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 0.253388 seconds.
    local lower bound updated to 0.214206
    local upper bound updated to 0.350352

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.27589 seconds.
    local lower bound updated to 0.350352
    local upper bound updated to 0.350352
The Primal step takes 0.531795 (S)
lower bound updated to 0.350352

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.49185
    local lower bound updated to 0.49185
The Dual step takes 0.0305265 (S)
upper bound updated to 0.49185
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.48242 seconds.
    local lower bound updated to 0.256008
    local upper bound updated to 0.359419

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.19055 seconds.
    local lower bound updated to 0.351556
    local upper bound updated to 0.354403

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.776 seconds.
    local lower bound updated to 0.353551
    local upper bound updated to 0.353951

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.66904 seconds.
    local lower bound updated to 0.353951
    local upper bound updated to 0.353951
The Primal step takes 22.1257 (S)
lower bound updated to 0.353951

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.453365
    local lower bound updated to 0.417557

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.423969
    local lower bound updated to 0.423969
The Dual step takes 0.156126 (S)
upper bound updated to 0.423969
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 15.7158 seconds.
    local lower bound updated to 0.29903
    local upper bound updated to 0.377498

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 10.0398 seconds.
    local lower bound updated to 0.363413
    local upper bound updated to 0.377062

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.36746 seconds.
    local lower bound updated to 0.363413
    local upper bound updated to 0.364901

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.89179 seconds.
    local lower bound updated to 0.363413
    local upper bound updated to 0.364763

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 9.34314 seconds.
    local lower bound updated to 0.363413
    local upper bound updated to 0.364499

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.8909 seconds.
    local lower bound updated to 0.363413
    local upper bound updated to 0.364343

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.02447 seconds.
    local lower bound updated to 0.364057
    local upper bound updated to 0.364281

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 10.4257 seconds.
    local lower bound updated to 0.364281
    local upper bound updated to 0.364281
The Primal step takes 75.723 (S)
lower bound updated to 0.364281

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.437849
    local lower bound updated to 0.385784

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.437849
    local lower bound updated to 0.390578

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.409873
    local lower bound updated to 0.393833

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.397384
    local lower bound updated to 0.394955

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.394955
    local lower bound updated to 0.394955
The Dual step takes 1.66727 (S)
upper bound updated to 0.394955
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 18.9343 seconds.
    local lower bound updated to 0.331492
    local upper bound updated to 0.391476

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.98909 seconds.
    local lower bound updated to 0.371701
    local upper bound updated to 0.389849

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 18.4397 seconds.
    local lower bound updated to 0.38067
    local upper bound updated to 0.388563

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 20.0419 seconds.
    local lower bound updated to 0.381546
    local upper bound updated to 0.388526

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 46.6359 seconds.
    local lower bound updated to 0.383176
    local upper bound updated to 0.387899

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.81374 seconds.
    local lower bound updated to 0.383176
    local upper bound updated to 0.386756

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 26.8187 seconds.
    local lower bound updated to 0.383176
    local upper bound updated to 0.386653

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 23.8839 seconds.
    local lower bound updated to 0.383176
    local upper bound updated to 0.385934

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 16.4865 seconds.
    local lower bound updated to 0.383176
    local upper bound updated to 0.385748

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 43.6681 seconds.
    local lower bound updated to 0.384488
    local upper bound updated to 0.385719

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0189 seconds.
    local lower bound updated to 0.384837
    local upper bound updated to 0.385673

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0196 seconds.
    local lower bound updated to 0.385229
    local upper bound updated to 0.38563

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0193 seconds.
    local lower bound updated to 0.385265
    local upper bound updated to 0.385619

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0156 seconds.
    local lower bound updated to 0.385484
    local upper bound updated to 0.385604

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0158 seconds.
    local lower bound updated to 0.385515
    local upper bound updated to 0.385595

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.0201 seconds.
    local lower bound updated to 0.385531
    local upper bound updated to 0.38558

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 60.0176 seconds.
    local lower bound updated to 0.385535
    local upper bound updated to 0.385579

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 46.4806 seconds.
    local lower bound updated to 0.385571
    local upper bound updated to 0.385579
The Primal step takes 694.41 (S)
lower bound updated to 0.385571

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.417425
    local lower bound updated to 0.385579

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.40679
    local lower bound updated to 0.386712

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.393216
    local lower bound updated to 0.386728

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.39265
    local lower bound updated to 0.386824

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.391875
    local lower bound updated to 0.3882

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.391285
    local lower bound updated to 0.388213

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.391111
    local lower bound updated to 0.388364

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.391111
    local lower bound updated to 0.388525

    ++ RESTRICTED DUAL ITERATION 9 ++
    local upper bound updated to 0.388525
    local lower bound updated to 0.388525
The Dual step takes 41.0565 (S)
upper bound updated to 0.388525
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 23.2915 seconds.
    local lower bound updated to 0.339223
    local upper bound updated to 0.388525

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0293 seconds.
    local lower bound updated to 0.381224
    local upper bound updated to 0.388229

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0258 seconds.
    local lower bound updated to 0.386786
    local upper bound updated to 0.388164

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0326 seconds.
    local lower bound updated to 0.387106
    local upper bound updated to 0.388008

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.024 seconds.
    local lower bound updated to 0.387292
    local upper bound updated to 0.387935

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0223 seconds.
    local lower bound updated to 0.387292
    local upper bound updated to 0.387917

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0168 seconds.
    local lower bound updated to 0.387683
    local upper bound updated to 0.387915

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0245 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387903

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0172 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387884

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0249 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387877

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0269 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387876

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0198 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387873

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0202 seconds.
    local lower bound updated to 0.387738
    local upper bound updated to 0.387866

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0224 seconds.
    local lower bound updated to 0.387782
    local upper bound updated to 0.387861

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0307 seconds.
    local lower bound updated to 0.387782
    local upper bound updated to 0.387857

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.0318 seconds.
    local lower bound updated to 0.387782
    local upper bound updated to 0.387854

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 60.0276 seconds.
    local lower bound updated to 0.387854
    local upper bound updated to 0.387854
The Primal step takes 983.833 (S)
lower bound updated to 0.387854

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.415795
    local lower bound updated to 0.387911

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.391404
    local lower bound updated to 0.387957

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.391404
    local lower bound updated to 0.387995

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.38889
    local lower bound updated to 0.388005

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.38889
    local lower bound updated to 0.388006

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.388752
    local lower bound updated to 0.388013

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.388013
    local lower bound updated to 0.388013
The Dual step takes 47.2927 (S)
upper bound updated to 0.388013
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0352 seconds.
    local lower bound updated to 0.35209
    local upper bound updated to 0.388013

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0275 seconds.
    local lower bound updated to 0.387817
    local upper bound updated to 0.387991

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0415 seconds.
    local lower bound updated to 0.387941
    local upper bound updated to 0.387991

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0333 seconds.
    local lower bound updated to 0.387941
    local upper bound updated to 0.387986

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0315 seconds.
    local lower bound updated to 0.387941
    local upper bound updated to 0.387976

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0337 seconds.
    local lower bound updated to 0.387941
    local upper bound updated to 0.387975

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0329 seconds.
    local lower bound updated to 0.387941
    local upper bound updated to 0.387975

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0361 seconds.
    local lower bound updated to 0.387968
    local upper bound updated to 0.387975
The Primal step takes 480.383 (S)
lower bound updated to 0.387968

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.415669
    local lower bound updated to 0.387975

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.390727
    local lower bound updated to 0.387975

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.387975
    local lower bound updated to 0.387975
The Dual step takes 29.205 (S)
upper bound updated to 0.387975
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0285 seconds.
    local lower bound updated to 0.348277
    local upper bound updated to 0.387975

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0361 seconds.
    local lower bound updated to 0.38796
    local upper bound updated to 0.387975

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0396 seconds.
    local lower bound updated to 0.387965
    local upper bound updated to 0.387975
The time obtain the optimal randomized assortment is 2556.56 (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_60.000000_62618.log"
The computation time limit for a lower bound is 83430
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 4544 rows, 3470 columns and 14961 nonzeros
Model fingerprint: 0xa0a901af
Variable types: 3405 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 1043 rows and 1955 columns
Presolve time: 0.06s
Presolved: 3501 rows, 1515 columns, 13720 nonzeros
Variable types: 1452 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.5043650
Found heuristic solution: objective 0.4573413

Root relaxation: objective 2.749764e-01, 394 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    0.27498    0   26    0.45734    0.27498  39.9%     -    0s
     0     0    0.27827    0   30    0.45734    0.27827  39.2%     -    0s
H    0     0                       0.4377067    0.27827  36.4%     -    0s
     0     0    0.27827    0   30    0.43771    0.27827  36.4%     -    0s
     0     0    0.30619    0   30    0.43771    0.30619  30.0%     -    0s
H    0     0                       0.4001553    0.30619  23.5%     -    0s
     0     0    0.30661    0   30    0.40016    0.30661  23.4%     -    0s
     0     0    0.32540    0   32    0.40016    0.32540  18.7%     -    0s
H    0     0                       0.3969501    0.32540  18.0%     -    1s
H    0     0                       0.3964150    0.32612  17.7%     -    1s
     0     0    0.32612    0   33    0.39641    0.32612  17.7%     -    1s
H    0     0                       0.3961665    0.32861  17.1%     -    1s
     0     0    0.32861    0   32    0.39617    0.32861  17.1%     -    1s
H    0     0                       0.3957880    0.32861  17.0%     -    1s
H    0     0                       0.3927340    0.32892  16.2%     -    1s
     0     0    0.32892    0   33    0.39273    0.32892  16.2%     -    1s
     0     0    0.32930    0   33    0.39273    0.32930  16.2%     -    1s
H    0     0                       0.3879747    0.32930  15.1%     -    6s
     0     2    0.32930    0   33    0.38797    0.32930  15.1%     -    6s
H   52    51                       0.3879378    0.33473  13.7%   122    7s
   100    76    0.34111    5   25    0.38794    0.33723  13.1%  94.3   11s
   200   125    0.36703   10   10    0.38794    0.33905  12.6%  67.4   15s
H  324   174                       0.3879378    0.33919  12.6%  63.4   15s
   498   216     cutoff   12         0.38794    0.34557  10.9%  60.8   20s
H  535   232                       0.3879378    0.34557  10.9%  62.7   21s
   986   338    0.38494   12   14    0.38794    0.35130  9.44%  58.1   25s
  2294   590    0.38627   15   10    0.38794    0.35633  8.15%  49.5   34s
  2322   606    0.38233   12   16    0.38794    0.35636  8.14%  49.4   35s
  2596   626    0.36937   12   16    0.38794    0.35713  7.94%  48.8   42s
  3101   732    0.37569   11   16    0.38794    0.35837  7.62%  47.8   45s
  3751   825    0.37916   15   14    0.38794    0.35993  7.22%  46.1   51s
  4180   847    0.36686   14   33    0.38794    0.36071  7.02%  45.4   56s
  4198   859    0.37907   15   34    0.38794    0.36071  7.02%  45.2   62s
  4400   938    0.36071   23   19    0.38794    0.36071  7.02%  48.3   65s
  4637   939    0.37303   27   12    0.38794    0.36071  7.02%  48.7   70s
  4925   895    0.36548   22   27    0.38794    0.36071  7.02%  48.8   75s
H 5163   818                       0.3879378    0.36071  7.02%  49.3   77s
  5490   797    0.36451   21   19    0.38794    0.36071  7.02%  49.4   82s
H 5554   741                       0.3879378    0.36071  7.02%  49.4   83s
  5796   696    0.37829   28   13    0.38794    0.36071  7.02%  49.3   86s
  5979   676    0.36180   25   18    0.38794    0.36071  7.02%  49.3   91s
  6080   679    0.37118   26   19    0.38794    0.36071  7.02%  49.4   95s
  6760   676    0.36394   23   18    0.38794    0.36071  7.02%  49.4  101s
  7369   772    0.37404   31   18    0.38794    0.36168  6.77%  49.4  106s
  7545   803    0.37962   29   17    0.38794    0.36195  6.70%  49.4  110s
  8555   890    0.37014   19   27    0.38794    0.36394  6.19%  49.2  117s
  9021   948    0.37750   23   20    0.38794    0.36487  5.95%  49.6  121s
  9374   961    0.38240   28   14    0.38794    0.36537  5.82%  49.6  126s
H 9491   961                       0.3879378    0.36540  5.81%  49.6  126s
  9862  1006    0.37593   28   16    0.38794    0.36605  5.64%  49.5  131s
 10017  1020    0.38017   28   16    0.38794    0.36636  5.56%  49.5  137s
 10415  1064    0.38088   27   14    0.38794    0.36671  5.47%  49.4  140s
 11252  1080     cutoff   31         0.38794    0.36779  5.19%  49.4  146s
 11605  1080    0.38587   27   18    0.38794    0.36795  5.15%  49.3  150s
 12436  1085    0.37711   26   15    0.38794    0.36934  4.80%  49.4  157s
 12896  1107    0.38301   26   21    0.38794    0.36969  4.70%  49.5  161s
 13416  1105     cutoff   28         0.38794    0.37031  4.54%  49.3  165s
 13865  1103     cutoff   27         0.38794    0.37081  4.42%  49.3  170s
 15113  1080    0.37656   26   18    0.38794    0.37196  4.12%  49.1  176s
 16099  1036    0.37984   27   14    0.38794    0.37283  3.89%  48.9  183s
 16734   986     cutoff   29         0.38794    0.37359  3.70%  48.8  186s
 17614   946    0.37985   23   20    0.38794    0.37415  3.55%  48.6  190s
 19139   812     cutoff   29         0.38794    0.37589  3.11%  48.1  195s
 20583   596     cutoff   29         0.38794    0.37792  2.58%  47.7  200s
 21861   244     cutoff   29         0.38794    0.37986  2.08%  47.2  205s

Cutting planes:
  Implied bound: 491
  MIR: 222
  Flow cover: 626
  RLT: 106
  Relax-and-lift: 161

Explored 22941 nodes (1072041 simplex iterations) in 205.73 seconds (180.56 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.387938 0.387938 0.387938 ... 0.400155

Optimal solution found (tolerance 1.00e-04)
Best objective 3.879377859417e-01, best bound 3.879377859417e-01, gap 0.0000%
The objective bound is 0.387938 while the objective upper bound is 0.387938

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.52 (ave)

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