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 3.2003 seconds.
    local lower bound updated to 0.277286
    local upper bound updated to 0.53658

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.957536 seconds.
    local lower bound updated to 0.527488
    local upper bound updated to 0.527488
The Primal step takes 4.16104 (S)
lower bound updated to 0.527488

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.610289
    local lower bound updated to 0.594952

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.610289
    local lower bound updated to 0.608471

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.608471
    local lower bound updated to 0.608471
The Dual step takes 0.0814645 (S)
upper bound updated to 0.608471
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.703016 seconds.
    local lower bound updated to 0.353463
    local upper bound updated to 0.557915

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.52067 seconds.
    local lower bound updated to 0.529229
    local upper bound updated to 0.536142

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.13445 seconds.
    local lower bound updated to 0.535814
    local upper bound updated to 0.535994

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.60908 seconds.
    local lower bound updated to 0.535994
    local upper bound updated to 0.535994
The Primal step takes 8.97357 (S)
lower bound updated to 0.535994

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.574911
    local lower bound updated to 0.559308

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.569944
    local lower bound updated to 0.559308

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.565342
    local lower bound updated to 0.559308

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.565237
    local lower bound updated to 0.560089

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.560089
    local lower bound updated to 0.560089
The Dual step takes 0.678099 (S)
upper bound updated to 0.560089
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.2563 seconds.
    local lower bound updated to 0.449827
    local upper bound updated to 0.560089

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.665377 seconds.
    local lower bound updated to 0.505784
    local upper bound updated to 0.558326

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.75168 seconds.
    local lower bound updated to 0.505784
    local upper bound updated to 0.553932

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.6999 seconds.
    local lower bound updated to 0.538778
    local upper bound updated to 0.550865

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 13.0477 seconds.
    local lower bound updated to 0.54402
    local upper bound updated to 0.54965

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 17.9784 seconds.
    local lower bound updated to 0.545809
    local upper bound updated to 0.549041

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 19.747 seconds.
    local lower bound updated to 0.54725
    local upper bound updated to 0.548631

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 15.1348 seconds.
    local lower bound updated to 0.547372
    local upper bound updated to 0.548337

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 16.7061 seconds.
    local lower bound updated to 0.547372
    local upper bound updated to 0.548124

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 20.6541 seconds.
    local lower bound updated to 0.548124
    local upper bound updated to 0.548124
The Primal step takes 128.67 (S)
lower bound updated to 0.548124

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.564623
    local lower bound updated to 0.549325

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.559831
    local lower bound updated to 0.552167

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.559831
    local lower bound updated to 0.553378

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.554731
    local lower bound updated to 0.553423

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.553682
    local lower bound updated to 0.553466

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.553467
    local lower bound updated to 0.553466
The Dual step takes 1.56933 (S)
upper bound updated to 0.553467
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 41.1099 seconds.
    local lower bound updated to 0.485382
    local upper bound updated to 0.553065

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 40.2462 seconds.
    local lower bound updated to 0.54776
    local upper bound updated to 0.55283

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 35.2911 seconds.
    local lower bound updated to 0.549416
    local upper bound updated to 0.552217

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 29.5822 seconds.
    local lower bound updated to 0.549416
    local upper bound updated to 0.5519

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.8394 seconds.
    local lower bound updated to 0.549416
    local upper bound updated to 0.551697

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 25.0832 seconds.
    local lower bound updated to 0.54947
    local upper bound updated to 0.551394

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 34.5552 seconds.
    local lower bound updated to 0.550024
    local upper bound updated to 0.551272

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 34.2266 seconds.
    local lower bound updated to 0.550024
    local upper bound updated to 0.551106

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 38.9741 seconds.
    local lower bound updated to 0.550024
    local upper bound updated to 0.55078

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 40.8224 seconds.
    local lower bound updated to 0.550024
    local upper bound updated to 0.550758

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 37.1136 seconds.
    local lower bound updated to 0.550024
    local upper bound updated to 0.550702

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 40.5668 seconds.
    local lower bound updated to 0.550268
    local upper bound updated to 0.550701

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 45.5103 seconds.
    local lower bound updated to 0.550486
    local upper bound updated to 0.550697

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 40.6008 seconds.
    local lower bound updated to 0.550525
    local upper bound updated to 0.550695

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 43.0864 seconds.
    local lower bound updated to 0.550615
    local upper bound updated to 0.550694

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.0194 seconds.
    local lower bound updated to 0.550615
    local upper bound updated to 0.550685

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 47.0304 seconds.
    local lower bound updated to 0.550685
    local upper bound updated to 0.550685
The Primal step takes 646.745 (S)
lower bound updated to 0.550685

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.557842
    local lower bound updated to 0.550685

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.557842
    local lower bound updated to 0.550736

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.55178
    local lower bound updated to 0.550842

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.55178
    local lower bound updated to 0.550844

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.550844
    local lower bound updated to 0.550844
The Dual step takes 8.56119 (S)
upper bound updated to 0.550844
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0218 seconds.
    local lower bound updated to 0.496755
    local upper bound updated to 0.550844

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0204 seconds.
    local lower bound updated to 0.549733
    local upper bound updated to 0.550823

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 56.9929 seconds.
    local lower bound updated to 0.55028
    local upper bound updated to 0.550814

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0212 seconds.
    local lower bound updated to 0.550689
    local upper bound updated to 0.550812

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0209 seconds.
    local lower bound updated to 0.550689
    local upper bound updated to 0.550805

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0174 seconds.
    local lower bound updated to 0.55076
    local upper bound updated to 0.550802

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0154 seconds.
    local lower bound updated to 0.550791
    local upper bound updated to 0.550801
The Primal step takes 417.152 (S)
lower bound updated to 0.550791

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.557668
    local lower bound updated to 0.550801

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.552192
    local lower bound updated to 0.550802

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.550802
    local lower bound updated to 0.550802
The Dual step takes 9.61303 (S)
upper bound updated to 0.550802
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.021 seconds.
    local lower bound updated to 0.494742
    local upper bound updated to 0.550802

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0202 seconds.
    local lower bound updated to 0.550791
    local upper bound updated to 0.550801

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 46.9569 seconds.
    local lower bound updated to 0.550801
    local upper bound updated to 0.550801
The Primal step takes 167.02 (S)
lower bound updated to 0.550801

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.556152
    local lower bound updated to 0.550801

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.550801
    local lower bound updated to 0.550801
The Dual step takes 6.74545 (S)
upper bound updated to 0.550801
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0311 seconds.
    local lower bound updated to 0.494742
    local upper bound updated to 0.550801

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0276 seconds.
    local lower bound updated to 0.550801
    local upper bound updated to 0.550801
The time obtain the optimal randomized assortment is 1520.05 (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_66316.log"
The computation time limit for a lower bound is 84473
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 128 physical cores, 256 logical processors, using up to 4 threads
Optimize a model with 2800 rows, 2268 columns and 8996 nonzeros
Model fingerprint: 0xf71713c6
Variable types: 2211 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [9e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e-01, 1e+00]
Presolve removed 747 rows and 1376 columns
Presolve time: 0.03s
Presolved: 2053 rows, 892 columns, 7893 nonzeros
Variable types: 837 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6755124
Found heuristic solution: objective 0.6377961
Found heuristic solution: objective 0.6311516

Root relaxation: objective 3.981338e-01, 219 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    0.39813    0   24    0.63115    0.39813  36.9%     -    0s
H    0     0                       0.5811122    0.39813  31.5%     -    0s
H    0     0                       0.5761400    0.42251  26.7%     -    0s
H    0     0                       0.5710092    0.42251  26.0%     -    0s
     0     0    0.42251    0   23    0.57101    0.42251  26.0%     -    0s
     0     0    0.42251    0   23    0.57101    0.42251  26.0%     -    0s
     0     0    0.45086    0   26    0.57101    0.45086  21.0%     -    0s
     0     0    0.45137    0   26    0.57101    0.45137  21.0%     -    0s
     0     0    0.46436    0   27    0.57101    0.46436  18.7%     -    0s
     0     0    0.46526    0   26    0.57101    0.46526  18.5%     -    0s
H    0     0                       0.5524674    0.47546  13.9%     -    0s
     0     0    0.47546    0   26    0.55247    0.47546  13.9%     -    0s
     0     0    0.47645    0   26    0.55247    0.47645  13.8%     -    0s
     0     0    0.47740    0   26    0.55247    0.47740  13.6%     -    0s
H    0     0                       0.5523805    0.47740  13.6%     -    0s
H    0     0                       0.5508010    0.47740  13.3%     -    2s
     0     2    0.47740    0   26    0.55080    0.47740  13.3%     -    2s
   212   116     cutoff   16         0.55080    0.48471  12.0%  36.0    5s
  2271   655     cutoff   13         0.55080    0.50823  7.73%  26.3   10s
  3973   956     cutoff   14         0.55080    0.51300  6.86%  25.6   15s
  4991   985    0.53965   24   10    0.55080    0.51324  6.82%  27.6   20s
  6571   716    0.53667   26   12    0.55080    0.51617  6.29%  29.2   25s
  7854   703     cutoff   27         0.55080    0.52097  5.42%  29.6   30s
  9661   779     cutoff   27         0.55080    0.52563  4.57%  29.9   35s
 10700   772     cutoff   29         0.55080    0.52744  4.24%  29.9   40s
 13104   547 infeasible   29         0.55080    0.53270  3.29%  29.6   45s
 14764   245     cutoff   24         0.55080    0.53639  2.62%  29.3   50s

Cutting planes:
  Implied bound: 249
  MIR: 174
  Flow cover: 429
  RLT: 66
  Relax-and-lift: 82

Explored 16118 nodes (465280 simplex iterations) in 52.77 seconds (40.06 work units)
Thread count was 4 (of 256 available processors)

Solution count 9: 0.550801 0.55238 0.552467 ... 0.675512

Optimal solution found (tolerance 1.00e-04)
Best objective 5.508010496675e-01, best bound 5.508010496675e-01, gap 0.0000%
The objective bound is 0.550801 while the objective upper bound is 0.550801

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.68 (ave)

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