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 2.60581 seconds.
    local lower bound updated to 0.259607
    local upper bound updated to 0.474562

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.58966 seconds.
    local lower bound updated to 0.445617
    local upper bound updated to 0.445617
The Primal step takes 5.19995 (S)
lower bound updated to 0.445617

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.612295
    local lower bound updated to 0.603637

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.603637
    local lower bound updated to 0.603637
The Dual step takes 0.057579 (S)
upper bound updated to 0.603637
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 26.2421 seconds.
    local lower bound updated to 0.326846
    local upper bound updated to 0.485354

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 34.2559 seconds.
    local lower bound updated to 0.478717
    local upper bound updated to 0.481456

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 25.2265 seconds.
    local lower bound updated to 0.478717
    local upper bound updated to 0.479155

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 31.1386 seconds.
    local lower bound updated to 0.479155
    local upper bound updated to 0.479155
The Primal step takes 116.876 (S)
lower bound updated to 0.479155

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.549291
    local lower bound updated to 0.528405

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.549291
    local lower bound updated to 0.528523

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.547535
    local lower bound updated to 0.534823

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.538151
    local lower bound updated to 0.538086

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.538086
    local lower bound updated to 0.538086
The Dual step takes 0.776177 (S)
upper bound updated to 0.538086
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 59.5634 seconds.
    local lower bound updated to 0.415666
    local upper bound updated to 0.496449

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.31092 seconds.
    local lower bound updated to 0.441683
    local upper bound updated to 0.494583

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 66.5779 seconds.
    local lower bound updated to 0.482264
    local upper bound updated to 0.491936

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 154.434 seconds.
    local lower bound updated to 0.48985
    local upper bound updated to 0.491798

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 137.13 seconds.
    local lower bound updated to 0.48985
    local upper bound updated to 0.491192

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.038 seconds.
    local lower bound updated to 0.491192
    local upper bound updated to 0.491192
The Primal step takes 624.09 (S)
lower bound updated to 0.491192

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.52279
    local lower bound updated to 0.492774

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518019
    local lower bound updated to 0.499122

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513827
    local lower bound updated to 0.501998

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.505327
    local lower bound updated to 0.502844

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.504012
    local lower bound updated to 0.50296

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.50296
    local lower bound updated to 0.50296
The Dual step takes 7.23127 (S)
upper bound updated to 0.50296
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.447673
    local upper bound updated to 0.502566

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 122.838 seconds.
    local lower bound updated to 0.478322
    local upper bound updated to 0.499605

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.047 seconds.
    local lower bound updated to 0.489831
    local upper bound updated to 0.497309

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.489831
    local upper bound updated to 0.496922

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.05 seconds.
    local lower bound updated to 0.491578
    local upper bound updated to 0.496432

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.038 seconds.
    local lower bound updated to 0.491842
    local upper bound updated to 0.496383

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.493095
    local upper bound updated to 0.496368

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.493631
    local upper bound updated to 0.496114

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.493631
    local upper bound updated to 0.495806

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.494456
    local upper bound updated to 0.495522

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.494831
    local upper bound updated to 0.495418

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.495139
    local upper bound updated to 0.495349

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 200.057 seconds.
    local lower bound updated to 0.495302
    local upper bound updated to 0.495345

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.495342
    local upper bound updated to 0.495345
The Primal step takes 2723.49 (S)
lower bound updated to 0.495342

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.521979
    local lower bound updated to 0.495345

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.502901
    local lower bound updated to 0.495614

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.500404
    local lower bound updated to 0.495794

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.497573
    local lower bound updated to 0.496039

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.497573
    local lower bound updated to 0.496145

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.496145
    local lower bound updated to 0.496145
The Dual step takes 31.4747 (S)
upper bound updated to 0.496145
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.450963
    local upper bound updated to 0.496145

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.495501
    local upper bound updated to 0.49609

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.495597
    local upper bound updated to 0.496049

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.034 seconds.
    local lower bound updated to 0.495773
    local upper bound updated to 0.495989

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.047 seconds.
    local lower bound updated to 0.495838
    local upper bound updated to 0.495977

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.495838
    local upper bound updated to 0.495955

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.044 seconds.
    local lower bound updated to 0.495908
    local upper bound updated to 0.495955

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.495912
    local upper bound updated to 0.495943

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.049 seconds.
    local lower bound updated to 0.495941
    local upper bound updated to 0.495943
The Primal step takes 1800.47 (S)
lower bound updated to 0.495941

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.515403
    local lower bound updated to 0.495943

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.495943
    local lower bound updated to 0.495943
The Dual step takes 17.6822 (S)
upper bound updated to 0.495943
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.450963
    local upper bound updated to 0.495943

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.495943
    local upper bound updated to 0.495943
The time obtain the optimal randomized assortment is 5727.46 (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_17_4_200.000000_204418.log"
The computation time limit for a lower bound is 80265
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 20 physical cores, 40 logical processors, using up to 4 threads
Optimize a model with 3186 rows, 2434 columns and 10482 nonzeros
Model fingerprint: 0x54014b88
Variable types: 2369 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [5e-05, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [7e-01, 1e+00]
Presolve removed 731 rows and 1353 columns
Presolve time: 0.06s
Presolved: 2455 rows, 1081 columns, 9627 nonzeros
Variable types: 1018 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.6917324
Found heuristic solution: objective 0.6171647

Root relaxation: objective 2.724865e-01, 266 iterations, 0.01 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.27249    0   33    0.61716    0.27249  55.8%     -    0s
H    0     0                       0.6154073    0.27249  55.7%     -    0s
H    0     0                       0.5783375    0.28642  50.5%     -    0s
     0     0    0.28642    0   32    0.57834    0.28642  50.5%     -    0s
H    0     0                       0.5102466    0.28642  43.9%     -    0s
     0     0    0.34764    0   32    0.51025    0.34764  31.9%     -    0s
     0     0    0.34776    0   33    0.51025    0.34776  31.8%     -    0s
     0     0    0.36753    0   34    0.51025    0.36753  28.0%     -    0s
     0     0    0.36850    0   32    0.51025    0.36850  27.8%     -    1s
H    0     0                       0.5057163    0.36850  27.1%     -    1s
     0     0    0.37287    0   31    0.50572    0.37287  26.3%     -    1s
     0     0    0.37389    0   33    0.50572    0.37389  26.1%     -    1s
     0     0    0.37542    0   32    0.50572    0.37542  25.8%     -    1s
H    0     0                       0.4989158    0.37542  24.8%     -    6s
     0     2    0.37542    0   32    0.49892    0.37542  24.8%     -    6s
H  100    88                       0.4959430    0.38637  22.1%  60.3    8s
   195   141    0.49331   17    8    0.49594    0.39634  20.1%  51.8   10s
   398   259    0.45264   14   23    0.49594    0.39634  20.1%  45.5   16s
  1083   546    0.44456    6   26    0.49594    0.41424  16.5%  38.3   21s
  1271   605    0.41882    8   29    0.49594    0.41635  16.0%  37.7   25s
  1386   681    0.47692   15   19    0.49594    0.41668  16.0%  37.0   32s
  1475   701    0.49394   15   15    0.49594    0.41722  15.9%  36.5   37s
  1579   725    0.44472   13   23    0.49594    0.41813  15.7%  36.3   42s
  1667   756    0.47233   14   17    0.49594    0.41862  15.6%  36.1   46s
  2246   953    0.46638   12   32    0.49594    0.41977  15.4%  35.9   51s
  2267   967    0.46698   14   36    0.49594    0.41977  15.4%  35.6   56s
  2399  1019    0.42476   20   21    0.49594    0.41977  15.4%  38.8   60s
H 2590  1030                       0.4959430    0.41977  15.4%  39.4   61s
H 2774  1011                       0.4959430    0.41977  15.4%  40.0   62s
  3293  1040    0.47567   25   16    0.49594    0.42244  14.8%  40.1   65s
H 3534  1025                       0.4959430    0.42436  14.4%  40.6   67s
  3897  1017     cutoff   30         0.49594    0.42687  13.9%  40.3   70s
  4475  1030    0.45637   26   16    0.49594    0.43004  13.3%  39.9   76s
  4886  1063    0.44633   24   24    0.49594    0.43184  12.9%  39.9   80s
H 5164  1107                       0.4959430    0.43337  12.6%  39.4   84s
  5169  1161    0.47103   27   14    0.49594    0.43373  12.5%  39.4   85s
  6166  1490 infeasible   31         0.49594    0.43705  11.9%  39.2   93s
  6351  1534    0.46632   25   14    0.49594    0.43745  11.8%  39.2   96s
  6809  1724    0.45279   24   21    0.49594    0.43912  11.5%  38.9  100s
  7368  1832    0.45785   23   26    0.49594    0.44077  11.1%  38.5  106s
  7702  1983    0.46350   26   20    0.49594    0.44113  11.1%  38.2  110s
  8339  2130    0.46571   25   20    0.49594    0.44382  10.5%  38.0  115s
  9164  2246     cutoff   30         0.49594    0.44579  10.1%  37.7  122s
  9342  2339    0.48924   26   22    0.49594    0.44630  10.0%  37.6  125s
 10324  2466    0.47701   29   16    0.49594    0.44777  9.71%  36.9  133s
 10749  2591    0.47093   29   20    0.49594    0.44825  9.62%  36.8  137s
 11633  2702    0.48618   28   15    0.49594    0.44945  9.37%  36.3  140s
 12821  2852     cutoff   34         0.49594    0.45099  9.06%  35.7  147s
 13455  2964    0.48812   28   13    0.49594    0.45257  8.74%  35.3  154s
 14093  3006    0.48286   27   14    0.49594    0.45327  8.60%  35.1  159s
 14351  3043    0.49172   29   14    0.49594    0.45334  8.59%  35.1  164s
 14740  3100    0.46583   27   19    0.49594    0.45403  8.45%  34.9  167s
 15906  3231     cutoff   32         0.49594    0.45488  8.28%  34.5  173s
 16510  3294     cutoff   27         0.49594    0.45553  8.15%  34.4  175s
 17021  3343 infeasible   37         0.49594    0.45632  7.99%  34.2  181s
 17894  3467    0.46439   24   14    0.49594    0.45687  7.88%  34.0  187s
 18818  3535     cutoff   34         0.49594    0.45709  7.83%  33.8  190s
 19480  3570     cutoff   30         0.49594    0.45824  7.60%  33.6  195s
 20321  3603    0.47375   30   19    0.49594    0.45873  7.50%  33.5  202s
 20329  3657    0.47859   31   17    0.49594    0.45875  7.50%  33.5  205s
 21331  3750    0.48669   31   17    0.49594    0.45968  7.31%  33.2  215s
 22109  3799    0.48326   28   14    0.49594    0.46026  7.20%  33.0  220s
 23073  3867     cutoff   31         0.49594    0.46094  7.06%  32.8  228s
 23692  3884    0.48624   31   15    0.49594    0.46135  6.98%  32.6  230s
 25107  3980    0.47896   30   18    0.49594    0.46246  6.75%  32.2  237s
 25872  4026    0.47703   29   14    0.49594    0.46295  6.65%  32.1  240s
 27041  4067     cutoff   35         0.49594    0.46370  6.50%  31.9  247s
 27686  4080 infeasible   34         0.49594    0.46399  6.44%  31.7  251s
 28228  4102    0.48892   33   15    0.49594    0.46440  6.36%  31.6  255s
 29425  4120    0.47503   29   15    0.49594    0.46520  6.20%  31.4  263s
 29907  4120    0.49512   30   12    0.49594    0.46556  6.13%  31.3  267s
 30283  4134     cutoff   30         0.49594    0.46587  6.06%  31.3  270s
 30759  4143     cutoff   28         0.49594    0.46591  6.06%  31.2  277s
 31427  4155    0.49583   26   22    0.49594    0.46626  5.99%  31.1  280s
 31994  4159    0.48673   28   20    0.49594    0.46677  5.88%  31.0  286s
 33387  4199     cutoff   33         0.49594    0.46754  5.73%  30.7  294s
 33876  4224    0.48202   25   23    0.49594    0.46794  5.65%  30.7  299s
 34554  4220     cutoff   32         0.49594    0.46806  5.62%  30.6  304s
 34745  4220     cutoff   27         0.49594    0.46832  5.57%  30.5  309s
 35173  4197     cutoff   26         0.49594    0.46864  5.50%  30.5  312s
 35968  4196     cutoff   31         0.49594    0.46899  5.44%  30.4  317s
H36003  4196                       0.4959430    0.46900  5.43%  30.4  317s
 36487  4209     cutoff   35         0.49594    0.46920  5.39%  30.3  320s
 37189  4203     cutoff   35         0.49594    0.46977  5.28%  30.2  327s
 37909  4162     cutoff   34         0.49594    0.47001  5.23%  30.1  330s
 39083  4114    0.48482   35   14    0.49594    0.47075  5.08%  29.9  335s
 40501  4109    0.48422   34   14    0.49594    0.47148  4.93%  29.7  342s
 40507  4101    0.48795   35   14    0.49594    0.47149  4.93%  29.7  347s
 41140  4088    0.48326   33   18    0.49594    0.47170  4.89%  29.6  351s
 41684  4079     cutoff   40         0.49594    0.47202  4.82%  29.6  355s
 42955  4025     cutoff   34         0.49594    0.47240  4.75%  29.4  361s
 43755  4028 infeasible   33         0.49594    0.47298  4.63%  29.3  366s
 45021  3976     cutoff   30         0.49594    0.47358  4.51%  29.1  372s
 45734  3956     cutoff   29         0.49594    0.47379  4.47%  29.0  375s
 46964  3891    0.49166   29   11    0.49594    0.47443  4.34%  28.8  383s
 47434  3857    0.48388   37   18    0.49594    0.47469  4.29%  28.8  389s
 48102  3811     cutoff   29         0.49594    0.47495  4.23%  28.7  391s
 48891  3797 infeasible   32         0.49594    0.47537  4.15%  28.7  396s
 49727  3691    0.48595   30   15    0.49594    0.47574  4.07%  28.6  402s
 50411  3619     cutoff   31         0.49594    0.47600  4.02%  28.5  405s
 51706  3561     cutoff   38         0.49594    0.47667  3.89%  28.4  412s
 52286  3534     cutoff   30         0.49594    0.47695  3.83%  28.3  417s
 52868  3440    0.48755   32   15    0.49594    0.47722  3.78%  28.3  421s
 54070  3368    0.48857   39   13    0.49594    0.47784  3.65%  28.2  425s
 55465  3260    0.49156   33   12    0.49594    0.47827  3.56%  28.0  432s
 56489  3140     cutoff   32         0.49594    0.47899  3.42%  27.9  437s
 56999  3110    0.49585   32   13    0.49594    0.47909  3.40%  27.9  440s
 57549  3007    0.49079   31   12    0.49594    0.47939  3.34%  27.9  447s
 58403  2878    0.48904   32   17    0.49594    0.47989  3.24%  27.8  452s
 59101  2743     cutoff   39         0.49594    0.48028  3.16%  27.7  455s
 60771  2554    0.49197   36   13    0.49594    0.48139  2.94%  27.6  462s
 61532  2399 infeasible   35         0.49594    0.48167  2.88%  27.6  465s
 63738  2106 infeasible   38         0.49594    0.48329  2.55%  27.4  473s
 64450  1990    0.48638   33   14    0.49594    0.48371  2.47%  27.4  475s
 65652  1782    0.48554   35   18    0.49594    0.48437  2.33%  27.3  480s
 66905  1529 infeasible   39         0.49594    0.48560  2.09%  27.2  485s
 68062  1235     cutoff   37         0.49594    0.48696  1.81%  27.1  490s
 70069   646    0.49106   36   14    0.49594    0.48919  1.36%  27.0  497s
 70535   399     cutoff   34         0.49594    0.49014  1.17%  26.9  500s

Cutting planes:
  Implied bound: 279
  MIR: 230
  Flow cover: 545
  RLT: 104
  Relax-and-lift: 122

Explored 71605 nodes (1916982 simplex iterations) in 501.11 seconds (294.03 work units)
Thread count was 4 (of 40 available processors)

Solution count 9: 0.495943 0.495943 0.498916 ... 0.691732

Optimal solution found (tolerance 1.00e-04)
Best objective 4.959430129345e-01, best bound 4.959429857257e-01, gap 0.0000%
The objective bound is 0.495943 while the objective upper bound is 0.495943

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.57 (ave)

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