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 0.249033 seconds.
    local lower bound updated to 0.273331
    local upper bound updated to 0.545583

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.524575 seconds.
    local lower bound updated to 0.541809
    local upper bound updated to 0.541809
The Primal step takes 0.776436 (S)
lower bound updated to 0.541809

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.645224
    local lower bound updated to 0.645074

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.645224
    local lower bound updated to 0.645172

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.645172
    local lower bound updated to 0.645172
The Dual step takes 0.113128 (S)
upper bound updated to 0.645172
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.27705 seconds.
    local lower bound updated to 0.403007
    local upper bound updated to 0.574335

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.314257 seconds.
    local lower bound updated to 0.454793
    local upper bound updated to 0.557791

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.15149 seconds.
    local lower bound updated to 0.541707
    local upper bound updated to 0.542541

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.04196 seconds.
    local lower bound updated to 0.541956
    local upper bound updated to 0.542462

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.05339 seconds.
    local lower bound updated to 0.542462
    local upper bound updated to 0.542462
The Primal step takes 10.8499 (S)
lower bound updated to 0.542462

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.616406
    local lower bound updated to 0.591341

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.616406
    local lower bound updated to 0.592876

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.593929
    local lower bound updated to 0.593538

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.593929
    local lower bound updated to 0.593854

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.593854
    local lower bound updated to 0.593854
The Dual step takes 0.585322 (S)
upper bound updated to 0.593854
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.72191 seconds.
    local lower bound updated to 0.436951
    local upper bound updated to 0.561895

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 12.5285 seconds.
    local lower bound updated to 0.54032
    local upper bound updated to 0.555765

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 31.1862 seconds.
    local lower bound updated to 0.54032
    local upper bound updated to 0.555085

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.8057 seconds.
    local lower bound updated to 0.54032
    local upper bound updated to 0.553078

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 44.5393 seconds.
    local lower bound updated to 0.54309
    local upper bound updated to 0.550831

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 15.2375 seconds.
    local lower bound updated to 0.548758
    local upper bound updated to 0.550242

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 24.0614 seconds.
    local lower bound updated to 0.549319
    local upper bound updated to 0.549903

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 25.3917 seconds.
    local lower bound updated to 0.549319
    local upper bound updated to 0.549892

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 20.7254 seconds.
    local lower bound updated to 0.549578
    local upper bound updated to 0.549856

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 18.1198 seconds.
    local lower bound updated to 0.549578
    local upper bound updated to 0.549822

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 21.4967 seconds.
    local lower bound updated to 0.549802
    local upper bound updated to 0.549817

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 24.8744 seconds.
    local lower bound updated to 0.549817
    local upper bound updated to 0.549817
The Primal step takes 258.739 (S)
lower bound updated to 0.549817

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.58043
    local lower bound updated to 0.55127

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.572171
    local lower bound updated to 0.554875

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.572171
    local lower bound updated to 0.559436

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.569946
    local lower bound updated to 0.563723

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.568891
    local lower bound updated to 0.564474

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.567604
    local lower bound updated to 0.564574

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.564883
    local lower bound updated to 0.564581

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.564581
    local lower bound updated to 0.564581
The Dual step takes 4.26616 (S)
upper bound updated to 0.564581
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0236 seconds.
    local lower bound updated to 0.496127
    local upper bound updated to 0.564581

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 32.9626 seconds.
    local lower bound updated to 0.549901
    local upper bound updated to 0.562318

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.48825 seconds.
    local lower bound updated to 0.549901
    local upper bound updated to 0.559956

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0266 seconds.
    local lower bound updated to 0.554741
    local upper bound updated to 0.558935

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 36.0191 seconds.
    local lower bound updated to 0.554741
    local upper bound updated to 0.557926

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 20.847 seconds.
    local lower bound updated to 0.555434
    local upper bound updated to 0.557749

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 33.3079 seconds.
    local lower bound updated to 0.555434
    local upper bound updated to 0.557616

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0179 seconds.
    local lower bound updated to 0.556325
    local upper bound updated to 0.557358

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0255 seconds.
    local lower bound updated to 0.556765
    local upper bound updated to 0.557321

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0205 seconds.
    local lower bound updated to 0.556765
    local upper bound updated to 0.557271

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0373 seconds.
    local lower bound updated to 0.557133
    local upper bound updated to 0.557246

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0309 seconds.
    local lower bound updated to 0.557133
    local upper bound updated to 0.557244

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0193 seconds.
    local lower bound updated to 0.557133
    local upper bound updated to 0.557236

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0191 seconds.
    local lower bound updated to 0.557236
    local upper bound updated to 0.557236
The Primal step takes 671.956 (S)
lower bound updated to 0.557236

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.570987
    local lower bound updated to 0.557256

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.560676
    local lower bound updated to 0.557357

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.560381
    local lower bound updated to 0.557602

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.560381
    local lower bound updated to 0.557675

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.557675
    local lower bound updated to 0.557675
The Dual step takes 20.0971 (S)
upper bound updated to 0.557675
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0285 seconds.
    local lower bound updated to 0.514509
    local upper bound updated to 0.557675

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0326 seconds.
    local lower bound updated to 0.556865
    local upper bound updated to 0.557556

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0299 seconds.
    local lower bound updated to 0.557544
    local upper bound updated to 0.557555

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0336 seconds.
    local lower bound updated to 0.557544
    local upper bound updated to 0.557553
The Primal step takes 240.159 (S)
lower bound updated to 0.557544

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.569628
    local lower bound updated to 0.557553

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.558074
    local lower bound updated to 0.557553

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.557553
    local lower bound updated to 0.557553
The Dual step takes 13.693 (S)
upper bound updated to 0.557553
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0281 seconds.
    local lower bound updated to 0.515286
    local upper bound updated to 0.557553

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0244 seconds.
    local lower bound updated to 0.557553
    local upper bound updated to 0.557553
The time obtain the optimal randomized assortment is 1341.31 (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_60.000000_65416.log"
The computation time limit for a lower bound is 84655
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 3280 rows, 2658 columns and 10551 nonzeros
Model fingerprint: 0xdf0d8b6a
Variable types: 2601 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 894 rows and 1628 columns
Presolve time: 0.04s
Presolved: 2386 rows, 1030 columns, 9268 nonzeros
Variable types: 975 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6396646
Found heuristic solution: objective 0.6265335
Found heuristic solution: objective 0.6063461
Found heuristic solution: objective 0.5880603

Root relaxation: objective 4.675298e-01, 270 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    0.46753    0   24    0.58806    0.46753  20.5%     -    0s
     0     0    0.47555    0   22    0.58806    0.47555  19.1%     -    0s
     0     0    0.49730    0   25    0.58806    0.49730  15.4%     -    0s
H    0     0                       0.5618162    0.49730  11.5%     -    0s
H    0     0                       0.5596813    0.49731  11.1%     -    0s
     0     0    0.49731    0   25    0.55968    0.49731  11.1%     -    0s
     0     0    0.50511    0   24    0.55968    0.50511  9.75%     -    0s
     0     0    0.50617    0   23    0.55968    0.50617  9.56%     -    0s
     0     0    0.50839    0   22    0.55968    0.50839  9.16%     -    1s
     0     0    0.50864    0   23    0.55968    0.50864  9.12%     -    1s
     0     0    0.50964    0   23    0.55968    0.50964  8.94%     -    1s
H    0     0                       0.5575526    0.50964  8.59%     -    3s
     0     2    0.50964    0   23    0.55755    0.50964  8.59%     -    3s
   405   207    0.53580    8   12    0.55755    0.51965  6.80%  45.5    5s
H  420   207                       0.5575526    0.51965  6.80%  45.5    5s
   798   331    0.55430   11    8    0.55755    0.52469  5.89%  42.2   11s
  1521   539    0.55537   13    6    0.55755    0.52774  5.35%  40.7   15s
  1956   740    0.55184   19    8    0.55755    0.52837  5.23%  38.6   20s
  2119   749    0.53668   11   23    0.55755    0.52842  5.22%  38.0   25s
H 2428   745                       0.5575526    0.52842  5.22%  41.0   26s
H 2548   715                       0.5575526    0.52842  5.22%  41.2   26s
  3498   605    0.55458   25   12    0.55755    0.53403  4.22%  40.5   31s
  4484   541    0.53809   23   18    0.55755    0.53650  3.78%  38.8   36s
  5786   661    0.55040   27   12    0.55755    0.53909  3.31%  38.2   40s
  5964   674     cutoff   32         0.55755    0.53957  3.23%  38.0   45s
  7136   688    0.55159   27   12    0.55755    0.54140  2.90%  37.3   50s
  8113   710    0.54867   24   14    0.55755    0.54256  2.69%  36.7   56s
  8922   698     cutoff   27         0.55755    0.54342  2.53%  36.5   61s
  9406   684     cutoff   31         0.55755    0.54421  2.39%  36.1   65s
 10806   585    0.55590   27    6    0.55755    0.54578  2.11%  35.5   70s
 12305   422     cutoff   30         0.55755    0.54759  1.79%  34.7   75s

Cutting planes:
  Gomory: 1
  Implied bound: 293
  MIR: 151
  Flow cover: 481
  RLT: 65
  Relax-and-lift: 99

Explored 14793 nodes (495673 simplex iterations) in 79.63 seconds (56.98 work units)
Thread count was 4 (of 40 available processors)

Solution count 8: 0.557553 0.557553 0.559681 ... 0.639665

Optimal solution found (tolerance 1.00e-04)
Best objective 5.575526126911e-01, best bound 5.575526126911e-01, gap 0.0000%
The objective bound is 0.557553 while the objective upper bound is 0.557553

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.43 (ave)

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