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 0.399413 seconds.
    local lower bound updated to 0.251841
    local upper bound updated to 0.48405

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.679851 seconds.
    local lower bound updated to 0.463588
    local upper bound updated to 0.463588
The Primal step takes 1.08197 (S)
lower bound updated to 0.463588

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.586074
    local lower bound updated to 0.56781

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.570535
    local lower bound updated to 0.570535
The Dual step takes 0.042962 (S)
upper bound updated to 0.570535
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.769003 seconds.
    local lower bound updated to 0.348396
    local upper bound updated to 0.507675

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.38889 seconds.
    local lower bound updated to 0.485931
    local upper bound updated to 0.499357

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.80115 seconds.
    local lower bound updated to 0.485931
    local upper bound updated to 0.489672

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.5473 seconds.
    local lower bound updated to 0.486669
    local upper bound updated to 0.489443

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.52875 seconds.
    local lower bound updated to 0.486828
    local upper bound updated to 0.488285

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.47629 seconds.
    local lower bound updated to 0.486828
    local upper bound updated to 0.487972

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.27481 seconds.
    local lower bound updated to 0.487972
    local upper bound updated to 0.487972
The Primal step takes 15.8011 (S)
lower bound updated to 0.487972

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.548994
    local lower bound updated to 0.520612

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.537874
    local lower bound updated to 0.526764

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.5314
    local lower bound updated to 0.528652

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.5314
    local lower bound updated to 0.529193

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.529193
    local lower bound updated to 0.529193
The Dual step takes 1.09468 (S)
upper bound updated to 0.529193
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.52274 seconds.
    local lower bound updated to 0.409673
    local upper bound updated to 0.494626

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.86569 seconds.
    local lower bound updated to 0.489218
    local upper bound updated to 0.49167

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.01527 seconds.
    local lower bound updated to 0.489218
    local upper bound updated to 0.491467

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.95494 seconds.
    local lower bound updated to 0.490706
    local upper bound updated to 0.491318

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.98869 seconds.
    local lower bound updated to 0.491057
    local upper bound updated to 0.491291

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 6.24562 seconds.
    local lower bound updated to 0.491161
    local upper bound updated to 0.49128

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 3.35759 seconds.
    local lower bound updated to 0.49128
    local upper bound updated to 0.49128
The Primal step takes 27.977 (S)
lower bound updated to 0.49128

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.528434
    local lower bound updated to 0.49128

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.514189
    local lower bound updated to 0.49128

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513753
    local lower bound updated to 0.495219

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.504372
    local lower bound updated to 0.503579

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.504372
    local lower bound updated to 0.503579

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.503579
    local lower bound updated to 0.503579
The Dual step takes 4.93761 (S)
upper bound updated to 0.503579
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.45972 seconds.
    local lower bound updated to 0.433754
    local upper bound updated to 0.503579

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.81168 seconds.
    local lower bound updated to 0.455568
    local upper bound updated to 0.500169

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.626 seconds.
    local lower bound updated to 0.494516
    local upper bound updated to 0.499708

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 18.8025 seconds.
    local lower bound updated to 0.496954
    local upper bound updated to 0.499363

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 20.8857 seconds.
    local lower bound updated to 0.497252
    local upper bound updated to 0.499319

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 12.4514 seconds.
    local lower bound updated to 0.497705
    local upper bound updated to 0.499022

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 7.96505 seconds.
    local lower bound updated to 0.499022
    local upper bound updated to 0.499022
The Primal step takes 79.0384 (S)
lower bound updated to 0.499022

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.525462
    local lower bound updated to 0.499022

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.523118
    local lower bound updated to 0.499081

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.512358
    local lower bound updated to 0.500916

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.500916
    local lower bound updated to 0.500916
The Dual step takes 3.6805 (S)
upper bound updated to 0.500916
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.961 seconds.
    local lower bound updated to 0.441997
    local upper bound updated to 0.500916

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.9056 seconds.
    local lower bound updated to 0.494942
    local upper bound updated to 0.500373

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 18.8639 seconds.
    local lower bound updated to 0.49919
    local upper bound updated to 0.500008

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 21.1409 seconds.
    local lower bound updated to 0.499987
    local upper bound updated to 0.500007

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 21.301 seconds.
    local lower bound updated to 0.500007
    local upper bound updated to 0.500007
The Primal step takes 93.2039 (S)
lower bound updated to 0.500007

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.522176
    local lower bound updated to 0.500007

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.502404
    local lower bound updated to 0.500176

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.500176
    local lower bound updated to 0.500176
The Dual step takes 5.43643 (S)
upper bound updated to 0.500176
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.38482 seconds.
    local lower bound updated to 0.445316
    local upper bound updated to 0.500176

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 30.1007 seconds.
    local lower bound updated to 0.499402
    local upper bound updated to 0.500072

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 23.9776 seconds.
    local lower bound updated to 0.499989
    local upper bound updated to 0.500046

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 19.1739 seconds.
    local lower bound updated to 0.499989
    local upper bound updated to 0.500042

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 19.7958 seconds.
    local lower bound updated to 0.500042
    local upper bound updated to 0.500042
The Primal step takes 102.467 (S)
lower bound updated to 0.500042

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.520229
    local lower bound updated to 0.500042

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.500042
    local lower bound updated to 0.500042
The Dual step takes 4.85754 (S)
upper bound updated to 0.500042
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.23929 seconds.
    local lower bound updated to 0.445316
    local upper bound updated to 0.500042

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 19.7067 seconds.
    local lower bound updated to 0.500042
    local upper bound updated to 0.500042
The time obtain the optimal randomized assortment is 368.578 (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_200.000000_209116.log"
The computation time limit for a lower bound is 85628
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 2480 rows, 2008 columns and 7909 nonzeros
Model fingerprint: 0x7099b441
Variable types: 1951 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        [5e-01, 1e+00]
Presolve removed 632 rows and 1206 columns
Presolve time: 0.02s
Presolved: 1848 rows, 802 columns, 6991 nonzeros
Variable types: 747 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5888680
Found heuristic solution: objective 0.5507583

Root relaxation: objective 3.166896e-01, 223 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    0.31669    0   19    0.55076    0.31669  42.5%     -    0s
H    0     0                       0.5416925    0.31669  41.5%     -    0s
H    0     0                       0.5376316    0.31936  40.6%     -    0s
H    0     0                       0.5362725    0.31936  40.4%     -    0s
H    0     0                       0.5273928    0.31936  39.4%     -    0s
     0     0    0.31936    0   17    0.52739    0.31936  39.4%     -    0s
H    0     0                       0.5261697    0.31936  39.3%     -    0s
H    0     0                       0.5232187    0.31936  39.0%     -    0s
     0     0    0.31936    0   17    0.52322    0.31936  39.0%     -    0s
     0     0    0.38113    0   21    0.52322    0.38113  27.2%     -    0s
H    0     0                       0.5067227    0.38113  24.8%     -    0s
     0     0    0.38219    0   23    0.50672    0.38219  24.6%     -    0s
     0     0    0.39796    0   26    0.50672    0.39796  21.5%     -    0s
     0     0    0.39975    0   26    0.50672    0.39975  21.1%     -    0s
H    0     0                       0.5035672    0.39975  20.6%     -    0s
H    0     0                       0.5027431    0.40594  19.3%     -    0s
     0     0    0.40594    0   26    0.50274    0.40594  19.3%     -    0s
     0     0    0.40644    0   24    0.50274    0.40644  19.2%     -    0s
     0     0    0.40769    0   24    0.50274    0.40769  18.9%     -    0s
H    0     0                       0.5000418    0.40769  18.5%     -    1s
     0     2    0.40769    0   24    0.50004    0.40769  18.5%     -    1s
   511   182    0.48538    9   16    0.50004    0.44119  11.8%  41.5    5s
  2599   368    0.49964   13    8    0.50004    0.46506  7.00%  33.4   10s
  5781   216    0.49802   14    7    0.50004    0.48222  3.56%  31.4   16s

Cutting planes:
  Implied bound: 291
  MIR: 71
  Flow cover: 269
  RLT: 40
  Relax-and-lift: 160

Explored 6707 nodes (206561 simplex iterations) in 18.44 seconds (14.06 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.500042 0.502743 0.503567 ... 0.541692

Optimal solution found (tolerance 1.00e-04)
Best objective 5.000418146572e-01, best bound 5.000418146572e-01, gap 0.0000%
The objective bound is 0.500042 while the objective upper bound is 0.500042

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.40 (ave)

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