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 0.0909034 seconds.
    local lower bound updated to 0.263381
    local upper bound updated to 0.429354

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.102793 seconds.
    local lower bound updated to 0.429354
    local upper bound updated to 0.429354
The Primal step takes 0.196015 (S)
lower bound updated to 0.429354

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.596477
    local lower bound updated to 0.596477
The Dual step takes 0.0115032 (S)
upper bound updated to 0.596477
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.228522 seconds.
    local lower bound updated to 0.303021
    local upper bound updated to 0.440614

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.277886 seconds.
    local lower bound updated to 0.431075
    local upper bound updated to 0.432027

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.514092 seconds.
    local lower bound updated to 0.431075
    local upper bound updated to 0.431791

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.381444 seconds.
    local lower bound updated to 0.431075
    local upper bound updated to 0.431577

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.384882 seconds.
    local lower bound updated to 0.431577
    local upper bound updated to 0.431577
The Primal step takes 1.79344 (S)
lower bound updated to 0.431577

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.491642
    local lower bound updated to 0.461841

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.471685
    local lower bound updated to 0.4654

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.470391
    local lower bound updated to 0.470391
The Dual step takes 0.124622 (S)
upper bound updated to 0.470391
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.587044 seconds.
    local lower bound updated to 0.353862
    local upper bound updated to 0.442857

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.618269 seconds.
    local lower bound updated to 0.438536
    local upper bound updated to 0.441328

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.647218 seconds.
    local lower bound updated to 0.438536
    local upper bound updated to 0.440766

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.656027 seconds.
    local lower bound updated to 0.438536
    local upper bound updated to 0.440326

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.363209 seconds.
    local lower bound updated to 0.438794
    local upper bound updated to 0.439716

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.633562 seconds.
    local lower bound updated to 0.439407
    local upper bound updated to 0.439691

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.537938 seconds.
    local lower bound updated to 0.439623
    local upper bound updated to 0.439671

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 0.477824 seconds.
    local lower bound updated to 0.439629
    local upper bound updated to 0.439665

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 0.474038 seconds.
    local lower bound updated to 0.439665
    local upper bound updated to 0.439665
The Primal step takes 5.01609 (S)
lower bound updated to 0.439665

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.461548
    local lower bound updated to 0.439669

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.457669
    local lower bound updated to 0.441152

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.44968
    local lower bound updated to 0.445663

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.448009
    local lower bound updated to 0.446273

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.446273
    local lower bound updated to 0.446273
The Dual step takes 1.8155 (S)
upper bound updated to 0.446273
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.11425 seconds.
    local lower bound updated to 0.386535
    local upper bound updated to 0.446273

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.582641 seconds.
    local lower bound updated to 0.413873
    local upper bound updated to 0.44477

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.46398 seconds.
    local lower bound updated to 0.438497
    local upper bound updated to 0.444239

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.59427 seconds.
    local lower bound updated to 0.438497
    local upper bound updated to 0.444001

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.6239 seconds.
    local lower bound updated to 0.440946
    local upper bound updated to 0.443758

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.71983 seconds.
    local lower bound updated to 0.440946
    local upper bound updated to 0.443407

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 1.32326 seconds.
    local lower bound updated to 0.441488
    local upper bound updated to 0.443328

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 2.94404 seconds.
    local lower bound updated to 0.441661
    local upper bound updated to 0.443256

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 2.25959 seconds.
    local lower bound updated to 0.441661
    local upper bound updated to 0.442828

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 3.66128 seconds.
    local lower bound updated to 0.441661
    local upper bound updated to 0.442799

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 2.10529 seconds.
    local lower bound updated to 0.441661
    local upper bound updated to 0.442771

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 2.70855 seconds.
    local lower bound updated to 0.442344
    local upper bound updated to 0.442755

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 3.09196 seconds.
    local lower bound updated to 0.442597
    local upper bound updated to 0.442738

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 2.32246 seconds.
    local lower bound updated to 0.442738
    local upper bound updated to 0.442738
The Primal step takes 30.5647 (S)
lower bound updated to 0.442738

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.476712
    local lower bound updated to 0.442738

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.450014
    local lower bound updated to 0.444025

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.444025
    local lower bound updated to 0.444025
The Dual step takes 4.91325 (S)
upper bound updated to 0.444025
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.5858 seconds.
    local lower bound updated to 0.39185
    local upper bound updated to 0.444025

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.79596 seconds.
    local lower bound updated to 0.440306
    local upper bound updated to 0.443941

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.1291 seconds.
    local lower bound updated to 0.44238
    local upper bound updated to 0.443838

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.15861 seconds.
    local lower bound updated to 0.442612
    local upper bound updated to 0.443779

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.58916 seconds.
    local lower bound updated to 0.44277
    local upper bound updated to 0.443686

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.47146 seconds.
    local lower bound updated to 0.443
    local upper bound updated to 0.443679

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 5.53372 seconds.
    local lower bound updated to 0.443027
    local upper bound updated to 0.443655

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.03918 seconds.
    local lower bound updated to 0.443027
    local upper bound updated to 0.44357

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 6.9228 seconds.
    local lower bound updated to 0.443157
    local upper bound updated to 0.443556

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 6.48287 seconds.
    local lower bound updated to 0.44339
    local upper bound updated to 0.443547

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 6.6285 seconds.
    local lower bound updated to 0.443413
    local upper bound updated to 0.443515

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 6.47815 seconds.
    local lower bound updated to 0.443467
    local upper bound updated to 0.443515

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 5.99922 seconds.
    local lower bound updated to 0.443467
    local upper bound updated to 0.443513

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 6.02491 seconds.
    local lower bound updated to 0.443467
    local upper bound updated to 0.443513

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 7.29271 seconds.
    local lower bound updated to 0.443513
    local upper bound updated to 0.443513
The Primal step takes 91.197 (S)
lower bound updated to 0.443513

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.48265
    local lower bound updated to 0.443513

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.448892
    local lower bound updated to 0.44356

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.44497
    local lower bound updated to 0.443621

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.444354
    local lower bound updated to 0.443621

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.443621
    local lower bound updated to 0.443621
The Dual step takes 14.6703 (S)
upper bound updated to 0.443621
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.30478 seconds.
    local lower bound updated to 0.400061
    local upper bound updated to 0.443621

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 7.74354 seconds.
    local lower bound updated to 0.442905
    local upper bound updated to 0.443591

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.40472 seconds.
    local lower bound updated to 0.443435
    local upper bound updated to 0.443583

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.45127 seconds.
    local lower bound updated to 0.443435
    local upper bound updated to 0.443572

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.1647 seconds.
    local lower bound updated to 0.443435
    local upper bound updated to 0.443569

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.36248 seconds.
    local lower bound updated to 0.443516
    local upper bound updated to 0.443566

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 7.9738 seconds.
    local lower bound updated to 0.443566
    local upper bound updated to 0.443566
The Primal step takes 54.4412 (S)
lower bound updated to 0.443566

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.484518
    local lower bound updated to 0.443566

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.44794
    local lower bound updated to 0.443566

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.447471
    local lower bound updated to 0.443566

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.445081
    local lower bound updated to 0.443566

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.443566
    local lower bound updated to 0.443566
The Dual step takes 14.7171 (S)
upper bound updated to 0.443566
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.87683 seconds.
    local lower bound updated to 0.397645
    local upper bound updated to 0.443566

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.4446 seconds.
    local lower bound updated to 0.443566
    local upper bound updated to 0.443566
The time obtain the optimal randomized assortment is 233.793 (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_13_4_100.000000_105914.log"
The computation time limit for a lower bound is 85764
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 2220 rows, 1954 columns and 6915 nonzeros
Model fingerprint: 0x85275dca
Variable types: 1905 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [3e-09, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 716 rows and 1312 columns
Presolve time: 0.02s
Presolved: 1504 rows, 642 columns, 5689 nonzeros
Variable types: 595 continuous, 47 integer (47 binary)
Found heuristic solution: objective 0.5028104
Found heuristic solution: objective 0.4645046

Root relaxation: objective 3.721590e-01, 187 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    0.37216    0   21    0.46450    0.37216  19.9%     -    0s
H    0     0                       0.4599317    0.37216  19.1%     -    0s
     0     0    0.38022    0   20    0.45993    0.38022  17.3%     -    0s
     0     0    0.38041    0   20    0.45993    0.38041  17.3%     -    0s
H    0     0                       0.4546403    0.38041  16.3%     -    0s
     0     0    0.40168    0   20    0.45464    0.40168  11.6%     -    0s
H    0     0                       0.4543185    0.40168  11.6%     -    0s
     0     0    0.40211    0   20    0.45432    0.40211  11.5%     -    0s
H    0     0                       0.4471197    0.40524  9.37%     -    0s
     0     0    0.40524    0   20    0.44712    0.40524  9.37%     -    0s
H    0     0                       0.4463821    0.40524  9.22%     -    0s
     0     0    0.40555    0   20    0.44638    0.40555  9.15%     -    0s
     0     0    0.40737    0   21    0.44638    0.40737  8.74%     -    0s
     0     0    0.40768    0   20    0.44638    0.40768  8.67%     -    0s
H    0     0                       0.4458354    0.40768  8.56%     -    0s
H    0     0                       0.4441215    0.40768  8.21%     -    0s
     0     0    0.40830    0   20    0.44412    0.40830  8.07%     -    0s
H    0     0                       0.4435659    0.40830  7.95%     -    1s
     0     2    0.40830    0   20    0.44357    0.40830  7.95%     -    1s
H  129    98                       0.4435659    0.41369  6.74%  31.6    1s
H  376   194                       0.4435659    0.42028  5.25%  27.8    2s
H  631   237                       0.4435659    0.42180  4.91%  26.1    3s
H  824   268                       0.4435659    0.42291  4.66%  25.9    3s
  1397   345     cutoff   18         0.44357    0.42754  3.61%  25.4    5s
H 3497   467                       0.4435659    0.43315  2.35%  24.1    9s
  4226   385    0.44118   16    4    0.44357    0.43473  1.99%  23.7   10s
H 5148   253                       0.4435659    0.43673  1.54%  22.9   11s
H 5526   172                       0.4435659    0.43735  1.40%  22.6   11s

Cutting planes:
  Implied bound: 235
  MIR: 69
  Flow cover: 226
  RLT: 10
  Relax-and-lift: 132

Explored 6006 nodes (134528 simplex iterations) in 11.93 seconds (8.77 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.443566 0.443566 0.443566 ... 0.445835

Optimal solution found (tolerance 1.00e-04)
Best objective 4.435659033617e-01, best bound 4.435659033617e-01, gap 0.0000%
The objective bound is 0.443566 while the objective upper bound is 0.443566

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.32 (ave)

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