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 0.337089 seconds.
    local lower bound updated to 0.272248
    local upper bound updated to 0.504494

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.669534 seconds.
    local lower bound updated to 0.479457
    local upper bound updated to 0.479457
The Primal step takes 1.00991 (S)
lower bound updated to 0.479457

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.608567
    local lower bound updated to 0.595118

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.595118
    local lower bound updated to 0.595118
The Dual step takes 0.036851 (S)
upper bound updated to 0.595118
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.60265 seconds.
    local lower bound updated to 0.361407
    local upper bound updated to 0.503704

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.597729 seconds.
    local lower bound updated to 0.474002
    local upper bound updated to 0.485945

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.406913 seconds.
    local lower bound updated to 0.479151
    local upper bound updated to 0.479457

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.321325 seconds.
    local lower bound updated to 0.479457
    local upper bound updated to 0.479457
The Primal step takes 3.9351 (S)
lower bound updated to 0.479457

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.553966
    local lower bound updated to 0.505869

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.533897
    local lower bound updated to 0.519583

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.531433
    local lower bound updated to 0.524324

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.524324
    local lower bound updated to 0.524324
The Dual step takes 0.467689 (S)
upper bound updated to 0.524324
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.94792 seconds.
    local lower bound updated to 0.436982
    local upper bound updated to 0.524324

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.406186 seconds.
    local lower bound updated to 0.462166
    local upper bound updated to 0.520844

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.55271 seconds.
    local lower bound updated to 0.49883
    local upper bound updated to 0.513065

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.19251 seconds.
    local lower bound updated to 0.506467
    local upper bound updated to 0.509167

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.12733 seconds.
    local lower bound updated to 0.506467
    local upper bound updated to 0.508911

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.61165 seconds.
    local lower bound updated to 0.50723
    local upper bound updated to 0.508872

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.15323 seconds.
    local lower bound updated to 0.507933
    local upper bound updated to 0.508866

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 3.21195 seconds.
    local lower bound updated to 0.508349
    local upper bound updated to 0.508859

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 3.4212 seconds.
    local lower bound updated to 0.508349
    local upper bound updated to 0.508817

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 3.9283 seconds.
    local lower bound updated to 0.508577
    local upper bound updated to 0.508779

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 3.30452 seconds.
    local lower bound updated to 0.508779
    local upper bound updated to 0.508779
The Primal step takes 31.8905 (S)
lower bound updated to 0.508779

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.554695
    local lower bound updated to 0.516098

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529139
    local lower bound updated to 0.518156

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.52163
    local lower bound updated to 0.519971

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.52163
    local lower bound updated to 0.520093

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.520093
    local lower bound updated to 0.520093
The Dual step takes 1.17543 (S)
upper bound updated to 0.520093
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.79062 seconds.
    local lower bound updated to 0.456593
    local upper bound updated to 0.515677

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.3008 seconds.
    local lower bound updated to 0.508485
    local upper bound updated to 0.514747

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.63748 seconds.
    local lower bound updated to 0.509594
    local upper bound updated to 0.514117

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.9863 seconds.
    local lower bound updated to 0.509594
    local upper bound updated to 0.513594

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.06039 seconds.
    local lower bound updated to 0.511757
    local upper bound updated to 0.513407

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.93599 seconds.
    local lower bound updated to 0.512366
    local upper bound updated to 0.513376

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 6.25208 seconds.
    local lower bound updated to 0.51257
    local upper bound updated to 0.513337

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.5254 seconds.
    local lower bound updated to 0.513294
    local upper bound updated to 0.513335

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 10.7251 seconds.
    local lower bound updated to 0.513294
    local upper bound updated to 0.513332

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 10.1484 seconds.
    local lower bound updated to 0.513332
    local upper bound updated to 0.513332
The Primal step takes 78.418 (S)
lower bound updated to 0.513332

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.53389
    local lower bound updated to 0.514806

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.517942
    local lower bound updated to 0.515281

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.516806
    local lower bound updated to 0.515462

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.515462
    local lower bound updated to 0.515462
The Dual step takes 3.56338 (S)
upper bound updated to 0.515462
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.1634 seconds.
    local lower bound updated to 0.470105
    local upper bound updated to 0.515191

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 28.5842 seconds.
    local lower bound updated to 0.513137
    local upper bound updated to 0.514875

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 9.17033 seconds.
    local lower bound updated to 0.513137
    local upper bound updated to 0.514672

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.4044 seconds.
    local lower bound updated to 0.513259
    local upper bound updated to 0.514608

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 15.4096 seconds.
    local lower bound updated to 0.513362
    local upper bound updated to 0.514602

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 10.9699 seconds.
    local lower bound updated to 0.513719
    local upper bound updated to 0.51452

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.65801 seconds.
    local lower bound updated to 0.513722
    local upper bound updated to 0.51447

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 14.4286 seconds.
    local lower bound updated to 0.51392
    local upper bound updated to 0.514461

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 9.32303 seconds.
    local lower bound updated to 0.514009
    local upper bound updated to 0.514365

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 15.8661 seconds.
    local lower bound updated to 0.514012
    local upper bound updated to 0.514319

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 13.4374 seconds.
    local lower bound updated to 0.514017
    local upper bound updated to 0.514286

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 16.3737 seconds.
    local lower bound updated to 0.514017
    local upper bound updated to 0.514284

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 24.4 seconds.
    local lower bound updated to 0.514074
    local upper bound updated to 0.514278

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 17.7171 seconds.
    local lower bound updated to 0.514081
    local upper bound updated to 0.514272

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 9.15199 seconds.
    local lower bound updated to 0.514246
    local upper bound updated to 0.51427

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 13.5335 seconds.
    local lower bound updated to 0.51427
    local upper bound updated to 0.51427
The Primal step takes 231.697 (S)
lower bound updated to 0.51427

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.530744
    local lower bound updated to 0.51427

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.519958
    local lower bound updated to 0.514275

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.516883
    local lower bound updated to 0.514525

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.516883
    local lower bound updated to 0.514527

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.514527
    local lower bound updated to 0.514527
The Dual step takes 7.15807 (S)
upper bound updated to 0.514527
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.9023 seconds.
    local lower bound updated to 0.47471
    local upper bound updated to 0.514519

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 9.55409 seconds.
    local lower bound updated to 0.514008
    local upper bound updated to 0.51449

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 13.0812 seconds.
    local lower bound updated to 0.514308
    local upper bound updated to 0.51448

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 14.1983 seconds.
    local lower bound updated to 0.514308
    local upper bound updated to 0.514453

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.7833 seconds.
    local lower bound updated to 0.514335
    local upper bound updated to 0.514444

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 14.4875 seconds.
    local lower bound updated to 0.514444
    local upper bound updated to 0.514444
The Primal step takes 78.0527 (S)
lower bound updated to 0.514444

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.529912
    local lower bound updated to 0.514444

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.51592
    local lower bound updated to 0.514446

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.514446
    local lower bound updated to 0.514446
The Dual step takes 2.33655 (S)
upper bound updated to 0.514446
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.5014 seconds.
    local lower bound updated to 0.475238
    local upper bound updated to 0.514446

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 14.2107 seconds.
    local lower bound updated to 0.514356
    local upper bound updated to 0.514444

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.0985 seconds.
    local lower bound updated to 0.514444
    local upper bound updated to 0.514444
The time obtain the optimal randomized assortment is 482.575 (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_200.000000_202114.log"
The computation time limit for a lower bound is 85515
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 6895 nonzeros
Model fingerprint: 0xa88c3d0e
Variable types: 1905 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [8e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e-01, 1e+00]
Presolve removed 766 rows and 1332 columns
Presolve time: 0.02s
Presolved: 1454 rows, 622 columns, 5542 nonzeros
Variable types: 575 continuous, 47 integer (47 binary)
Found heuristic solution: objective 0.6098245
Found heuristic solution: objective 0.6052106
Found heuristic solution: objective 0.5376099

Root relaxation: objective 3.040674e-01, 232 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    0.30407    0   17    0.53761    0.30407  43.4%     -    0s
H    0     0                       0.5373074    0.33649  37.4%     -    0s
     0     0    0.33649    0   24    0.53731    0.33649  37.4%     -    0s
     0     0    0.33649    0   24    0.53731    0.33649  37.4%     -    0s
     0     0    0.38668    0   23    0.53731    0.38668  28.0%     -    0s
H    0     0                       0.5295638    0.38668  27.0%     -    0s
     0     0    0.38681    0   23    0.52956    0.38681  27.0%     -    0s
H    0     0                       0.5257665    0.40250  23.4%     -    0s
     0     0    0.40250    0   23    0.52577    0.40250  23.4%     -    0s
     0     0    0.40313    0   22    0.52577    0.40313  23.3%     -    0s
     0     0    0.41385    0   23    0.52577    0.41385  21.3%     -    0s
     0     0    0.41414    0   24    0.52577    0.41414  21.2%     -    0s
     0     0    0.41693    0   24    0.52577    0.41693  20.7%     -    0s
H    0     0                       0.5256871    0.41693  20.7%     -    0s
H    0     0                       0.5211906    0.41693  20.0%     -    1s
     0     2    0.41693    0   24    0.52119    0.41693  20.0%     -    1s
H   51    32                       0.5144438    0.43400  15.6%  34.6    2s
  2164   330     cutoff   15         0.51444    0.48163  6.38%  17.8    5s
H 4912   316                       0.5144438    0.49782  3.23%  15.6    9s
  5089   300     cutoff   15         0.51444    0.49811  3.18%  15.5   10s

Cutting planes:
  Implied bound: 206
  MIR: 102
  Flow cover: 196
  RLT: 10
  Relax-and-lift: 87

Explored 6777 nodes (97272 simplex iterations) in 12.50 seconds (7.21 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.514444 0.514444 0.521191 ... 0.609825

Optimal solution found (tolerance 1.00e-04)
Best objective 5.144438272170e-01, best bound 5.144438272170e-01, gap 0.0000%
The objective bound is 0.514444 while the objective upper bound is 0.514444

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.53 (ave)

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