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 0.303881 seconds.
    local lower bound updated to 0.226942
    local upper bound updated to 0.436773

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.331036 seconds.
    local lower bound updated to 0.42177
    local upper bound updated to 0.42177
The Primal step takes 0.638622 (S)
lower bound updated to 0.42177

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.485137
    local lower bound updated to 0.42177

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.455787
    local lower bound updated to 0.4504

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.455787
    local lower bound updated to 0.453536

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.453536
    local lower bound updated to 0.453536
The Dual step takes 0.367336 (S)
upper bound updated to 0.453536
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.10794 seconds.
    local lower bound updated to 0.325684
    local upper bound updated to 0.427867

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.71263 seconds.
    local lower bound updated to 0.415153
    local upper bound updated to 0.424587

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.02681 seconds.
    local lower bound updated to 0.415592
    local upper bound updated to 0.421876

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.922384 seconds.
    local lower bound updated to 0.421768
    local upper bound updated to 0.421775
The Primal step takes 9.78498 (S)
lower bound updated to 0.42177

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.462543
    local lower bound updated to 0.43365

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.445371
    local lower bound updated to 0.441936

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.445371
    local lower bound updated to 0.443076

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.443996
    local lower bound updated to 0.44333

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.44333
    local lower bound updated to 0.44333
The Dual step takes 1.89549 (S)
upper bound updated to 0.44333
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.0439 seconds.
    local lower bound updated to 0.375415
    local upper bound updated to 0.440913

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.8893 seconds.
    local lower bound updated to 0.420902
    local upper bound updated to 0.438018

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.00294 seconds.
    local lower bound updated to 0.426152
    local upper bound updated to 0.435353

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.59497 seconds.
    local lower bound updated to 0.426424
    local upper bound updated to 0.433759

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 13.1778 seconds.
    local lower bound updated to 0.428222
    local upper bound updated to 0.43269

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.12359 seconds.
    local lower bound updated to 0.43267
    local upper bound updated to 0.432683

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 12.4315 seconds.
    local lower bound updated to 0.43267
    local upper bound updated to 0.432682

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 13.0248 seconds.
    local lower bound updated to 0.432682
    local upper bound updated to 0.432682
The Primal step takes 79.3377 (S)
lower bound updated to 0.432682

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.45041
    local lower bound updated to 0.432682

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.435963
    local lower bound updated to 0.433526

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.435963
    local lower bound updated to 0.433742

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.433865
    local lower bound updated to 0.433768

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.433768
    local lower bound updated to 0.433768
The Dual step takes 4.96309 (S)
upper bound updated to 0.433768
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 32.6757 seconds.
    local lower bound updated to 0.3915
    local upper bound updated to 0.433768

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 22.48 seconds.
    local lower bound updated to 0.426463
    local upper bound updated to 0.43363

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 23.599 seconds.
    local lower bound updated to 0.432038
    local upper bound updated to 0.433517

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 25.032 seconds.
    local lower bound updated to 0.432333
    local upper bound updated to 0.433348

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 29.988 seconds.
    local lower bound updated to 0.432905
    local upper bound updated to 0.43305

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 24.4934 seconds.
    local lower bound updated to 0.43305
    local upper bound updated to 0.43305
The Primal step takes 158.323 (S)
lower bound updated to 0.43305

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.45115
    local lower bound updated to 0.43305

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.43305
    local lower bound updated to 0.43305
The Dual step takes 3.46472 (S)
upper bound updated to 0.43305
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 31.4835 seconds.
    local lower bound updated to 0.3915
    local upper bound updated to 0.43305

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.9152 seconds.
    local lower bound updated to 0.43305
    local upper bound updated to 0.43305
The time obtain the optimal randomized assortment is 311.19 (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_109516.log"
The computation time limit for a lower bound is 85686
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 2160 rows, 1748 columns and 6944 nonzeros
Model fingerprint: 0x5974705b
Variable types: 1691 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 600 rows and 1066 columns
Presolve time: 0.03s
Presolved: 1560 rows, 682 columns, 6059 nonzeros
Variable types: 627 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5362486
Found heuristic solution: objective 0.5137346
Found heuristic solution: objective 0.5047276

Root relaxation: objective 3.260806e-01, 205 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    0.32608    0   20    0.50473    0.32608  35.4%     -    0s
H    0     0                       0.4997643    0.32608  34.8%     -    0s
H    0     0                       0.4951806    0.33378  32.6%     -    0s
H    0     0                       0.4845524    0.33378  31.1%     -    0s
     0     0    0.33388    0   24    0.48455    0.33388  31.1%     -    0s
H    0     0                       0.4589584    0.33388  27.3%     -    0s
H    0     0                       0.4544569    0.33388  26.5%     -    0s
     0     0    0.33388    0   24    0.45446    0.33388  26.5%     -    0s
     0     0    0.36712    0   28    0.45446    0.36712  19.2%     -    0s
H    0     0                       0.4425084    0.36712  17.0%     -    0s
     0     0    0.36712    0   28    0.44251    0.36712  17.0%     -    0s
H    0     0                       0.4348886    0.37381  14.0%     -    0s
     0     0    0.37381    0   26    0.43489    0.37381  14.0%     -    0s
     0     0    0.37488    0   25    0.43489    0.37488  13.8%     -    0s
H    0     0                       0.4344977    0.37488  13.7%     -    0s
     0     0    0.37782    0   26    0.43450    0.37782  13.0%     -    0s
     0     0    0.37819    0   24    0.43450    0.37819  13.0%     -    0s
     0     0    0.38013    0   27    0.43450    0.38013  12.5%     -    0s
H    0     0                       0.4342382    0.38013  12.5%     -    2s
     0     2    0.38013    0   27    0.43424    0.38013  12.5%     -    2s
*  106    58              16       0.4330499    0.38628  10.8%  29.1    3s
   469   149     cutoff   11         0.43305    0.40028  7.57%  29.6    5s
  1111   281    0.43236    8   14    0.43305    0.40968  5.40%  26.4   10s
  3542   352    0.43108   15    8    0.43305    0.41995  3.02%  21.9   15s

Cutting planes:
  Gomory: 2
  Implied bound: 253
  MIR: 111
  Flow cover: 266
  RLT: 21
  Relax-and-lift: 127

Explored 5492 nodes (109077 simplex iterations) in 18.98 seconds (7.85 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.43305 0.434238 0.434498 ... 0.499764

Optimal solution found (tolerance 1.00e-04)
Best objective 4.330498707924e-01, best bound 4.330498707924e-01, gap 0.0000%
The objective bound is 0.43305 while the objective upper bound is 0.43305

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.06 (ave)

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