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 0.106358 seconds.
    local lower bound updated to 0.234246
    local upper bound updated to 0.365317

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.139628 seconds.
    local lower bound updated to 0.365317
    local upper bound updated to 0.365317
The Primal step takes 0.248201 (S)
lower bound updated to 0.365317

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.455199
    local lower bound updated to 0.455199
The Dual step takes 0.00699845 (S)
upper bound updated to 0.455199
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.15887 seconds.
    local lower bound updated to 0.268368
    local upper bound updated to 0.391154

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.244312 seconds.
    local lower bound updated to 0.385881
    local upper bound updated to 0.387116

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.269878 seconds.
    local lower bound updated to 0.387116
    local upper bound updated to 0.387116
The Primal step takes 0.677336 (S)
lower bound updated to 0.387116

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.443873
    local lower bound updated to 0.428345

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.43649
    local lower bound updated to 0.42917

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.434942
    local lower bound updated to 0.430522

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.430522
    local lower bound updated to 0.430522
The Dual step takes 0.168759 (S)
upper bound updated to 0.430522
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.505963 seconds.
    local lower bound updated to 0.334485
    local upper bound updated to 0.429014

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.75896 seconds.
    local lower bound updated to 0.37411
    local upper bound updated to 0.399575

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.803436 seconds.
    local lower bound updated to 0.394373
    local upper bound updated to 0.398997

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.41371 seconds.
    local lower bound updated to 0.398988
    local upper bound updated to 0.398992
The Primal step takes 3.49267 (S)
lower bound updated to 0.398988

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.425055
    local lower bound updated to 0.409389

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.416002
    local lower bound updated to 0.410284

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.413969
    local lower bound updated to 0.411205

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.411831
    local lower bound updated to 0.411674

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.411674
    local lower bound updated to 0.411674
The Dual step takes 0.880177 (S)
upper bound updated to 0.411674
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.46379 seconds.
    local lower bound updated to 0.366681
    local upper bound updated to 0.410592

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.5323 seconds.
    local lower bound updated to 0.402902
    local upper bound updated to 0.408449

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.34239 seconds.
    local lower bound updated to 0.402902
    local upper bound updated to 0.407836

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.79604 seconds.
    local lower bound updated to 0.403027
    local upper bound updated to 0.406199

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.7824 seconds.
    local lower bound updated to 0.403982
    local upper bound updated to 0.406154

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.0763 seconds.
    local lower bound updated to 0.405394
    local upper bound updated to 0.406151

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 1.7632 seconds.
    local lower bound updated to 0.405485
    local upper bound updated to 0.406099

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 2.49639 seconds.
    local lower bound updated to 0.405583
    local upper bound updated to 0.405977

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 2.35889 seconds.
    local lower bound updated to 0.405583
    local upper bound updated to 0.405942

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 1.97795 seconds.
    local lower bound updated to 0.405805
    local upper bound updated to 0.405934

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 3.00943 seconds.
    local lower bound updated to 0.405909
    local upper bound updated to 0.405932

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 3.04205 seconds.
    local lower bound updated to 0.405932
    local upper bound updated to 0.405932
The Primal step takes 26.6855 (S)
lower bound updated to 0.405932

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.418675
    local lower bound updated to 0.405932

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.417223
    local lower bound updated to 0.406552

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.413563
    local lower bound updated to 0.407479

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.411662
    local lower bound updated to 0.408688

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.411662
    local lower bound updated to 0.408807

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.409255
    local lower bound updated to 0.408821

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.408821
    local lower bound updated to 0.408821
The Dual step takes 5.87037 (S)
upper bound updated to 0.408821
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.34639 seconds.
    local lower bound updated to 0.377651
    local upper bound updated to 0.408679

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.23883 seconds.
    local lower bound updated to 0.377651
    local upper bound updated to 0.408275

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.80014 seconds.
    local lower bound updated to 0.405917
    local upper bound updated to 0.408188

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.97879 seconds.
    local lower bound updated to 0.406434
    local upper bound updated to 0.408032

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.74906 seconds.
    local lower bound updated to 0.406434
    local upper bound updated to 0.408028

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.67371 seconds.
    local lower bound updated to 0.407539
    local upper bound updated to 0.408016

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 10.3969 seconds.
    local lower bound updated to 0.40772
    local upper bound updated to 0.408011

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 10.0893 seconds.
    local lower bound updated to 0.407935
    local upper bound updated to 0.408011

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 12.7314 seconds.
    local lower bound updated to 0.407981
    local upper bound updated to 0.40801

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 8.06818 seconds.
    local lower bound updated to 0.407984
    local upper bound updated to 0.408006

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 11.6854 seconds.
    local lower bound updated to 0.407985
    local upper bound updated to 0.408006

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 12.4295 seconds.
    local lower bound updated to 0.408006
    local upper bound updated to 0.408006
The Primal step takes 100.261 (S)
lower bound updated to 0.408006

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.423797
    local lower bound updated to 0.408006

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.410652
    local lower bound updated to 0.408431

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.408431
    local lower bound updated to 0.408431
The Dual step takes 5.21948 (S)
upper bound updated to 0.408431
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.60469 seconds.
    local lower bound updated to 0.37673
    local upper bound updated to 0.408431

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 9.68479 seconds.
    local lower bound updated to 0.404246
    local upper bound updated to 0.408364

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 12.1728 seconds.
    local lower bound updated to 0.407398
    local upper bound updated to 0.408324

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 9.28049 seconds.
    local lower bound updated to 0.407924
    local upper bound updated to 0.408319

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.2595 seconds.
    local lower bound updated to 0.40824
    local upper bound updated to 0.408319

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.41693 seconds.
    local lower bound updated to 0.408253
    local upper bound updated to 0.408318

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.32334 seconds.
    local lower bound updated to 0.408302
    local upper bound updated to 0.408315

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 10.7137 seconds.
    local lower bound updated to 0.408315
    local upper bound updated to 0.408315
The Primal step takes 75.5079 (S)
lower bound updated to 0.408315

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.424615
    local lower bound updated to 0.408315

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.409752
    local lower bound updated to 0.408386

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.408386
    local lower bound updated to 0.408386
The Dual step takes 7.09962 (S)
upper bound updated to 0.408386
*** OUTER ITERATION 6 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.88804 seconds.
    local lower bound updated to 0.375784
    local upper bound updated to 0.408386

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 12.2917 seconds.
    local lower bound updated to 0.407507
    local upper bound updated to 0.408383

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 13.8124 seconds.
    local lower bound updated to 0.407845
    local upper bound updated to 0.408353

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.328 seconds.
    local lower bound updated to 0.408239
    local upper bound updated to 0.40835

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 9.49946 seconds.
    local lower bound updated to 0.40835
    local upper bound updated to 0.40835
The Primal step takes 49.8567 (S)
lower bound updated to 0.40835

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.426238
    local lower bound updated to 0.40835

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.40835
    local lower bound updated to 0.40835
The Dual step takes 4.2839 (S)
upper bound updated to 0.40835
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.87972 seconds.
    local lower bound updated to 0.375784
    local upper bound updated to 0.40835

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 9.45836 seconds.
    local lower bound updated to 0.40835
    local upper bound updated to 0.40835
The time obtain the optimal randomized assortment is 293.61 (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_13_4_60.000000_62914.log"
The computation time limit for a lower bound is 85705
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 2220 rows, 1954 columns and 6854 nonzeros
Model fingerprint: 0x6bfce1ab
Variable types: 1905 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [5e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 715 rows and 1322 columns
Presolve time: 0.02s
Presolved: 1505 rows, 632 columns, 5541 nonzeros
Variable types: 588 continuous, 44 integer (44 binary)
Found heuristic solution: objective 0.5021913
Found heuristic solution: objective 0.4924645
Found heuristic solution: objective 0.4550316

Root relaxation: objective 2.057771e-01, 162 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    0.20578    0   16    0.45503    0.20578  54.8%     -    0s
H    0     0                       0.4261426    0.20578  51.7%     -    0s
H    0     0                       0.4123075    0.21816  47.1%     -    0s
     0     0    0.21843    0   21    0.41231    0.21843  47.0%     -    0s
     0     0    0.24266    0   18    0.41231    0.24266  41.1%     -    0s
     0     0    0.25845    0   25    0.41231    0.25845  37.3%     -    0s
     0     0    0.28363    0   24    0.41231    0.28363  31.2%     -    0s
     0     0    0.28363    0   24    0.41231    0.28363  31.2%     -    0s
     0     0    0.29384    0   23    0.41231    0.29384  28.7%     -    0s
     0     0    0.29384    0   23    0.41231    0.29384  28.7%     -    0s
     0     0    0.30598    0   23    0.41231    0.30598  25.8%     -    0s
H    0     0                       0.4083499    0.30598  25.1%     -    1s
     0     2    0.30598    0   23    0.40835    0.30598  25.1%     -    1s
  2309   386    0.39479   13   10    0.40835    0.38580  5.52%  21.2    5s
H 3266   435                       0.4083498    0.39004  4.48%  20.4    6s
H 6437   273                       0.4083498    0.40109  1.78%  18.6    9s
  6929    12     cutoff   21         0.40835    0.40326  1.25%  18.3   10s

Cutting planes:
  Gomory: 2
  Implied bound: 273
  MIR: 68
  Flow cover: 222
  RLT: 33
  Relax-and-lift: 164

Explored 7403 nodes (133821 simplex iterations) in 10.06 seconds (6.47 work units)
Thread count was 4 (of 48 available processors)

Solution count 7: 0.40835 0.40835 0.412308 ... 0.502191

Optimal solution found (tolerance 1.00e-04)
Best objective 4.083498421851e-01, best bound 4.083498421851e-01, gap 0.0000%
The objective bound is 0.40835 while the objective upper bound is 0.40835

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.28 (ave)

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