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 0.298332 seconds.
    local lower bound updated to 0.232331
    local upper bound updated to 0.441165

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.398842 seconds.
    local lower bound updated to 0.433185
    local upper bound updated to 0.433185
The Primal step takes 0.700479 (S)
lower bound updated to 0.433185

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.518783
    local lower bound updated to 0.505157

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.511341
    local lower bound updated to 0.5087

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.5087
    local lower bound updated to 0.5087
The Dual step takes 0.213763 (S)
upper bound updated to 0.5087
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.20945 seconds.
    local lower bound updated to 0.347488
    local upper bound updated to 0.460813

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.94906 seconds.
    local lower bound updated to 0.439028
    local upper bound updated to 0.450177

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.13156 seconds.
    local lower bound updated to 0.439551
    local upper bound updated to 0.447569

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.57181 seconds.
    local lower bound updated to 0.442854
    local upper bound updated to 0.446513

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.5747 seconds.
    local lower bound updated to 0.444167
    local upper bound updated to 0.445816

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.68924 seconds.
    local lower bound updated to 0.445225
    local upper bound updated to 0.445742

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 11.5047 seconds.
    local lower bound updated to 0.445632
    local upper bound updated to 0.445704

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 9.20199 seconds.
    local lower bound updated to 0.445704
    local upper bound updated to 0.445704
The Primal step takes 55.8495 (S)
lower bound updated to 0.445704

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.496707
    local lower bound updated to 0.460859

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.496707
    local lower bound updated to 0.476552

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.496707
    local lower bound updated to 0.478257

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.487923
    local lower bound updated to 0.47945

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.483993
    local lower bound updated to 0.480963

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.480963
    local lower bound updated to 0.480963
The Dual step takes 1.85684 (S)
upper bound updated to 0.480963
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.02638 seconds.
    local lower bound updated to 0.397996
    local upper bound updated to 0.471135

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.29124 seconds.
    local lower bound updated to 0.450568
    local upper bound updated to 0.46351

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.17853 seconds.
    local lower bound updated to 0.450568
    local upper bound updated to 0.461894

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 19.2922 seconds.
    local lower bound updated to 0.452709
    local upper bound updated to 0.45995

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.8269 seconds.
    local lower bound updated to 0.455711
    local upper bound updated to 0.459188

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 19.9293 seconds.
    local lower bound updated to 0.455711
    local upper bound updated to 0.458441

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.57189 seconds.
    local lower bound updated to 0.455711
    local upper bound updated to 0.458435

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 5.63771 seconds.
    local lower bound updated to 0.455711
    local upper bound updated to 0.458426

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 21.029 seconds.
    local lower bound updated to 0.457575
    local upper bound updated to 0.45815

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 11.0491 seconds.
    local lower bound updated to 0.457575
    local upper bound updated to 0.45806

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 20.2419 seconds.
    local lower bound updated to 0.457575
    local upper bound updated to 0.457973

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 18.0246 seconds.
    local lower bound updated to 0.457575
    local upper bound updated to 0.457941

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 17.8886 seconds.
    local lower bound updated to 0.457635
    local upper bound updated to 0.457875

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 20.1504 seconds.
    local lower bound updated to 0.457875
    local upper bound updated to 0.457875
The Primal step takes 185.192 (S)
lower bound updated to 0.457875

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.474006
    local lower bound updated to 0.457875

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.468961
    local lower bound updated to 0.460755

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.463527
    local lower bound updated to 0.460948

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.463527
    local lower bound updated to 0.461094

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.463527
    local lower bound updated to 0.461211

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.462247
    local lower bound updated to 0.461271

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.461271
    local lower bound updated to 0.461271
The Dual step takes 15.507 (S)
upper bound updated to 0.461271
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.8934 seconds.
    local lower bound updated to 0.419562
    local upper bound updated to 0.461271

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 24.4706 seconds.
    local lower bound updated to 0.454929
    local upper bound updated to 0.46123

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 18.9979 seconds.
    local lower bound updated to 0.455702
    local upper bound updated to 0.461132

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 42.6425 seconds.
    local lower bound updated to 0.459313
    local upper bound updated to 0.461017

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 45.244 seconds.
    local lower bound updated to 0.459313
    local upper bound updated to 0.460805

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 34.0894 seconds.
    local lower bound updated to 0.459313
    local upper bound updated to 0.460707

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 54.9457 seconds.
    local lower bound updated to 0.46001
    local upper bound updated to 0.46059

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 33.8451 seconds.
    local lower bound updated to 0.46001
    local upper bound updated to 0.460576

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 55.7567 seconds.
    local lower bound updated to 0.460119
    local upper bound updated to 0.460492

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 43.2828 seconds.
    local lower bound updated to 0.46033
    local upper bound updated to 0.460485

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 52.1841 seconds.
    local lower bound updated to 0.460417
    local upper bound updated to 0.460483

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 51.9967 seconds.
    local lower bound updated to 0.460483
    local upper bound updated to 0.460483
The Primal step takes 472.433 (S)
lower bound updated to 0.460483

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.471168
    local lower bound updated to 0.460483

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.465175
    local lower bound updated to 0.46064

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.461407
    local lower bound updated to 0.46067

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.461407
    local lower bound updated to 0.460707

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.460707
    local lower bound updated to 0.460707
The Dual step takes 22.2056 (S)
upper bound updated to 0.460707
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 18.9258 seconds.
    local lower bound updated to 0.422216
    local upper bound updated to 0.460707

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 53.2353 seconds.
    local lower bound updated to 0.460503
    local upper bound updated to 0.460688

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 61.988 seconds.
    local lower bound updated to 0.460688
    local upper bound updated to 0.460688
The Primal step takes 134.171 (S)
lower bound updated to 0.460688

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.470707
    local lower bound updated to 0.460688

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.460688
    local lower bound updated to 0.460688
The Dual step takes 9.75243 (S)
upper bound updated to 0.460688
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 20.1806 seconds.
    local lower bound updated to 0.422216
    local upper bound updated to 0.460688

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 52.4906 seconds.
    local lower bound updated to 0.460688
    local upper bound updated to 0.460688
The time obtain the optimal randomized assortment is 970.569 (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_200616.log"
The computation time limit for a lower bound is 85025
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 8906 nonzeros
Model fingerprint: 0x44417646
Variable types: 2211 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 779 rows and 1409 columns
Presolve time: 0.03s
Presolved: 2021 rows, 859 columns, 7822 nonzeros
Variable types: 804 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5240973
Found heuristic solution: objective 0.5213840

Root relaxation: objective 3.309506e-01, 251 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    0.33095    0   17    0.52138    0.33095  36.5%     -    0s
H    0     0                       0.4679462    0.33095  29.3%     -    0s
H    0     0                       0.4673070    0.33858  27.5%     -    0s
     0     0    0.33858    0   22    0.46731    0.33858  27.5%     -    0s
     0     0    0.33858    0   22    0.46731    0.33858  27.5%     -    0s
     0     0    0.37321    0   25    0.46731    0.37321  20.1%     -    0s
H    0     0                       0.4609958    0.37321  19.0%     -    0s
     0     0    0.37328    0   25    0.46100    0.37328  19.0%     -    0s
     0     0    0.38097    0   27    0.46100    0.38097  17.4%     -    0s
     0     0    0.38412    0   26    0.46100    0.38412  16.7%     -    0s
     0     0    0.39631    0   26    0.46100    0.39631  14.0%     -    0s
H    0     0                       0.4609044    0.39631  14.0%     -    0s
     0     0    0.39751    0   25    0.46090    0.39751  13.8%     -    0s
     0     0    0.39984    0   26    0.46090    0.39984  13.2%     -    0s
H    0     0                       0.4606882    0.39984  13.2%     -    3s
     0     2    0.39984    0   26    0.46069    0.39984  13.2%     -    3s
   393   188    0.41684    4   23    0.46069    0.41463  10.0%  33.8    5s
H 1763   552                       0.4606882    0.42866  6.95%  28.3    9s
  1897   594    0.45504   11   13    0.46069    0.42945  6.78%  28.3   10s
  2700   744     cutoff   11         0.46069    0.43309  5.99%  27.9   15s
  3424   900     cutoff   10         0.46069    0.43516  5.54%  27.6   20s
  4296   959    0.44804   14   26    0.46069    0.43749  5.04%  27.0   25s
  5163   969    0.44136   18   20    0.46069    0.43749  5.04%  28.9   30s
  6487   725    0.46009   23   14    0.46069    0.43829  4.86%  29.0   35s
  7651   554    0.44672   22   12    0.46069    0.44235  3.98%  28.9   40s
  8595   610     cutoff   24         0.46069    0.44419  3.58%  28.6   45s
 10555   572     cutoff   26         0.46069    0.44744  2.88%  27.8   50s
 12234   422    0.46013   26    8    0.46069    0.44969  2.39%  27.3   55s

Cutting planes:
  Implied bound: 239
  MIR: 155
  Flow cover: 432
  RLT: 95
  Relax-and-lift: 78
  BQP: 1

Explored 14216 nodes (380322 simplex iterations) in 58.92 seconds (48.41 work units)
Thread count was 4 (of 48 available processors)

Solution count 8: 0.460688 0.460688 0.460904 ... 0.524097

Optimal solution found (tolerance 1.00e-04)
Best objective 4.606882382245e-01, best bound 4.606882382245e-01, gap 0.0000%
The objective bound is 0.460688 while the objective upper bound is 0.460688

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.54 (ave)

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