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 0.701221 seconds.
    local lower bound updated to 0.288939
    local upper bound updated to 0.494795

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.71627 seconds.
    local lower bound updated to 0.494795
    local upper bound updated to 0.494795
The Primal step takes 1.4203 (S)
lower bound updated to 0.494795

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.645299
    local lower bound updated to 0.645258

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.645258
    local lower bound updated to 0.645258
The Dual step takes 0.0193447 (S)
upper bound updated to 0.645258
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.679211 seconds.
    local lower bound updated to 0.332415
    local upper bound updated to 0.524868

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.09269 seconds.
    local lower bound updated to 0.511724
    local upper bound updated to 0.514477

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.68956 seconds.
    local lower bound updated to 0.511724
    local upper bound updated to 0.512218

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.99209 seconds.
    local lower bound updated to 0.512218
    local upper bound updated to 0.512218
The Primal step takes 7.46102 (S)
lower bound updated to 0.512218

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.568258
    local lower bound updated to 0.530219

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.562821
    local lower bound updated to 0.538436

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.557901
    local lower bound updated to 0.546374

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.554444
    local lower bound updated to 0.549368

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.554444
    local lower bound updated to 0.550117

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.551663
    local lower bound updated to 0.550669

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.550669
    local lower bound updated to 0.550669
The Dual step takes 0.868356 (S)
upper bound updated to 0.550669
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.40984 seconds.
    local lower bound updated to 0.422545
    local upper bound updated to 0.521913

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.23469 seconds.
    local lower bound updated to 0.498394
    local upper bound updated to 0.514614

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.93328 seconds.
    local lower bound updated to 0.5116
    local upper bound updated to 0.513985

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 15.3819 seconds.
    local lower bound updated to 0.5116
    local upper bound updated to 0.513468

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.0441 seconds.
    local lower bound updated to 0.512824
    local upper bound updated to 0.513305

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 12.0149 seconds.
    local lower bound updated to 0.513096
    local upper bound updated to 0.513242

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 12.119 seconds.
    local lower bound updated to 0.513242
    local upper bound updated to 0.513242
The Primal step takes 69.1652 (S)
lower bound updated to 0.513242

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.535866
    local lower bound updated to 0.513242

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.531518
    local lower bound updated to 0.518053

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.531518
    local lower bound updated to 0.518756

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.526802
    local lower bound updated to 0.519967

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.524404
    local lower bound updated to 0.520294

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.524404
    local lower bound updated to 0.521485

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.521485
    local lower bound updated to 0.521485
The Dual step takes 3.3338 (S)
upper bound updated to 0.521485
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 8.82662 seconds.
    local lower bound updated to 0.443335
    local upper bound updated to 0.52027

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.67871 seconds.
    local lower bound updated to 0.473848
    local upper bound updated to 0.518787

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 29.0288 seconds.
    local lower bound updated to 0.497109
    local upper bound updated to 0.517409

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 47.8371 seconds.
    local lower bound updated to 0.500873
    local upper bound updated to 0.517084

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 42.7411 seconds.
    local lower bound updated to 0.509593
    local upper bound updated to 0.516364

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 42.0256 seconds.
    local lower bound updated to 0.512858
    local upper bound updated to 0.515786

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 33.2343 seconds.
    local lower bound updated to 0.514027
    local upper bound updated to 0.51558

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 36.1875 seconds.
    local lower bound updated to 0.514133
    local upper bound updated to 0.514857

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 32.6563 seconds.
    local lower bound updated to 0.514635
    local upper bound updated to 0.514804

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 41.764 seconds.
    local lower bound updated to 0.514804
    local upper bound updated to 0.514804
The Primal step takes 321.04 (S)
lower bound updated to 0.514804

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.529114
    local lower bound updated to 0.515972

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518069
    local lower bound updated to 0.516153

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.516153
    local lower bound updated to 0.516153
The Dual step takes 4.44966 (S)
upper bound updated to 0.516153
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 14.1047 seconds.
    local lower bound updated to 0.446888
    local upper bound updated to 0.516153

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 56.0881 seconds.
    local lower bound updated to 0.51474
    local upper bound updated to 0.516011

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 61.0808 seconds.
    local lower bound updated to 0.515669
    local upper bound updated to 0.515967

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 63.2955 seconds.
    local lower bound updated to 0.515669
    local upper bound updated to 0.51596

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 68.147 seconds.
    local lower bound updated to 0.515669
    local upper bound updated to 0.515958

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.7346 seconds.
    local lower bound updated to 0.515743
    local upper bound updated to 0.515889

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 63.2291 seconds.
    local lower bound updated to 0.515772
    local upper bound updated to 0.515884

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 67.8517 seconds.
    local lower bound updated to 0.515785
    local upper bound updated to 0.51587

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 63.4762 seconds.
    local lower bound updated to 0.51587
    local upper bound updated to 0.51587
The Primal step takes 518.069 (S)
lower bound updated to 0.51587

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.529069
    local lower bound updated to 0.51587

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.51587
    local lower bound updated to 0.51587
The Dual step takes 5.60941 (S)
upper bound updated to 0.51587
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.4804 seconds.
    local lower bound updated to 0.446888
    local upper bound updated to 0.51587

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 51.0782 seconds.
    local lower bound updated to 0.51587
    local upper bound updated to 0.51587
The time obtain the optimal randomized assortment is 996.008 (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_100.000000_105816.log"
The computation time limit for a lower bound is 84996
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 2640 rows, 2138 columns and 8463 nonzeros
Model fingerprint: 0xf2680703
Variable types: 2081 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        [6e-01, 1e+00]
Presolve removed 721 rows and 1303 columns
Presolve time: 0.02s
Presolved: 1919 rows, 835 columns, 7379 nonzeros
Variable types: 779 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.6692847
Found heuristic solution: objective 0.6394861
Found heuristic solution: objective 0.5676979

Root relaxation: objective 2.615943e-01, 215 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    0.26159    0   16    0.56770    0.26159  53.9%     -    0s
H    0     0                       0.5572204    0.26159  53.1%     -    0s
H    0     0                       0.5530806    0.28600  48.3%     -    0s
H    0     0                       0.5301029    0.28600  46.0%     -    0s
     0     0    0.31531    0   24    0.53010    0.31531  40.5%     -    0s
     0     0    0.31775    0   24    0.53010    0.31775  40.1%     -    0s
     0     0    0.35219    0   25    0.53010    0.35219  33.6%     -    0s
     0     0    0.35220    0   25    0.53010    0.35220  33.6%     -    0s
     0     0    0.36948    0   24    0.53010    0.36948  30.3%     -    0s
     0     0    0.37562    0   24    0.53010    0.37562  29.1%     -    0s
     0     0    0.38805    0   25    0.53010    0.38805  26.8%     -    0s
     0     0    0.38869    0   26    0.53010    0.38869  26.7%     -    0s
     0     0    0.39040    0   25    0.53010    0.39040  26.4%     -    0s
H    0     0                       0.5226429    0.39040  25.3%     -    1s
     0     2    0.39040    0   25    0.52264    0.39040  25.3%     -    1s
H  203   136                       0.5163334    0.41181  20.2%  40.2    3s
H  301   183                       0.5163334    0.41181  20.2%  35.8    3s
H  403   231                       0.5158699    0.41734  19.1%  36.2    3s
   597   299     cutoff   16         0.51587    0.42860  16.9%  34.3    5s
  2060   714    0.48959   12   12    0.51587    0.44347  14.0%  26.4   10s
  4109  1059    0.47508   13   25    0.51587    0.45278  12.2%  24.4   15s
H 4445  1102                       0.5158699    0.45278  12.2%  26.7   19s
  4659  1069 infeasible   25         0.51587    0.45278  12.2%  27.5   20s
H 5100   988                       0.5158699    0.45278  12.2%  28.3   24s
  5338   942     cutoff   27         0.51587    0.45407  12.0%  28.8   25s
  6074   804    0.51115   30   10    0.51587    0.45968  10.9%  29.6   30s
  6834   686     cutoff   25         0.51587    0.46348  10.2%  30.2   35s
  8611   766     cutoff   30         0.51587    0.47225  8.46%  30.2   40s
 10394   829    0.51261   27   10    0.51587    0.47778  7.38%  29.9   45s
 11891   864    0.51101   30   10    0.51587    0.48098  6.76%  29.5   51s
 13743   868     cutoff   29         0.51587    0.48574  5.84%  29.3   55s
 15602   798    0.49730   31   12    0.51587    0.48993  5.03%  28.9   60s
 17378   585     cutoff   28         0.51587    0.49525  4.00%  28.5   65s
 19571   105     cutoff   25         0.51587    0.50702  1.72%  27.9   70s

Cutting planes:
  Implied bound: 249
  MIR: 139
  Flow cover: 389
  RLT: 72
  Relax-and-lift: 101

Explored 19924 nodes (552942 simplex iterations) in 70.62 seconds (55.53 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.51587 0.516333 0.522643 ... 0.669285

Optimal solution found (tolerance 1.00e-04)
Best objective 5.158698547077e-01, best bound 5.158698547077e-01, gap 0.0000%
The objective bound is 0.51587 while the objective upper bound is 0.51587

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.30 (ave)

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