 15.9206 (S)
upper bound updated to 0.513254
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 156.38 seconds.
    local lower bound updated to 0.448626
    local upper bound updated to 0.513254

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.512441
    local upper bound updated to 0.513236

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.512803
    local upper bound updated to 0.513171

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 151.474 seconds.
    local lower bound updated to 0.513171
    local upper bound updated to 0.513171
The Primal step takes 707.959 (S)
lower bound updated to 0.513171

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.51904
    local lower bound updated to 0.513171

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.513171
    local lower bound updated to 0.513171
The Dual step takes 12.679 (S)
upper bound updated to 0.513171
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 158.806 seconds.
    local lower bound updated to 0.448626
    local upper bound updated to 0.513171

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 148.348 seconds.
    local lower bound updated to 0.513171
    local upper bound updated to 0.513171
The time obtain the optimal randomized assortment is 4307.05 (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_206416.log"
The computation time limit for a lower bound is 81681
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 2800 rows, 2268 columns and 8923 nonzeros
Model fingerprint: 0xc4b3f82e
Variable types: 2211 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [7e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e-01, 1e+00]
Presolve removed 767 rows and 1393 columns
Presolve time: 0.04s
Presolved: 2033 rows, 875 columns, 7663 nonzeros
Variable types: 819 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.6283774
Found heuristic solution: objective 0.6179094
Found heuristic solution: objective 0.5593159

Root relaxation: objective 3.586734e-01, 231 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    0.35867    0   18    0.55932    0.35867  35.9%     -    0s
H    0     0                       0.5515602    0.35867  35.0%     -    0s
     0     0    0.36171    0   22    0.55156    0.36171  34.4%     -    0s
H    0     0                       0.5420478    0.36171  33.3%     -    0s
     0     0    0.39701    0   26    0.54205    0.39701  26.8%     -    0s
H    0     0                       0.5358305    0.39701  25.9%     -    0s
     0     0    0.39788    0   26    0.53583    0.39788  25.7%     -    0s
H    0     0                       0.5298397    0.41897  20.9%     -    0s
     0     0    0.41897    0   24    0.52984    0.41897  20.9%     -    0s
     0     0    0.41984    0   24    0.52984    0.41984  20.8%     -    0s
     0     0    0.42695    0   26    0.52984    0.42695  19.4%     -    0s
H    0     0                       0.5289962    0.42729  19.2%     -    0s
H    0     0                       0.5282104    0.42729  19.1%     -    0s
     0     0    0.42729    0   28    0.52821    0.42729  19.1%     -    0s
     0     0    0.42792    0   25    0.52821    0.42792  19.0%     -    0s
H    0     0                       0.5216882    0.42792  18.0%     -    0s
H    0     0                       0.5131927    0.42792  16.6%     -    2s
     0     2    0.42792    0   25    0.51319    0.42792  16.6%     -    2s
H  300   159                       0.5131706    0.43853  14.5%  35.8    4s
   557   271    0.50888   13    8    0.51317    0.44410  13.5%  34.3    5s
  1300   581    0.49529   12   15    0.51317    0.44955  12.4%  30.7   10s
H 1997   767                       0.5131706    0.45582  11.2%  29.3   12s
  2170   856    0.46738    9   29    0.51317    0.45582  11.2%  28.9   16s
H 2378   903                       0.5131706    0.45582  11.2%  31.8   17s
H 2425   859                       0.5131706    0.45582  11.2%  31.8   18s
H 2625   810                       0.5131706    0.45582  11.2%  32.5   19s
  2973   808    0.47527   24   18    0.51317    0.45582  11.2%  32.9   20s
  4166   761    0.48279   21   17    0.51317    0.46330  9.72%  33.0   26s
H 4284   704                       0.5131706    0.46330  9.72%  33.0   26s
H 4295   704                       0.5131706    0.46330  9.72%  33.0   26s
  5422   855    0.48244   24   15    0.51317    0.46682  9.03%  32.2   30s
  6789  1112    0.48095   24   14    0.51317    0.47057  8.30%  31.9   35s
  7558  1206    0.49687   26   12    0.51317    0.47133  8.15%  31.7   40s
  8569  1397    0.48215   25   15    0.51317    0.47338  7.75%  31.4   45s
 10128  1597    0.49864   26   12    0.51317    0.47576  7.29%  30.8   50s
 11778  1714    0.50959   28   10    0.51317    0.47734  6.98%  30.6   57s
 12228  1812     cutoff   24         0.51317    0.47790  6.87%  30.5   61s
 14092  1980    0.50497   25   12    0.51317    0.47997  6.47%  30.0   65s
 15850  2115    0.49706   29   17    0.51317    0.48142  6.19%  29.5   70s
 17341  2175    0.50263   28   10    0.51317    0.48255  5.97%  29.3   75s
 18705  2280    0.50951   29   12    0.51317    0.48357  5.77%  29.0   80s
 20197  2326    0.50641   30   12    0.51317    0.48450  5.59%  28.8   85s
 22745  2395    0.50732   25   10    0.51317    0.48600  5.29%  28.4   91s
 24693  2404    0.50474   25   16    0.51317    0.48736  5.03%  28.2   95s
 26719  2397    0.50601   26   16    0.51317    0.48856  4.80%  27.9  101s
 28304  2402    0.50207   28    8    0.51317    0.48939  4.63%  27.8  105s
 30464  2322     cutoff   28         0.51317    0.49040  4.44%  27.5  110s
 32237  2255 infeasible   29         0.51317    0.49141  4.24%  27.3  115s
 32828  2233     cutoff   30         0.51317    0.49175  4.17%  27.2  120s
 34914  2139 infeasible   25         0.51317    0.49319  3.89%  27.0  125s
 36461  1993     cutoff   29         0.51317    0.49406  3.72%  26.9  130s
 38028  1850     cutoff   25         0.51317    0.49510  3.52%  26.7  135s
 39767  1719 infeasible   28         0.51317    0.49616  3.31%  26.6  141s
 41284  1504    0.50332   26   12    0.51317    0.49745  3.06%  26.5  145s
 43576  1069    0.51026   27   10    0.51317    0.49983  2.60%  26.2  151s
 45515   356     cutoff   28         0.51317    0.50403  1.78%  26.0  155s

Cutting planes:
  Implied bound: 273
  MIR: 176
  Flow cover: 380
  RLT: 92
  Relax-and-lift: 137

Explored 46642 nodes (1207055 simplex iterations) in 155.36 seconds (112.64 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.513171 0.513171 0.513171 ... 0.542048

Optimal solution found (tolerance 1.00e-04)
Best objective 5.131706432326e-01, best bound 5.131706248222e-01, gap 0.0000%
The objective bound is 0.513171 while the objective upper bound is 0.513171

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.76 (ave)

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