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 1.03554 seconds.
    local lower bound updated to 0.18859
    local upper bound updated to 0.375344

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.21916 seconds.
    local lower bound updated to 0.375344
    local upper bound updated to 0.375344
The Primal step takes 2.25725 (S)
lower bound updated to 0.375344

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.534624
    local lower bound updated to 0.534624
The Dual step takes 0.0343009 (S)
upper bound updated to 0.534624
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 8.489 seconds.
    local lower bound updated to 0.258064
    local upper bound updated to 0.415201

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.33476 seconds.
    local lower bound updated to 0.397191
    local upper bound updated to 0.40004

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.98443 seconds.
    local lower bound updated to 0.397191
    local upper bound updated to 0.398372

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.30892 seconds.
    local lower bound updated to 0.398372
    local upper bound updated to 0.398372
The Primal step takes 27.1257 (S)
lower bound updated to 0.398372

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.483098
    local lower bound updated to 0.438768

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.439614
    local lower bound updated to 0.439614
The Dual step takes 0.191485 (S)
upper bound updated to 0.439614
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 25.523 seconds.
    local lower bound updated to 0.326473
    local upper bound updated to 0.415394

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.53182 seconds.
    local lower bound updated to 0.35233
    local upper bound updated to 0.414183

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.0947 seconds.
    local lower bound updated to 0.383989
    local upper bound updated to 0.412895

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 29.1258 seconds.
    local lower bound updated to 0.404522
    local upper bound updated to 0.412828

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 25.3501 seconds.
    local lower bound updated to 0.407341
    local upper bound updated to 0.412679

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 26.203 seconds.
    local lower bound updated to 0.409454
    local upper bound updated to 0.412534

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 37.6804 seconds.
    local lower bound updated to 0.410969
    local upper bound updated to 0.412275

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 32.6626 seconds.
    local lower bound updated to 0.410984
    local upper bound updated to 0.411798

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 42.0026 seconds.
    local lower bound updated to 0.411632
    local upper bound updated to 0.411795

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 51.3295 seconds.
    local lower bound updated to 0.411699
    local upper bound updated to 0.411789

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 36.2366 seconds.
    local lower bound updated to 0.411713
    local upper bound updated to 0.411774

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 34.5048 seconds.
    local lower bound updated to 0.411774
    local upper bound updated to 0.411774
The Primal step takes 357.285 (S)
lower bound updated to 0.411774

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.477432
    local lower bound updated to 0.412652

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.419263
    local lower bound updated to 0.4135

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.415941
    local lower bound updated to 0.414622

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.415941
    local lower bound updated to 0.414654

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.414654
    local lower bound updated to 0.414654
The Dual step takes 1.30793 (S)
upper bound updated to 0.414654
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 11.9747 seconds.
    local lower bound updated to 0.354571
    local upper bound updated to 0.413478

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 32.2404 seconds.
    local lower bound updated to 0.400109
    local upper bound updated to 0.413367

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 36.3647 seconds.
    local lower bound updated to 0.404185
    local upper bound updated to 0.41276

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 54.2198 seconds.
    local lower bound updated to 0.409751
    local upper bound updated to 0.412735

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 48.2273 seconds.
    local lower bound updated to 0.409923
    local upper bound updated to 0.412528

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 42.5419 seconds.
    local lower bound updated to 0.41087
    local upper bound updated to 0.412471

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 47.662 seconds.
    local lower bound updated to 0.412296
    local upper bound updated to 0.412471

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 39.9358 seconds.
    local lower bound updated to 0.412458
    local upper bound updated to 0.412466
The Primal step takes 313.209 (S)
lower bound updated to 0.412458

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.461301
    local lower bound updated to 0.412466

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.414275
    local lower bound updated to 0.412475

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.412475
    local lower bound updated to 0.412475
The Dual step takes 1.53362 (S)
upper bound updated to 0.412475
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 16.2996 seconds.
    local lower bound updated to 0.358827
    local upper bound updated to 0.412475

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 71.2299 seconds.
    local lower bound updated to 0.41243
    local upper bound updated to 0.412473

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 69.5407 seconds.
    local lower bound updated to 0.412473
    local upper bound updated to 0.412473
The Primal step takes 157.087 (S)
lower bound updated to 0.412473

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.460126
    local lower bound updated to 0.412473

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.412473
    local lower bound updated to 0.412473
The Dual step takes 0.93491 (S)
upper bound updated to 0.412473
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 16.206 seconds.
    local lower bound updated to 0.358827
    local upper bound updated to 0.412473

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.412473
    local upper bound updated to 0.412473
The time obtain the optimal randomized assortment is 977.201 (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_19_4_100.000000_101720.log"
The computation time limit for a lower bound is 85014
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 2364 rows, 1734 columns and 7992 nonzeros
Model fingerprint: 0x38a76321
Variable types: 1661 continuous, 73 integer (73 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e-01, 1e+00]
Presolve removed 439 rows and 817 columns
Presolve time: 0.02s
Presolved: 1925 rows, 917 columns, 7449 nonzeros
Variable types: 846 continuous, 71 integer (71 binary)
Found heuristic solution: objective 0.6337730
Found heuristic solution: objective 0.5434869

Root relaxation: objective 2.510672e-01, 225 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    0.25107    0   27    0.54349    0.25107  53.8%     -    0s
H    0     0                       0.5358672    0.25107  53.1%     -    0s
H    0     0                       0.5262504    0.25107  52.3%     -    0s
H    0     0                       0.5012225    0.25138  49.8%     -    0s
     0     0    0.25138    0   27    0.50122    0.25138  49.8%     -    0s
H    0     0                       0.4539154    0.25138  44.6%     -    0s
     0     0    0.30491    0   34    0.45392    0.30491  32.8%     -    0s
H    0     0                       0.4242436    0.30491  28.1%     -    0s
     0     0    0.30527    0   34    0.42424    0.30527  28.0%     -    0s
H    0     0                       0.4189110    0.32731  21.9%     -    0s
     0     0    0.32731    0   36    0.41891    0.32731  21.9%     -    0s
     0     0    0.32841    0   36    0.41891    0.32841  21.6%     -    0s
     0     0    0.33314    0   38    0.41891    0.33314  20.5%     -    0s
     0     0    0.33370    0   37    0.41891    0.33370  20.3%     -    0s
     0     0    0.33502    0   36    0.41891    0.33502  20.0%     -    0s
H    0     0                       0.4170021    0.33502  19.7%     -    2s
     0     2    0.33502    0   36    0.41700    0.33502  19.7%     -    2s
H   92    80                       0.4142746    0.34251  17.3%  33.9    2s
H   97    80                       0.4127695    0.34251  17.0%  34.1    2s
H  308   161                       0.4124732    0.34384  16.6%  32.4    3s
   800   291    0.36785    6   24    0.41247    0.35347  14.3%  30.3    6s
  2252   721    0.39654   14   37    0.41247    0.36231  12.2%  28.7   11s
  2798   799    0.40659   26   15    0.41247    0.36231  12.2%  30.6   15s
  4096   712    0.41028   23   18    0.41247    0.37049  10.2%  31.1   20s
  5090   788     cutoff   27         0.41247    0.37500  9.08%  31.1   25s
  6173   952    0.40148   23   21    0.41247    0.37801  8.36%  31.1   30s
  7458  1071     cutoff   26         0.41247    0.38132  7.55%  30.9   35s
  8958  1148    0.40825   30   18    0.41247    0.38409  6.88%  30.9   41s
 10478  1154    0.39894   23   17    0.41247    0.38741  6.08%  30.8   45s
 11669  1104     cutoff   28         0.41247    0.38935  5.61%  30.6   50s
 13069  1035     cutoff   22         0.41247    0.39088  5.23%  30.6   55s
 14842   801 infeasible   28         0.41247    0.39437  4.39%  30.2   61s
 16598   525     cutoff   26         0.41247    0.39846  3.40%  30.0   66s

Cutting planes:
  Implied bound: 214
  MIR: 144
  Flow cover: 371
  RLT: 45
  Relax-and-lift: 65

Explored 18103 nodes (537819 simplex iterations) in 69.50 seconds (65.64 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.412473 0.41277 0.414275 ... 0.535867

Optimal solution found (tolerance 1.00e-04)
Best objective 4.124731547062e-01, best bound 4.124731547062e-01, gap 0.0000%
The objective bound is 0.412473 while the objective upper bound is 0.412473

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.14 (ave)

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