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 0.439378 seconds.
    local lower bound updated to 0.20766
    local upper bound updated to 0.414045

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.710911 seconds.
    local lower bound updated to 0.410006
    local upper bound updated to 0.410006
The Primal step takes 1.15283 (S)
lower bound updated to 0.410006

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.544171
    local lower bound updated to 0.527087

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.527087
    local lower bound updated to 0.527087
The Dual step takes 0.0500233 (S)
upper bound updated to 0.527087
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.96332 seconds.
    local lower bound updated to 0.273302
    local upper bound updated to 0.423834

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.13814 seconds.
    local lower bound updated to 0.413714
    local upper bound updated to 0.419108

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.19878 seconds.
    local lower bound updated to 0.413714
    local upper bound updated to 0.415469

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.42092 seconds.
    local lower bound updated to 0.414973
    local upper bound updated to 0.41508

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.99545 seconds.
    local lower bound updated to 0.415079
    local upper bound updated to 0.41508
The Primal step takes 15.7253 (S)
lower bound updated to 0.415079

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.486684
    local lower bound updated to 0.446287

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.457721
    local lower bound updated to 0.453722

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.457721
    local lower bound updated to 0.454516

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.456495
    local lower bound updated to 0.454853

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.454853
    local lower bound updated to 0.454853
The Dual step takes 1.89136 (S)
upper bound updated to 0.454853
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.00941 seconds.
    local lower bound updated to 0.32397
    local upper bound updated to 0.433725

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.53842 seconds.
    local lower bound updated to 0.41914
    local upper bound updated to 0.429558

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.35476 seconds.
    local lower bound updated to 0.41914
    local upper bound updated to 0.429148

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.981 seconds.
    local lower bound updated to 0.423534
    local upper bound updated to 0.428607

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.91707 seconds.
    local lower bound updated to 0.423534
    local upper bound updated to 0.425725

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.6902 seconds.
    local lower bound updated to 0.423534
    local upper bound updated to 0.425536

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 8.07938 seconds.
    local lower bound updated to 0.423534
    local upper bound updated to 0.424893

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 14.7806 seconds.
    local lower bound updated to 0.423534
    local upper bound updated to 0.424877

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 18.5878 seconds.
    local lower bound updated to 0.424281
    local upper bound updated to 0.424864

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 22.9786 seconds.
    local lower bound updated to 0.424724
    local upper bound updated to 0.424863

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 24.1782 seconds.
    local lower bound updated to 0.424803
    local upper bound updated to 0.424862

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 24.887 seconds.
    local lower bound updated to 0.424862
    local upper bound updated to 0.424862
The Primal step takes 143.023 (S)
lower bound updated to 0.424862

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.476164
    local lower bound updated to 0.434774

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.451746
    local lower bound updated to 0.440103

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.451746
    local lower bound updated to 0.440104

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.448415
    local lower bound updated to 0.441646

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.447429
    local lower bound updated to 0.442019

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.445436
    local lower bound updated to 0.442257

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.444539
    local lower bound updated to 0.442278

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.442729
    local lower bound updated to 0.442384

    ++ RESTRICTED DUAL ITERATION 9 ++
    local upper bound updated to 0.442431
    local lower bound updated to 0.44239

    ++ RESTRICTED DUAL ITERATION 10 ++
    local upper bound updated to 0.442391
    local lower bound updated to 0.44239
The Dual step takes 25.5641 (S)
upper bound updated to 0.442391
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0244 seconds.
    local lower bound updated to 0.399365
    local upper bound updated to 0.44239

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.5455 seconds.
    local lower bound updated to 0.399365
    local upper bound updated to 0.442236

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 24.3283 seconds.
    local lower bound updated to 0.418065
    local upper bound updated to 0.439918

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 9.54644 seconds.
    local lower bound updated to 0.421751
    local upper bound updated to 0.439745

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 18.6461 seconds.
    local lower bound updated to 0.426144
    local upper bound updated to 0.438507

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 27.2057 seconds.
    local lower bound updated to 0.426144
    local upper bound updated to 0.436024

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 21.5198 seconds.
    local lower bound updated to 0.426144
    local upper bound updated to 0.435503

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 48.7821 seconds.
    local lower bound updated to 0.427298
    local upper bound updated to 0.435195

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0258 seconds.
    local lower bound updated to 0.428086
    local upper bound updated to 0.433859

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 24.5716 seconds.
    local lower bound updated to 0.428086
    local upper bound updated to 0.433858

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0293 seconds.
    local lower bound updated to 0.432326
    local upper bound updated to 0.433839

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0357 seconds.
    local lower bound updated to 0.432326
    local upper bound updated to 0.433838

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0241 seconds.
    local lower bound updated to 0.432525
    local upper bound updated to 0.433772

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0291 seconds.
    local lower bound updated to 0.432525
    local upper bound updated to 0.433403

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.025 seconds.
    local lower bound updated to 0.432525
    local upper bound updated to 0.433359

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.019 seconds.
    local lower bound updated to 0.433096
    local upper bound updated to 0.433315

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 60.0194 seconds.
    local lower bound updated to 0.433096
    local upper bound updated to 0.43325

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 60.0183 seconds.
    local lower bound updated to 0.43325
    local upper bound updated to 0.43325
The Primal step takes 778.547 (S)
lower bound updated to 0.43325

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.469203
    local lower bound updated to 0.438407

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.460269
    local lower bound updated to 0.438915

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.441846
    local lower bound updated to 0.439099

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.441846
    local lower bound updated to 0.439296

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.44072
    local lower bound updated to 0.439322

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.439322
    local lower bound updated to 0.439322
The Dual step takes 38.3327 (S)
upper bound updated to 0.439322
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0416 seconds.
    local lower bound updated to 0.408222
    local upper bound updated to 0.438346

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 57.5823 seconds.
    local lower bound updated to 0.431865
    local upper bound updated to 0.437261

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 39.7037 seconds.
    local lower bound updated to 0.433088
    local upper bound updated to 0.437246

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0259 seconds.
    local lower bound updated to 0.435013
    local upper bound updated to 0.437202

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0439 seconds.
    local lower bound updated to 0.435013
    local upper bound updated to 0.437124

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0281 seconds.
    local lower bound updated to 0.435685
    local upper bound updated to 0.436903

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0329 seconds.
    local lower bound updated to 0.435685
    local upper bound updated to 0.436747

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.038 seconds.
    local lower bound updated to 0.435685
    local upper bound updated to 0.436641

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0324 seconds.
    local lower bound updated to 0.435685
    local upper bound updated to 0.43663

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 53.8496 seconds.
    local lower bound updated to 0.43588
    local upper bound updated to 0.436613

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0208 seconds.
    local lower bound updated to 0.435984
    local upper bound updated to 0.436549

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0239 seconds.
    local lower bound updated to 0.435984
    local upper bound updated to 0.436517

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0208 seconds.
    local lower bound updated to 0.435984
    local upper bound updated to 0.436472

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0267 seconds.
    local lower bound updated to 0.436021
    local upper bound updated to 0.436446

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0204 seconds.
    local lower bound updated to 0.436256
    local upper bound updated to 0.436431

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.0225 seconds.
    local lower bound updated to 0.436339
    local upper bound updated to 0.436425

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 60.0357 seconds.
    local lower bound updated to 0.436425
    local upper bound updated to 0.436425
The Primal step takes 991.742 (S)
lower bound updated to 0.436425

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.456387
    local lower bound updated to 0.436425

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.437368
    local lower bound updated to 0.43645

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.436451
    local lower bound updated to 0.43645
The Dual step takes 25.4889 (S)
upper bound updated to 0.436451
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0226 seconds.
    local lower bound updated to 0.40861
    local upper bound updated to 0.43645

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0266 seconds.
    local lower bound updated to 0.435898
    local upper bound updated to 0.436443

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0343 seconds.
    local lower bound updated to 0.436318
    local upper bound updated to 0.436439

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0372 seconds.
    local lower bound updated to 0.436325
    local upper bound updated to 0.436437

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0337 seconds.
    local lower bound updated to 0.436423
    local upper bound updated to 0.436436

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0272 seconds.
    local lower bound updated to 0.436436
    local upper bound updated to 0.436436
The Primal step takes 360.251 (S)
lower bound updated to 0.436436

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.452522
    local lower bound updated to 0.436436

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.436684
    local lower bound updated to 0.436441

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.436441
    local lower bound updated to 0.436441
The Dual step takes 33.4951 (S)
upper bound updated to 0.436441
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0251 seconds.
    local lower bound updated to 0.410148
    local upper bound updated to 0.436441

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0265 seconds.
    local lower bound updated to 0.43626
    local upper bound updated to 0.43644

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0359 seconds.
    local lower bound updated to 0.436287
    local upper bound updated to 0.436438

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0375 seconds.
    local lower bound updated to 0.43637
    local upper bound updated to 0.436438

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0427 seconds.
    local lower bound updated to 0.436395
    local upper bound updated to 0.436438

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0331 seconds.
    local lower bound updated to 0.436438
    local upper bound updated to 0.436438
The time obtain the optimal randomized assortment is 2775.55 (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_60.000000_66416.log"
The computation time limit for a lower bound is 83219
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 20 physical cores, 40 logical processors, using up to 4 threads
Optimize a model with 3920 rows, 3178 columns and 12615 nonzeros
Model fingerprint: 0x93480d5d
Variable types: 3121 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [3e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 1060 rows and 1974 columns
Presolve time: 0.04s
Presolved: 2860 rows, 1204 columns, 11092 nonzeros
Variable types: 1148 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.5823338
Found heuristic solution: objective 0.5428568
Found heuristic solution: objective 0.5358471

Root relaxation: objective 2.516217e-01, 306 iterations, 0.01 seconds (0.00 work units)

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

     0     0    0.25162    0   28    0.53585    0.25162  53.0%     -    0s
H    0     0                       0.4703164    0.25162  46.5%     -    0s
H    0     0                       0.4699630    0.26729  43.1%     -    0s
H    0     0                       0.4523105    0.26729  40.9%     -    0s
     0     0    0.26729    0   30    0.45231    0.26729  40.9%     -    0s
     0     0    0.26729    0   30    0.45231    0.26729  40.9%     -    0s
     0     0    0.32147    0   30    0.45231    0.32147  28.9%     -    0s
     0     0    0.32157    0   30    0.45231    0.32157  28.9%     -    0s
     0     0    0.33650    0   30    0.45231    0.33650  25.6%     -    0s
H    0     0                       0.4471721    0.33650  24.7%     -    0s
H    0     0                       0.4425920    0.33650  24.0%     -    0s
     0     0    0.33866    0   30    0.44259    0.33866  23.5%     -    0s
H    0     0                       0.4411569    0.33866  23.2%     -    0s
     0     0    0.34759    0   31    0.44116    0.34759  21.2%     -    1s
     0     0    0.34936    0   32    0.44116    0.34936  20.8%     -    1s
     0     0    0.35261    0   32    0.44116    0.35261  20.1%     -    1s
H    0     0                       0.4395410    0.35261  19.8%     -    3s
     0     2    0.35261    0   32    0.43954    0.35261  19.8%     -    3s
H   50    49                       0.4386982    0.36288  17.3%  71.8    4s
H  207   114                       0.4386982    0.37306  15.0%  50.2    4s
   282   148    0.40492    7   20    0.43870    0.37740  14.0%  48.8    5s
H  287   148                       0.4386982    0.37740  14.0%  48.4    5s
H  295   148                       0.4386982    0.37740  14.0%  47.8    5s
H  371   171                       0.4371611    0.38774  11.3%  46.4    5s
H  508   234                       0.4364379    0.39193  10.2%  44.8    6s
   978   346    0.43136   15   12    0.43644    0.39775  8.86%  37.7   10s
  1562   483     cutoff   10         0.43644    0.40397  7.44%  35.9   15s
  2570   704     cutoff   17         0.43644    0.40863  6.37%  32.8   20s
  3201   857    0.41389   12   16    0.43644    0.41080  5.87%  31.5   25s
  3551   872    0.43129   17   34    0.43644    0.41156  5.70%  30.7   32s
H 3915   867                       0.4364379    0.41156  5.70%  33.5   34s
  3989   862    0.41156   20   23    0.43644    0.41156  5.70%  33.8   35s
  4296   838    0.41156   24   24    0.43644    0.41156  5.70%  34.3   40s
  4699   804     cutoff   30         0.43644    0.41156  5.70%  35.0   45s
H 4754   744                       0.4364379    0.41156  5.70%  35.0   45s
  5172   697     cutoff   28         0.43644    0.41331  5.30%  34.9   51s
  5943   544    0.43490   32   10    0.43644    0.41602  4.68%  34.8   55s
  6894   687     cutoff   32         0.43644    0.41874  4.05%  34.3   61s
  7435   795    0.42633   26   18    0.43644    0.41972  3.83%  34.2   65s
  8623   896    0.42528   28   12    0.43644    0.42107  3.52%  33.5   70s
 10702  1037    0.42728   28   14    0.43644    0.42346  2.97%  32.7   76s
H12210  1046                       0.4364379    0.42466  2.70%  32.2   79s
 12211  1070    0.43332   34   10    0.43644    0.42466  2.70%  32.2   80s
H12800  1070                       0.4364379    0.42550  2.51%  31.9   81s
 13698  1050     cutoff   33         0.43644    0.42616  2.36%  31.8   85s
H15277  1014                       0.4364379    0.42763  2.02%  31.3   88s
 15278   985 infeasible   38         0.43644    0.42763  2.02%  31.3   90s
 16867   923    0.43278   33   12    0.43644    0.42860  1.79%  30.9   95s
 19379   601    0.43410   36    6    0.43644    0.43097  1.25%  30.2  100s

Cutting planes:
  Implied bound: 337
  MIR: 187
  Flow cover: 697
  RLT: 104
  Relax-and-lift: 120

Explored 21909 nodes (649176 simplex iterations) in 104.66 seconds (65.73 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.436438 0.436438 0.436438 ... 0.447172

Optimal solution found (tolerance 1.00e-04)
Best objective 4.364378723027e-01, best bound 4.364378723027e-01, gap 0.0000%
The objective bound is 0.436438 while the objective upper bound is 0.436438

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.59 (ave)

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