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 0.854025 seconds.
    local lower bound updated to 0.257397
    local upper bound updated to 0.499195

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.08424 seconds.
    local lower bound updated to 0.495839
    local upper bound updated to 0.495839
The Primal step takes 1.9416 (S)
lower bound updated to 0.495839

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.573452
    local lower bound updated to 0.558085

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.56105
    local lower bound updated to 0.56105
The Dual step takes 0.0889964 (S)
upper bound updated to 0.56105
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 54.5192 seconds.
    local lower bound updated to 0.402669
    local upper bound updated to 0.550896

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.03186 seconds.
    local lower bound updated to 0.463444
    local upper bound updated to 0.531492

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.05526 seconds.
    local lower bound updated to 0.508261
    local upper bound updated to 0.52757

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.52226 seconds.
    local lower bound updated to 0.508261
    local upper bound updated to 0.524069

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 52.2693 seconds.
    local lower bound updated to 0.517967
    local upper bound updated to 0.523458

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 48.6447 seconds.
    local lower bound updated to 0.519349
    local upper bound updated to 0.520386

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 41.2133 seconds.
    local lower bound updated to 0.519349
    local upper bound updated to 0.519934

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.9191 seconds.
    local lower bound updated to 0.519594
    local upper bound updated to 0.519911

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 55.9857 seconds.
    local lower bound updated to 0.519819
    local upper bound updated to 0.519892

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.4074 seconds.
    local lower bound updated to 0.519892
    local upper bound updated to 0.519892
The Primal step takes 385.592 (S)
lower bound updated to 0.519892

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.554858
    local lower bound updated to 0.526512

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.551942
    local lower bound updated to 0.532067

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.538771
    local lower bound updated to 0.533514

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.538771
    local lower bound updated to 0.535922

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.536213
    local lower bound updated to 0.535961

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.535961
    local lower bound updated to 0.535961
The Dual step takes 3.87374 (S)
upper bound updated to 0.535961
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.466366
    local upper bound updated to 0.533491

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.526259
    local upper bound updated to 0.532369

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 89.3147 seconds.
    local lower bound updated to 0.526259
    local upper bound updated to 0.530688

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.029 seconds.
    local lower bound updated to 0.526896
    local upper bound updated to 0.529816

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.019 seconds.
    local lower bound updated to 0.528077
    local upper bound updated to 0.529285

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.025 seconds.
    local lower bound updated to 0.528444
    local upper bound updated to 0.529143

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.528666
    local upper bound updated to 0.529141

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.528862
    local upper bound updated to 0.529138

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.528963
    local upper bound updated to 0.529138

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.529129
    local upper bound updated to 0.529137
The Primal step takes 1889.65 (S)
lower bound updated to 0.529129

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.547373
    local lower bound updated to 0.529137

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529137
    local lower bound updated to 0.529137
The Dual step takes 6.75612 (S)
upper bound updated to 0.529137
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.466366
    local upper bound updated to 0.529137

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.529137
    local upper bound updated to 0.529137
The time obtain the optimal randomized assortment is 2687.99 (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_21_4_200.000000_208122.log"
The computation time limit for a lower bound is 83307
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 2444 rows, 1738 columns and 8392 nonzeros
Model fingerprint: 0xa7668a77
Variable types: 1657 continuous, 81 integer (81 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 414 rows and 758 columns
Presolve time: 0.03s
Presolved: 2030 rows, 980 columns, 8000 nonzeros
Variable types: 902 continuous, 78 integer (78 binary)
Found heuristic solution: objective 0.7280252
Found heuristic solution: objective 0.7041862
Found heuristic solution: objective 0.6998612

Root relaxation: objective 4.218646e-01, 181 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    0.42186    0   20    0.69986    0.42186  39.7%     -    0s
H    0     0                       0.6096085    0.42186  30.8%     -    0s
     0     0    0.42186    0   20    0.60961    0.42186  30.8%     -    0s
H    0     0                       0.5534112    0.44717  19.2%     -    0s
H    0     0                       0.5420527    0.44717  17.5%     -    0s
     0     0    0.44723    0   37    0.54205    0.44723  17.5%     -    0s
     0     0    0.45328    0   40    0.54205    0.45328  16.4%     -    0s
H    0     0                       0.5417329    0.45434  16.1%     -    0s
     0     0    0.45681    0   42    0.54173    0.45681  15.7%     -    0s
     0     0    0.46401    0   36    0.54173    0.46401  14.3%     -    0s
H    0     0                       0.5337895    0.46401  13.1%     -    0s
     0     0    0.46415    0   36    0.53379    0.46415  13.0%     -    0s
     0     0    0.46641    0   37    0.53379    0.46641  12.6%     -    0s
H    0     0                       0.5291374    0.46641  11.9%     -    0s
     0     2    0.46641    0   37    0.52914    0.46641  11.9%     -    3s
   652   388    0.52548   15   14    0.52914    0.48507  8.33%  22.1    5s
  1200   655    0.50666   28   19    0.52914    0.48749  7.87%  24.7   10s
  1500   708    0.52397   26   21    0.52914    0.48900  7.58%  25.0   15s
  2096   729    0.50446   23   26    0.52914    0.49273  6.88%  24.9   20s
H 2586   712                       0.5291374    0.49533  6.39%  24.7   22s
  2711   742 infeasible   26         0.52914    0.49608  6.25%  24.6   25s
  3782  1126     cutoff   34         0.52914    0.49878  5.74%  24.5   30s
  4866  1463 infeasible   31         0.52914    0.50038  5.43%  24.1   35s
  5521  1621    0.52397   26   13    0.52914    0.50143  5.24%  23.8   40s
  6712  1866    0.51465   30   19    0.52914    0.50265  5.01%  23.6   46s
  7918  2171    0.52179   28   17    0.52914    0.50371  4.81%  23.3   52s
H 8179  2171                       0.5291374    0.50373  4.80%  23.3   52s
  8262  2279    0.51450   21   29    0.52914    0.50413  4.73%  23.3   55s
  9470  2380    0.50716   22   23    0.52914    0.50486  4.59%  23.0   60s
  9892  2491    0.51526   28   19    0.52914    0.50548  4.47%  23.0   65s
 11150  2765    0.52571   30   15    0.52914    0.50613  4.35%  22.9   71s
 12218  2909    0.52058   25   28    0.52914    0.50655  4.27%  22.9   76s
 13432  3010    0.51898   31   19    0.52914    0.50719  4.15%  22.8   81s
 14605  3190    0.51577   29   24    0.52914    0.50784  4.02%  22.6   85s
 16758  3424    0.51973   28   23    0.52914    0.50881  3.84%  22.4   90s
 17592  3456    0.52469   30   15    0.52914    0.50907  3.79%  22.4   95s
 18931  3628    0.51872   27   21    0.52914    0.50965  3.68%  22.4  100s
 20197  3735    0.52390   31   25    0.52914    0.51015  3.59%  22.4  105s
 21649  3827    0.51919   22   27    0.52914    0.51065  3.49%  22.3  111s
 22333  3847    0.51404   24   25    0.52914    0.51091  3.44%  22.3  116s
 23370  3910    0.51407   28   25    0.52914    0.51123  3.39%  22.3  121s
 23789  3921    0.51967   31   16    0.52914    0.51131  3.37%  22.3  125s
 25403  3971    0.51659   29   19    0.52914    0.51199  3.24%  22.2  132s
 27331  3970     cutoff   28         0.52914    0.51254  3.14%  22.1  137s
 28648  3956    0.52222   29   15    0.52914    0.51325  3.00%  22.1  141s
 29980  3960    0.51906   29   17    0.52914    0.51368  2.92%  22.1  146s
 30714  3920    0.52096   23   31    0.52914    0.51384  2.89%  22.1  151s
 31509  3905     cutoff   26         0.52914    0.51405  2.85%  22.1  156s
 32810  3853    0.51705   32   19    0.52914    0.51441  2.78%  22.1  161s
 34900  3811     cutoff   34         0.52914    0.51520  2.63%  22.0  165s
 35986  3703    0.51829   27   22    0.52914    0.51559  2.56%  22.1  170s
 36985  3589    0.52268   24   19    0.52914    0.51590  2.50%  22.1  175s
 38369  3479    0.52581   34   13    0.52914    0.51641  2.41%  22.1  180s
 40171  3275    0.52626   34    6    0.52914    0.51704  2.29%  22.1  185s
 41191  3152    0.52237   26   25    0.52914    0.51741  2.22%  22.1  190s
 42766  2903    0.52221   29   19    0.52914    0.51785  2.13%  22.1  196s
 44680  2532     cutoff   32         0.52914    0.51879  1.96%  22.2  200s
 45697  2418     cutoff   32         0.52914    0.51914  1.89%  22.2  205s
 47057  2006    0.52688   25   23    0.52914    0.51991  1.74%  22.2  210s
 49130  1628 infeasible   31         0.52914    0.52097  1.54%  22.1  216s
 50253  1203     cutoff   27         0.52914    0.52166  1.41%  22.1  220s
 52163   557 infeasible   36         0.52914    0.52373  1.02%  22.0  226s

Cutting planes:
  Implied bound: 260
  MIR: 116
  Flow cover: 339
  RLT: 65
  Relax-and-lift: 99

Explored 53302 nodes (1165446 simplex iterations) in 229.08 seconds (209.26 work units)
Thread count was 4 (of 256 available processors)

Solution count 10: 0.529137 0.529137 0.529137 ... 0.704186

Optimal solution found (tolerance 1.00e-04)
Best objective 5.291374144016e-01, best bound 5.291374125504e-01, gap 0.0000%
The objective bound is 0.529137 while the objective upper bound is 0.529137

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.71 (ave)

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