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 0.165045 seconds.
    local lower bound updated to 0.243689
    local upper bound updated to 0.477587

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.148332 seconds.
    local lower bound updated to 0.474979
    local upper bound updated to 0.474979
The Primal step takes 0.31574 (S)
lower bound updated to 0.474979

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.514462
    local lower bound updated to 0.491386

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.497239
    local lower bound updated to 0.497239
The Dual step takes 0.0590867 (S)
upper bound updated to 0.497239
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.95715 seconds.
    local lower bound updated to 0.364494
    local upper bound updated to 0.478843

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.292039 seconds.
    local lower bound updated to 0.472494
    local upper bound updated to 0.477037

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.509036 seconds.
    local lower bound updated to 0.474572
    local upper bound updated to 0.476191

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.370362 seconds.
    local lower bound updated to 0.475714
    local upper bound updated to 0.475907

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.411103 seconds.
    local lower bound updated to 0.475907
    local upper bound updated to 0.475907
The Primal step takes 4.54949 (S)
lower bound updated to 0.475907

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.490413
    local lower bound updated to 0.476537

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.487478
    local lower bound updated to 0.483816

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.487478
    local lower bound updated to 0.485179

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.487478
    local lower bound updated to 0.485737

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.485737
    local lower bound updated to 0.485737
The Dual step takes 0.393127 (S)
upper bound updated to 0.485737
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.09601 seconds.
    local lower bound updated to 0.410709
    local upper bound updated to 0.485239

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.596011 seconds.
    local lower bound updated to 0.464805
    local upper bound updated to 0.479881

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.931863 seconds.
    local lower bound updated to 0.474494
    local upper bound updated to 0.479695

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.975538 seconds.
    local lower bound updated to 0.476702
    local upper bound updated to 0.479594

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.808214 seconds.
    local lower bound updated to 0.477236
    local upper bound updated to 0.479469

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.58792 seconds.
    local lower bound updated to 0.478998
    local upper bound updated to 0.479447

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.039 seconds.
    local lower bound updated to 0.479447
    local upper bound updated to 0.479447
The Primal step takes 9.05751 (S)
lower bound updated to 0.479447

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.495349
    local lower bound updated to 0.482731

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.488478
    local lower bound updated to 0.482877

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.482877
    local lower bound updated to 0.482877
The Dual step takes 0.590274 (S)
upper bound updated to 0.482877
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.89306 seconds.
    local lower bound updated to 0.423917
    local upper bound updated to 0.481434

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.79355 seconds.
    local lower bound updated to 0.474274
    local upper bound updated to 0.480919

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.78875 seconds.
    local lower bound updated to 0.477597
    local upper bound updated to 0.480376

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.94133 seconds.
    local lower bound updated to 0.479003
    local upper bound updated to 0.480324

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.65393 seconds.
    local lower bound updated to 0.479003
    local upper bound updated to 0.480173

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.01679 seconds.
    local lower bound updated to 0.479465
    local upper bound updated to 0.480089

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 3.24498 seconds.
    local lower bound updated to 0.479465
    local upper bound updated to 0.480072

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 2.17899 seconds.
    local lower bound updated to 0.479565
    local upper bound updated to 0.479927

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 3.63912 seconds.
    local lower bound updated to 0.479809
    local upper bound updated to 0.479922

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 3.45738 seconds.
    local lower bound updated to 0.479837
    local upper bound updated to 0.479914

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 2.89923 seconds.
    local lower bound updated to 0.479899
    local upper bound updated to 0.479913

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 3.08138 seconds.
    local lower bound updated to 0.479913
    local upper bound updated to 0.479913
The Primal step takes 31.6379 (S)
lower bound updated to 0.479913

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.490169
    local lower bound updated to 0.480151

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.483814
    local lower bound updated to 0.480775

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.480775
    local lower bound updated to 0.480775
The Dual step takes 2.82227 (S)
upper bound updated to 0.480775
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.33312 seconds.
    local lower bound updated to 0.431721
    local upper bound updated to 0.480775

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.6067 seconds.
    local lower bound updated to 0.48059
    local upper bound updated to 0.480762

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.4813 seconds.
    local lower bound updated to 0.480655
    local upper bound updated to 0.480745

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.71913 seconds.
    local lower bound updated to 0.480701
    local upper bound updated to 0.480737

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.069 seconds.
    local lower bound updated to 0.480737
    local upper bound updated to 0.480737
The Primal step takes 9.23354 (S)
lower bound updated to 0.480737

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.492247
    local lower bound updated to 0.480737

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.480737
    local lower bound updated to 0.480737
The Dual step takes 5.05128 (S)
upper bound updated to 0.480737
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.34413 seconds.
    local lower bound updated to 0.431721
    local upper bound updated to 0.480737

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.02024 seconds.
    local lower bound updated to 0.480737
    local upper bound updated to 0.480737
The time obtain the optimal randomized assortment is 68.0841 (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_63816.log"
The computation time limit for a lower bound is 85930
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 2000 rows, 1618 columns and 6440 nonzeros
Model fingerprint: 0x43c9c501
Variable types: 1561 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 511 rows and 965 columns
Presolve time: 0.02s
Presolved: 1489 rows, 653 columns, 5754 nonzeros
Variable types: 598 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5508754
Found heuristic solution: objective 0.5432366

Root relaxation: objective 4.349811e-01, 203 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    0.43498    0   16    0.54324    0.43498  19.9%     -    0s
H    0     0                       0.5374163    0.43498  19.1%     -    0s
H    0     0                       0.5259647    0.43498  17.3%     -    0s
     0     0    0.43732    0   22    0.52596    0.43732  16.9%     -    0s
H    0     0                       0.5154045    0.43732  15.1%     -    0s
     0     0    0.45124    0   24    0.51540    0.45124  12.5%     -    0s
H    0     0                       0.4824366    0.45124  6.47%     -    0s
     0     0    0.45162    0   24    0.48244    0.45162  6.39%     -    0s
H    0     0                       0.4818033    0.45707  5.13%     -    0s
     0     0    0.45707    0   24    0.48180    0.45707  5.13%     -    0s
H    0     0                       0.4811432    0.45739  4.94%     -    0s
     0     0    0.45739    0   24    0.48114    0.45739  4.94%     -    0s
H    0     0                       0.4811073    0.45739  4.93%     -    0s
     0     0    0.45922    0   25    0.48111    0.45922  4.55%     -    0s
     0     0    0.45954    0   25    0.48111    0.45954  4.48%     -    0s
     0     0    0.45981    0   23    0.48111    0.45981  4.43%     -    0s
H    0     0                       0.4807372    0.45981  4.35%     -    0s
     0     2    0.45981    0   23    0.48074    0.45981  4.35%     -    0s

Cutting planes:
  Implied bound: 227
  MIR: 42
  Flow cover: 169
  RLT: 18
  Relax-and-lift: 80

Explored 586 nodes (15502 simplex iterations) in 2.01 seconds (1.34 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.480737 0.481107 0.481143 ... 0.550875

Optimal solution found (tolerance 1.00e-04)
Best objective 4.807372458617e-01, best bound 4.807372458617e-01, gap 0.0000%
The objective bound is 0.480737 while the objective upper bound is 0.480737

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.21 (ave)

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