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 1.19206 seconds.
    local lower bound updated to 0.232909
    local upper bound updated to 0.416864

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.58922 seconds.
    local lower bound updated to 0.416864
    local upper bound updated to 0.416864
The Primal step takes 2.78405 (S)
lower bound updated to 0.416864

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.536216
    local lower bound updated to 0.536216
The Dual step takes 0.0534573 (S)
upper bound updated to 0.536216
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.524906 seconds.
    local lower bound updated to 0.273631
    local upper bound updated to 0.43487

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.17887 seconds.
    local lower bound updated to 0.42711
    local upper bound updated to 0.429115

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.85771 seconds.
    local lower bound updated to 0.42711
    local upper bound updated to 0.42779

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.20948 seconds.
    local lower bound updated to 0.42757
    local upper bound updated to 0.427643

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.09345 seconds.
    local lower bound updated to 0.427624
    local upper bound updated to 0.427636

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.8341 seconds.
    local lower bound updated to 0.427636
    local upper bound updated to 0.427636
The Primal step takes 22.7098 (S)
lower bound updated to 0.427636

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.565875
    local lower bound updated to 0.479251

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.565875
    local lower bound updated to 0.513133

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513133
    local lower bound updated to 0.513133
The Dual step takes 0.291484 (S)
upper bound updated to 0.513133
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.1633 seconds.
    local lower bound updated to 0.325776
    local upper bound updated to 0.449838

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.15234 seconds.
    local lower bound updated to 0.400695
    local upper bound updated to 0.442088

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.90036 seconds.
    local lower bound updated to 0.432404
    local upper bound updated to 0.439048

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.03432 seconds.
    local lower bound updated to 0.436584
    local upper bound updated to 0.437975

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.98958 seconds.
    local lower bound updated to 0.437619
    local upper bound updated to 0.437858

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.77231 seconds.
    local lower bound updated to 0.437858
    local upper bound updated to 0.437858
The Primal step takes 24.0286 (S)
lower bound updated to 0.437858

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.509537
    local lower bound updated to 0.437858

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.473192
    local lower bound updated to 0.450879

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.473192
    local lower bound updated to 0.455123

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.462539
    local lower bound updated to 0.455751

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.457835
    local lower bound updated to 0.456298

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.456298
    local lower bound updated to 0.456298
The Dual step takes 1.55498 (S)
upper bound updated to 0.456298
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.1337 seconds.
    local lower bound updated to 0.380696
    local upper bound updated to 0.442527

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 7.34473 seconds.
    local lower bound updated to 0.43938
    local upper bound updated to 0.442295

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.0867 seconds.
    local lower bound updated to 0.441427
    local upper bound updated to 0.441892

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 13.6884 seconds.
    local lower bound updated to 0.441778
    local upper bound updated to 0.441884

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.4517 seconds.
    local lower bound updated to 0.441778
    local upper bound updated to 0.44187

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.21009 seconds.
    local lower bound updated to 0.44187
    local upper bound updated to 0.44187
The Primal step takes 63.9464 (S)
lower bound updated to 0.44187

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.48482
    local lower bound updated to 0.444039

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.464256
    local lower bound updated to 0.446816

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.459064
    local lower bound updated to 0.447192

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.452005
    local lower bound updated to 0.447227

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.447602
    local lower bound updated to 0.447247

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.447247
    local lower bound updated to 0.447247
The Dual step takes 11.7128 (S)
upper bound updated to 0.447247
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 15.372 seconds.
    local lower bound updated to 0.393267
    local upper bound updated to 0.447247

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0303 seconds.
    local lower bound updated to 0.445223
    local upper bound updated to 0.447062

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0225 seconds.
    local lower bound updated to 0.446651
    local upper bound updated to 0.447041

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0164 seconds.
    local lower bound updated to 0.446809
    local upper bound updated to 0.44702

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0265 seconds.
    local lower bound updated to 0.446908
    local upper bound updated to 0.447012

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0222 seconds.
    local lower bound updated to 0.446978
    local upper bound updated to 0.447009

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0178 seconds.
    local lower bound updated to 0.447009
    local upper bound updated to 0.447009
The Primal step takes 375.554 (S)
lower bound updated to 0.447009

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.476745
    local lower bound updated to 0.447009

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.447009
    local lower bound updated to 0.447009
The Dual step takes 7.43184 (S)
upper bound updated to 0.447009
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.9889 seconds.
    local lower bound updated to 0.393267
    local upper bound updated to 0.447009

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0283 seconds.
    local lower bound updated to 0.447009
    local upper bound updated to 0.447009
The time obtain the optimal randomized assortment is 585.099 (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_60.000000_65918.log"
The computation time limit for a lower bound is 85405
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 2798 rows, 2138 columns and 9212 nonzeros
Model fingerprint: 0x18d5f04d
Variable types: 2073 continuous, 65 integer (65 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 641 rows and 1177 columns
Presolve time: 0.03s
Presolved: 2157 rows, 961 columns, 8390 nonzeros
Variable types: 897 continuous, 64 integer (64 binary)
Found heuristic solution: objective 0.5877378
Found heuristic solution: objective 0.5554373

Root relaxation: objective 3.141721e-01, 302 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    0.31417    0   16    0.55544    0.31417  43.4%     -    0s
H    0     0                       0.5070910    0.31417  38.0%     -    0s
H    0     0                       0.4571930    0.31417  31.3%     -    0s
     0     0    0.31513    0   16    0.45719    0.31513  31.1%     -    0s
H    0     0                       0.4556104    0.31513  30.8%     -    0s
H    0     0                       0.4509099    0.33562  25.6%     -    0s
     0     0    0.33562    0   27    0.45091    0.33562  25.6%     -    0s
     0     0    0.33711    0   27    0.45091    0.33711  25.2%     -    0s
     0     0    0.34074    0   31    0.45091    0.34074  24.4%     -    0s
H    0     0                       0.4501436    0.34079  24.3%     -    0s
     0     0    0.34079    0   31    0.45014    0.34079  24.3%     -    0s
     0     0    0.35241    0   28    0.45014    0.35241  21.7%     -    0s
     0     0    0.35610    0   30    0.45014    0.35610  20.9%     -    0s
     0     0    0.36019    0   32    0.45014    0.36019  20.0%     -    0s
H    0     0                       0.4492021    0.36019  19.8%     -    0s
H    0     0                       0.4470808    0.36019  19.4%     -    2s
     0     2    0.36019    0   32    0.44708    0.36019  19.4%     -    2s
H  310   172                       0.4470807    0.38510  13.9%  33.0    3s
H  700   295                       0.4470407    0.40238  10.0%  29.3    4s
H  768   313                       0.4470406    0.40395  9.64%  28.8    4s
  1194   464    0.43536   12   14    0.44704    0.40772  8.80%  26.3    5s
H 1352   499                       0.4470092    0.40870  8.57%  26.0    5s
  3225   914    0.42885   13   33    0.44701    0.41731  6.64%  22.2   10s
  3795   968    0.42484   22   21    0.44701    0.41731  6.64%  25.1   15s
  4523   822    0.43063   26   16    0.44701    0.41731  6.64%  25.6   20s
H 4781   712                       0.4470092    0.41731  6.64%  25.7   21s
  5474   580    0.43906   22   21    0.44701    0.41747  6.61%  25.9   25s
* 6058   525              35       0.4470092    0.41983  6.08%  25.8   29s
  6296   535    0.43577   25   19    0.44701    0.42103  5.81%  25.9   30s
  7199   589    0.44382   31    6    0.44701    0.42393  5.16%  25.7   35s
  7898   608     cutoff   24         0.44701    0.42631  4.63%  25.8   40s
  9119   614    0.44220   27   10    0.44701    0.42951  3.91%  25.6   45s
  9873   581    0.44274   27   10    0.44701    0.43122  3.53%  25.6   50s
 11332   461     cutoff   27         0.44701    0.43410  2.89%  25.4   55s
 14082     3     cutoff   28         0.44701    0.44110  1.32%  24.3   60s

Cutting planes:
  Implied bound: 301
  MIR: 99
  Flow cover: 366
  RLT: 36
  Relax-and-lift: 104

Explored 14495 nodes (351306 simplex iterations) in 60.18 seconds (46.41 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.447009 0.447009 0.447041 ... 0.457193

Optimal solution found (tolerance 1.00e-04)
Best objective 4.470091745698e-01, best bound 4.470091745698e-01, gap 0.0000%
The objective bound is 0.447009 while the objective upper bound is 0.447009

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.80 (ave)

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