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 0.280065 seconds.
    local lower bound updated to 0.240074
    local upper bound updated to 0.41722

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.311229 seconds.
    local lower bound updated to 0.413316
    local upper bound updated to 0.413316
The Primal step takes 0.593226 (S)
lower bound updated to 0.413316

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.481731
    local lower bound updated to 0.478918

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.478918
    local lower bound updated to 0.478918
The Dual step takes 0.0568211 (S)
upper bound updated to 0.478918
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.485946 seconds.
    local lower bound updated to 0.285611
    local upper bound updated to 0.42869

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.992592 seconds.
    local lower bound updated to 0.416329
    local upper bound updated to 0.41949

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.634058 seconds.
    local lower bound updated to 0.418357
    local upper bound updated to 0.419154

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.06628 seconds.
    local lower bound updated to 0.419154
    local upper bound updated to 0.419154
The Primal step takes 3.18465 (S)
lower bound updated to 0.419154

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.444113
    local lower bound updated to 0.441015

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.442208
    local lower bound updated to 0.441099

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.441099
    local lower bound updated to 0.441099
The Dual step takes 0.991479 (S)
upper bound updated to 0.441099
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.91764 seconds.
    local lower bound updated to 0.323864
    local upper bound updated to 0.434443

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.65393 seconds.
    local lower bound updated to 0.391112
    local upper bound updated to 0.431165

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.05298 seconds.
    local lower bound updated to 0.410505
    local upper bound updated to 0.424917

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.13472 seconds.
    local lower bound updated to 0.417246
    local upper bound updated to 0.421581

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.73834 seconds.
    local lower bound updated to 0.418311
    local upper bound updated to 0.421561

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.61112 seconds.
    local lower bound updated to 0.418311
    local upper bound updated to 0.419987

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 1.01065 seconds.
    local lower bound updated to 0.419939
    local upper bound updated to 0.41996

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.16884 seconds.
    local lower bound updated to 0.41996
    local upper bound updated to 0.41996
The Primal step takes 18.3064 (S)
lower bound updated to 0.41996

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.447036
    local lower bound updated to 0.427585

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.446075
    local lower bound updated to 0.433151

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.446075
    local lower bound updated to 0.43806

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.43806
    local lower bound updated to 0.43806
The Dual step takes 2.8512 (S)
upper bound updated to 0.43806
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 20.2553 seconds.
    local lower bound updated to 0.365788
    local upper bound updated to 0.437321

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.26632 seconds.
    local lower bound updated to 0.411811
    local upper bound updated to 0.435883

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.39188 seconds.
    local lower bound updated to 0.411811
    local upper bound updated to 0.434346

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 14.7734 seconds.
    local lower bound updated to 0.420122
    local upper bound updated to 0.431858

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.12226 seconds.
    local lower bound updated to 0.420122
    local upper bound updated to 0.429502

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 20.6123 seconds.
    local lower bound updated to 0.420122
    local upper bound updated to 0.429395

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 21.1736 seconds.
    local lower bound updated to 0.422333
    local upper bound updated to 0.426141

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 23.4126 seconds.
    local lower bound updated to 0.422333
    local upper bound updated to 0.425977

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 30.7352 seconds.
    local lower bound updated to 0.423394
    local upper bound updated to 0.425201

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 20.6698 seconds.
    local lower bound updated to 0.423394
    local upper bound updated to 0.424712

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 20.9468 seconds.
    local lower bound updated to 0.423394
    local upper bound updated to 0.424678

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 19.3324 seconds.
    local lower bound updated to 0.424233
    local upper bound updated to 0.424674

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 25.2087 seconds.
    local lower bound updated to 0.424233
    local upper bound updated to 0.42466

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 25.083 seconds.
    local lower bound updated to 0.424233
    local upper bound updated to 0.424657

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 27.4402 seconds.
    local lower bound updated to 0.424252
    local upper bound updated to 0.424562

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 27.2824 seconds.
    local lower bound updated to 0.424252
    local upper bound updated to 0.424544

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 23.7808 seconds.
    local lower bound updated to 0.424252
    local upper bound updated to 0.42453

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 22.92 seconds.
    local lower bound updated to 0.424348
    local upper bound updated to 0.424529

    ++ RESTRICTED PRIMAL ITERATION 19 ++
One worst-case parameter optimization takes 29.2512 seconds.
    local lower bound updated to 0.424369
    local upper bound updated to 0.424515

    ++ RESTRICTED PRIMAL ITERATION 20 ++
One worst-case parameter optimization takes 22.8036 seconds.
    local lower bound updated to 0.424515
    local upper bound updated to 0.424515
The Primal step takes 408.531 (S)
lower bound updated to 0.424515

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.442372
    local lower bound updated to 0.426821

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.431767
    local lower bound updated to 0.426901

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.429102
    local lower bound updated to 0.427337

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.429102
    local lower bound updated to 0.427571

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.428996
    local lower bound updated to 0.428372

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.428372
    local lower bound updated to 0.428372
The Dual step takes 18.6596 (S)
upper bound updated to 0.428372
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 44.1784 seconds.
    local lower bound updated to 0.390392
    local upper bound updated to 0.428372

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.89085 seconds.
    local lower bound updated to 0.417103
    local upper bound updated to 0.428179

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.7298 seconds.
    local lower bound updated to 0.417103
    local upper bound updated to 0.427849

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 17.3823 seconds.
    local lower bound updated to 0.426987
    local upper bound updated to 0.427847

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.2408 seconds.
    local lower bound updated to 0.426987
    local upper bound updated to 0.427829

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 24.4051 seconds.
    local lower bound updated to 0.427121
    local upper bound updated to 0.427803

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 31.7519 seconds.
    local lower bound updated to 0.427467
    local upper bound updated to 0.427795

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 24.3482 seconds.
    local lower bound updated to 0.427795
    local upper bound updated to 0.427795
The Primal step takes 172.963 (S)
lower bound updated to 0.427795

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.4431
    local lower bound updated to 0.427795

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.427795
    local lower bound updated to 0.427795
The Dual step takes 8.99417 (S)
upper bound updated to 0.427795
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 47.7228 seconds.
    local lower bound updated to 0.390392
    local upper bound updated to 0.427795

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 22.5189 seconds.
    local lower bound updated to 0.427795
    local upper bound updated to 0.427795
The time obtain the optimal randomized assortment is 705.383 (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_65516.log"
The computation time limit for a lower bound is 85290
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 2160 rows, 1748 columns and 6899 nonzeros
Model fingerprint: 0xa98c16b2
Variable types: 1691 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        [4e-01, 1e+00]
Presolve removed 564 rows and 1048 columns
Presolve time: 0.02s
Presolved: 1596 rows, 700 columns, 6101 nonzeros
Variable types: 646 continuous, 54 integer (54 binary)
Found heuristic solution: objective 0.6116317
Found heuristic solution: objective 0.4949357

Root relaxation: objective 3.080439e-01, 212 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    0.30804    0   19    0.49494    0.30804  37.8%     -    0s
H    0     0                       0.4893382    0.30804  37.0%     -    0s
H    0     0                       0.4786217    0.30804  35.6%     -    0s
     0     0    0.31066    0   19    0.47862    0.31066  35.1%     -    0s
H    0     0                       0.4767234    0.31066  34.8%     -    0s
     0     0    0.31066    0   19    0.47672    0.31066  34.8%     -    0s
H    0     0                       0.4690838    0.31066  33.8%     -    0s
H    0     0                       0.4649693    0.34213  26.4%     -    0s
     0     0    0.34213    0   22    0.46497    0.34213  26.4%     -    0s
H    0     0                       0.4295032    0.34213  20.3%     -    0s
     0     0    0.34427    0   22    0.42950    0.34427  19.8%     -    0s
H    0     0                       0.4288222    0.34837  18.8%     -    0s
     0     0    0.34837    0   23    0.42882    0.34837  18.8%     -    0s
     0     0    0.34918    0   23    0.42882    0.34918  18.6%     -    0s
H    0     0                       0.4277947    0.34918  18.4%     -    0s
     0     0    0.36060    0   25    0.42779    0.36060  15.7%     -    0s
     0     0    0.36118    0   23    0.42779    0.36118  15.6%     -    0s
     0     0    0.36387    0   23    0.42779    0.36387  14.9%     -    0s
     0     2    0.36387    0   23    0.42779    0.36387  14.9%     -    1s
H  426   164                       0.4277947    0.37957  11.3%  25.6    1s
  1583   450    0.42152   13   11    0.42779    0.39158  8.47%  23.0    5s
  3371   717    0.41354   10   10    0.42779    0.39995  6.51%  21.2   10s
H 4830   795                       0.4277947    0.40373  5.62%  20.4   13s
  5511   797     cutoff   15         0.42779    0.40580  5.14%  20.1   15s
H 8312   608                       0.4277947    0.41210  3.67%  19.3   18s
H 8812   527                       0.4277947    0.41353  3.34%  19.2   19s
  8965   454     cutoff   13         0.42779    0.41428  3.16%  19.2   20s
H 9167   454                       0.4277947    0.41436  3.14%  19.2   20s

Cutting planes:
  Implied bound: 243
  MIR: 79
  Flow cover: 224
  RLT: 17
  Relax-and-lift: 107

Explored 10211 nodes (194869 simplex iterations) in 21.70 seconds (18.13 work units)
Thread count was 4 (of 256 available processors)

Solution count 10: 0.427795 0.427795 0.427795 ... 0.489338

Optimal solution found (tolerance 1.00e-04)
Best objective 4.277947001855e-01, best bound 4.277947001855e-01, gap 0.0000%
The objective bound is 0.427795 while the objective upper bound is 0.427795

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.63 (ave)

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