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 0.323459 seconds.
    local lower bound updated to 0.249982
    local upper bound updated to 0.456704

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.757747 seconds.
    local lower bound updated to 0.453355
    local upper bound updated to 0.453355
The Primal step takes 1.08369 (S)
lower bound updated to 0.453355

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.622367
    local lower bound updated to 0.622299

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.622299
    local lower bound updated to 0.622299
The Dual step takes 0.0456018 (S)
upper bound updated to 0.622299
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.09446 seconds.
    local lower bound updated to 0.337313
    local upper bound updated to 0.503535

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.74362 seconds.
    local lower bound updated to 0.458512
    local upper bound updated to 0.460805

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.07207 seconds.
    local lower bound updated to 0.458512
    local upper bound updated to 0.460358

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.2915 seconds.
    local lower bound updated to 0.460358
    local upper bound updated to 0.460358
The Primal step takes 6.20922 (S)
lower bound updated to 0.460358

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.532511
    local lower bound updated to 0.505935

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518974
    local lower bound updated to 0.508851

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.508851
    local lower bound updated to 0.508851
The Dual step takes 0.839107 (S)
upper bound updated to 0.508851
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 35.9124 seconds.
    local lower bound updated to 0.404324
    local upper bound updated to 0.495355

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 10.4274 seconds.
    local lower bound updated to 0.474502
    local upper bound updated to 0.493914

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 13.8818 seconds.
    local lower bound updated to 0.479948
    local upper bound updated to 0.4908

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.7183 seconds.
    local lower bound updated to 0.48272
    local upper bound updated to 0.489297

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 13.897 seconds.
    local lower bound updated to 0.48282
    local upper bound updated to 0.485443

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 21.0074 seconds.
    local lower bound updated to 0.48345
    local upper bound updated to 0.484671

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 12.6728 seconds.
    local lower bound updated to 0.483615
    local upper bound updated to 0.483734

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 18.3557 seconds.
    local lower bound updated to 0.483723
    local upper bound updated to 0.483734

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 17.7453 seconds.
    local lower bound updated to 0.483734
    local upper bound updated to 0.483734
The Primal step takes 156.644 (S)
lower bound updated to 0.483734

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.516876
    local lower bound updated to 0.483734

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.516876
    local lower bound updated to 0.493963

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.503889
    local lower bound updated to 0.494662

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.503889
    local lower bound updated to 0.497288

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.503889
    local lower bound updated to 0.498866

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.503889
    local lower bound updated to 0.499188

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.500902
    local lower bound updated to 0.49958

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.49958
    local lower bound updated to 0.49958
The Dual step takes 13.3846 (S)
upper bound updated to 0.49958
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 56.3979 seconds.
    local lower bound updated to 0.437465
    local upper bound updated to 0.495863

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 35.9122 seconds.
    local lower bound updated to 0.470376
    local upper bound updated to 0.495411

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 89.9401 seconds.
    local lower bound updated to 0.487348
    local upper bound updated to 0.493825

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 94.6155 seconds.
    local lower bound updated to 0.489098
    local upper bound updated to 0.493667

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 114.255 seconds.
    local lower bound updated to 0.491327
    local upper bound updated to 0.493272

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 70.0923 seconds.
    local lower bound updated to 0.491327
    local upper bound updated to 0.492737

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 81.0426 seconds.
    local lower bound updated to 0.491327
    local upper bound updated to 0.492501

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 115.946 seconds.
    local lower bound updated to 0.491327
    local upper bound updated to 0.492141

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 103.644 seconds.
    local lower bound updated to 0.491327
    local upper bound updated to 0.491909

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 91.6213 seconds.
    local lower bound updated to 0.491853
    local upper bound updated to 0.4919

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 99.8976 seconds.
    local lower bound updated to 0.491853
    local upper bound updated to 0.491893

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 108.835 seconds.
    local lower bound updated to 0.491893
    local upper bound updated to 0.491893
The Primal step takes 1062.28 (S)
lower bound updated to 0.491893

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.508956
    local lower bound updated to 0.491893

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.498586
    local lower bound updated to 0.492629

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.498586
    local lower bound updated to 0.49265

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.494859
    local lower bound updated to 0.492702

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.492702
    local lower bound updated to 0.492702
The Dual step takes 24.2664 (S)
upper bound updated to 0.492702
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 144.477 seconds.
    local lower bound updated to 0.450492
    local upper bound updated to 0.49268

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.033 seconds.
    local lower bound updated to 0.491092
    local upper bound updated to 0.492537

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.491092
    local upper bound updated to 0.492521

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.034 seconds.
    local lower bound updated to 0.491862
    local upper bound updated to 0.492476

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.492124
    local upper bound updated to 0.492455

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.025 seconds.
    local lower bound updated to 0.492221
    local upper bound updated to 0.492428

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.492221
    local upper bound updated to 0.492396

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.492262
    local upper bound updated to 0.492393

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.492283
    local upper bound updated to 0.492376

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.492337
    local upper bound updated to 0.492373

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.492373
    local upper bound updated to 0.492373
The Primal step takes 2144.88 (S)
lower bound updated to 0.492373

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.506364
    local lower bound updated to 0.492373

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.498596
    local lower bound updated to 0.492377

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.495408
    local lower bound updated to 0.492435

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.492435
    local lower bound updated to 0.492435
The Dual step takes 30.5289 (S)
upper bound updated to 0.492435
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.447 seconds.
    local lower bound updated to 0.449986
    local upper bound updated to 0.492435

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.048 seconds.
    local lower bound updated to 0.492435
    local upper bound updated to 0.492435
The Primal step takes 300.512 (S)
lower bound updated to 0.492435

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.505856
    local lower bound updated to 0.492435

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.492435
    local lower bound updated to 0.492435
The Dual step takes 16.2038 (S)
upper bound updated to 0.492435
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.281 seconds.
    local lower bound updated to 0.449986
    local upper bound updated to 0.492435

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.024 seconds.
    local lower bound updated to 0.492435
    local upper bound updated to 0.492435
The time obtain the optimal randomized assortment is 4057.2 (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_200.000000_201618.log"
The computation time limit for a lower bound is 81935
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 3574 rows, 2730 columns and 11795 nonzeros
Model fingerprint: 0x8d67e3c6
Variable types: 2665 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [3e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 815 rows and 1503 columns
Presolve time: 0.03s
Presolved: 2759 rows, 1227 columns, 10768 nonzeros
Variable types: 1164 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.6132213
Found heuristic solution: objective 0.5972564
Found heuristic solution: objective 0.5555490

Root relaxation: objective 3.533114e-01, 306 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    0.35331    0   27    0.55555    0.35331  36.4%     -    0s
H    0     0                       0.5551987    0.35331  36.4%     -    0s
H    0     0                       0.5483077    0.35331  35.6%     -    0s
     0     0    0.36227    0   33    0.54831    0.36227  33.9%     -    0s
H    0     0                       0.5302998    0.36227  31.7%     -    0s
     0     0    0.36227    0   33    0.53030    0.36227  31.7%     -    0s
     0     0    0.40288    0   31    0.53030    0.40288  24.0%     -    0s
H    0     0                       0.5174534    0.40288  22.1%     -    0s
     0     0    0.40288    0   31    0.51745    0.40288  22.1%     -    0s
     0     0    0.41335    0   29    0.51745    0.41335  20.1%     -    0s
H    0     0                       0.4990877    0.41335  17.2%     -    0s
     0     0    0.41443    0   29    0.49909    0.41443  17.0%     -    0s
     0     0    0.41899    0   30    0.49909    0.41899  16.0%     -    0s
     0     0    0.41978    0   30    0.49909    0.41978  15.9%     -    0s
     0     0    0.42042    0   28    0.49909    0.42042  15.8%     -    0s
H    0     0                       0.4951954    0.42042  15.1%     -    0s
H    0     0                       0.4934971    0.42042  14.8%     -    0s
H    0     0                       0.4924351    0.42042  14.6%     -    3s
     0     2    0.42042    0   28    0.49244    0.42042  14.6%     -    3s
   199   130    0.48784   13   12    0.49244    0.43414  11.8%  55.3    6s
H  505   276                       0.4924351    0.44226  10.2%  50.8    8s
H  552   299                       0.4924350    0.44226  10.2%  50.0    9s
   698   361    0.45002   10   20    0.49244    0.44509  9.62%  47.1   10s
  1388   548    0.47656    7   21    0.49244    0.44905  8.81%  44.2   15s
  1885   694    0.47400   11   14    0.49244    0.45106  8.40%  43.9   20s
  3203   962 infeasible   15         0.49244    0.45437  7.73%  41.5   25s
  3892  1052    0.48489   24   28    0.49244    0.45567  7.47%  40.3   31s
  3912  1070    0.45567   13   29    0.49244    0.45567  7.47%  41.0   35s
  4699  1185    0.49081   24   14    0.49244    0.45567  7.47%  43.6   42s
  4798  1202     cutoff   30         0.49244    0.45567  7.47%  44.0   45s
  6291  1099     cutoff   27         0.49244    0.45965  6.66%  44.1   51s
H 6400  1044                       0.4924350    0.45993  6.60%  44.0   53s
  7195  1080    0.47054   23   18    0.49244    0.46174  6.23%  43.3   56s
  7460  1166    0.48894   23    8    0.49244    0.46238  6.10%  43.2   60s
  8695  1446    0.48911   29   10    0.49244    0.46400  5.77%  42.3   65s
  9123  1554    0.48278   21   18    0.49244    0.46465  5.64%  42.1   70s
  9699  1654    0.47462   25   12    0.49244    0.46547  5.48%  41.9   75s
 10579  1882     cutoff   28         0.49244    0.46614  5.34%  41.5   81s
 11487  1955    0.47478   27   14    0.49244    0.46692  5.18%  41.2   85s
 12191  2092     cutoff   30         0.49244    0.46762  5.04%  40.7   90s
 13382  2283    0.47531   30   12    0.49244    0.46866  4.83%  40.2   96s
 15072  2527     cutoff   29         0.49244    0.46967  4.62%  39.5  103s
 15560  2601    0.49226   25   14    0.49244    0.47004  4.55%  39.4  105s
 17274  2777    0.49127   28    4    0.49244    0.47087  4.38%  38.8  110s
 17863  2919    0.48109   29   16    0.49244    0.47117  4.32%  38.6  115s
H18000  2919                       0.4924350    0.47117  4.32%  38.6  115s
H18501  2946                       0.4924350    0.47149  4.25%  38.4  117s
 19518  3057    0.48452   30   10    0.49244    0.47217  4.12%  38.1  120s
 20889  3135     cutoff   24         0.49244    0.47260  4.03%  37.6  125s
 22055  3293    0.48601   28   15    0.49244    0.47316  3.91%  37.3  131s
 23171  3394    0.48309   24   20    0.49244    0.47343  3.86%  37.0  137s
 24553  3480    0.48579   26   12    0.49244    0.47389  3.77%  36.6  142s
 25481  3509     cutoff   23         0.49244    0.47429  3.68%  36.4  146s
 26327  3577     cutoff   26         0.49244    0.47457  3.63%  36.2  150s
H27538  3612                       0.4924350    0.47487  3.57%  36.0  154s
 27687  3628    0.48096   29   14    0.49244    0.47507  3.53%  35.9  156s
 28853  3692    0.48200   25   16    0.49244    0.47537  3.47%  35.7  161s
 30717  3791    0.49201   32    8    0.49244    0.47590  3.36%  35.3  166s
 31754  3835     cutoff   28         0.49244    0.47626  3.28%  35.1  171s
H32760  3835                       0.4924350    0.47653  3.23%  34.9  171s
 34435  3901     cutoff   37         0.49244    0.47695  3.15%  34.7  176s
 35110  3891    0.49116   29   10    0.49244    0.47712  3.11%  34.6  182s
 36197  3936    0.48444   28   10    0.49244    0.47741  3.05%  34.4  186s
 36687  3922    0.48700   25   16    0.49244    0.47743  3.05%  34.4  190s
 37769  3920    0.48964   21   14    0.49244    0.47783  2.97%  34.2  195s
 39352  3956    0.49198   23   10    0.49244    0.47817  2.90%  34.0  200s
 40706  3938     cutoff   33         0.49244    0.47855  2.82%  33.8  207s
 42405  3890    0.48706   30   14    0.49244    0.47893  2.74%  33.6  211s
 43412  3854    0.48662   25   10    0.49244    0.47915  2.70%  33.5  216s
 44151  3833     cutoff   31         0.49244    0.47944  2.64%  33.4  220s
 45214  3771 infeasible   29         0.49244    0.47969  2.59%  33.3  225s
 47240  3666     cutoff   29         0.49244    0.48021  2.48%  33.1  230s
 49236  3562     cutoff   36         0.49244    0.48071  2.38%  32.9  235s
 50828  3445    0.49030   28   10    0.49244    0.48096  2.33%  32.8  241s
 52594  3323     cutoff   29         0.49244    0.48163  2.19%  32.6  245s
 53686  3213    0.48880   31   14    0.49244    0.48184  2.15%  32.5  250s
 54526  3118     cutoff   37         0.49244    0.48209  2.10%  32.4  255s
 55755  3002    0.48535   32    8    0.49244    0.48250  2.02%  32.3  260s
 56853  2855     cutoff   29         0.49244    0.48276  1.97%  32.2  267s
 58059  2705     cutoff   29         0.49244    0.48313  1.89%  32.0  271s
H58398  2705                       0.4924350    0.48314  1.89%  32.0  271s
 59802  2491    0.48546   23   13    0.49244    0.48372  1.77%  31.9  277s
H59999  2491                       0.4924350    0.48373  1.77%  31.9  277s
 60634  2399    0.48528   23   20    0.49244    0.48388  1.74%  31.9  282s
 61737  2220     cutoff   28         0.49244    0.48429  1.65%  31.8  286s
 62982  2111    0.48628   33   10    0.49244    0.48464  1.58%  31.7  290s
 63912  1742     cutoff   28         0.49244    0.48506  1.50%  31.6  296s
 66011  1210     cutoff   30         0.49244    0.48609  1.29%  31.4  300s

Cutting planes:
  Gomory: 3
  Implied bound: 355
  MIR: 196
  Flow cover: 438
  RLT: 94
  Relax-and-lift: 112

Explored 69172 nodes (2148320 simplex iterations) in 304.71 seconds (274.54 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.492435 0.493497 0.495195 ... 0.597256

Optimal solution found (tolerance 1.00e-04)
Best objective 4.924350639933e-01, best bound 4.924350260652e-01, gap 0.0000%
The objective bound is 0.492435 while the objective upper bound is 0.492435

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.46 (ave)

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