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 2.44522 seconds.
    local lower bound updated to 0.254539
    local upper bound updated to 0.488551

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.607594 seconds.
    local lower bound updated to 0.45731
    local upper bound updated to 0.45731
The Primal step takes 3.05517 (S)
lower bound updated to 0.45731

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.668712
    local lower bound updated to 0.64412

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.64412
    local lower bound updated to 0.64412
The Dual step takes 0.055969 (S)
upper bound updated to 0.64412
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.25759 seconds.
    local lower bound updated to 0.307186
    local upper bound updated to 0.49044

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.25744 seconds.
    local lower bound updated to 0.46517
    local upper bound updated to 0.467179

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.09841 seconds.
    local lower bound updated to 0.46517
    local upper bound updated to 0.466122

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.1058 seconds.
    local lower bound updated to 0.46517
    local upper bound updated to 0.465914

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.54192 seconds.
    local lower bound updated to 0.465914
    local upper bound updated to 0.465914
The Primal step takes 13.2716 (S)
lower bound updated to 0.465914

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.511525
    local lower bound updated to 0.487885

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.503586
    local lower bound updated to 0.489132

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.50098
    local lower bound updated to 0.492475

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.494781
    local lower bound updated to 0.492601

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.493429
    local lower bound updated to 0.492634

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.492634
    local lower bound updated to 0.492634
The Dual step takes 1.81343 (S)
upper bound updated to 0.492634
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.016 seconds.
    local lower bound updated to 0.407928
    local upper bound updated to 0.491345

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.014 seconds.
    local lower bound updated to 0.47019
    local upper bound updated to 0.490515

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.022 seconds.
    local lower bound updated to 0.479629
    local upper bound updated to 0.489427

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0142 seconds.
    local lower bound updated to 0.484611
    local upper bound updated to 0.489244

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0143 seconds.
    local lower bound updated to 0.484611
    local upper bound updated to 0.486865

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0186 seconds.
    local lower bound updated to 0.484611
    local upper bound updated to 0.486226

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0222 seconds.
    local lower bound updated to 0.485746
    local upper bound updated to 0.486224

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0139 seconds.
    local lower bound updated to 0.485913
    local upper bound updated to 0.486219

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.015 seconds.
    local lower bound updated to 0.485913
    local upper bound updated to 0.486216

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0129 seconds.
    local lower bound updated to 0.485913
    local upper bound updated to 0.486143

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0137 seconds.
    local lower bound updated to 0.485913
    local upper bound updated to 0.486052

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0119 seconds.
    local lower bound updated to 0.486052
    local upper bound updated to 0.486052
The Primal step takes 720.237 (S)
lower bound updated to 0.486052

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.505012
    local lower bound updated to 0.486228

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.501223
    local lower bound updated to 0.488193

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.493523
    local lower bound updated to 0.488442

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.493523
    local lower bound updated to 0.489069

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.491937
    local lower bound updated to 0.489346

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.489346
    local lower bound updated to 0.489346
The Dual step takes 9.59844 (S)
upper bound updated to 0.489346
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0189 seconds.
    local lower bound updated to 0.431781
    local upper bound updated to 0.489337

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0179 seconds.
    local lower bound updated to 0.481346
    local upper bound updated to 0.488587

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0157 seconds.
    local lower bound updated to 0.486265
    local upper bound updated to 0.488515

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.022 seconds.
    local lower bound updated to 0.487468
    local upper bound updated to 0.488378

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0175 seconds.
    local lower bound updated to 0.487497
    local upper bound updated to 0.488194

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0231 seconds.
    local lower bound updated to 0.487673
    local upper bound updated to 0.488141

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0204 seconds.
    local lower bound updated to 0.48802
    local upper bound updated to 0.488084

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0247 seconds.
    local lower bound updated to 0.48802
    local upper bound updated to 0.488083

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0189 seconds.
    local lower bound updated to 0.488083
    local upper bound updated to 0.488083
The Primal step takes 540.232 (S)
lower bound updated to 0.488083

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.501623
    local lower bound updated to 0.488083

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.491335
    local lower bound updated to 0.48826

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.489133
    local lower bound updated to 0.488288

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.488288
    local lower bound updated to 0.488288
The Dual step takes 11.6726 (S)
upper bound updated to 0.488288
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0178 seconds.
    local lower bound updated to 0.435836
    local upper bound updated to 0.488288

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0177 seconds.
    local lower bound updated to 0.487571
    local upper bound updated to 0.488287

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0251 seconds.
    local lower bound updated to 0.488254
    local upper bound updated to 0.488287

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0212 seconds.
    local lower bound updated to 0.488254
    local upper bound updated to 0.488283

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0246 seconds.
    local lower bound updated to 0.48827
    local upper bound updated to 0.488282

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0207 seconds.
    local lower bound updated to 0.488282
    local upper bound updated to 0.488282
The Primal step takes 360.167 (S)
lower bound updated to 0.488282

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.498025
    local lower bound updated to 0.488282

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.488282
    local lower bound updated to 0.488282
The Dual step takes 8.34921 (S)
upper bound updated to 0.488282
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0201 seconds.
    local lower bound updated to 0.435836
    local upper bound updated to 0.488282

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0198 seconds.
    local lower bound updated to 0.488282
    local upper bound updated to 0.488282
The time obtain the optimal randomized assortment is 1788.51 (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_60718.log"
The computation time limit for a lower bound is 84208
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 2992 rows, 2286 columns and 9826 nonzeros
Model fingerprint: 0x33a665bf
Variable types: 2221 continuous, 65 integer (65 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 709 rows and 1275 columns
Presolve time: 0.03s
Presolved: 2283 rows, 1011 columns, 8972 nonzeros
Variable types: 948 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.5710004
Found heuristic solution: objective 0.5287946

Root relaxation: objective 3.922943e-01, 236 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    0.39229    0   24    0.52879    0.39229  25.8%     -    0s
H    0     0                       0.5186332    0.39229  24.4%     -    0s
     0     0    0.39291    0   27    0.51863    0.39291  24.2%     -    0s
     0     0    0.39291    0   27    0.51863    0.39291  24.2%     -    0s
H    0     0                       0.5152994    0.41657  19.2%     -    0s
     0     0    0.41657    0   27    0.51530    0.41657  19.2%     -    0s
H    0     0                       0.4974168    0.41657  16.3%     -    0s
     0     0    0.41702    0   26    0.49742    0.41702  16.2%     -    0s
     0     0    0.42272    0   28    0.49742    0.42272  15.0%     -    0s
     0     0    0.42307    0   28    0.49742    0.42307  14.9%     -    0s
     0     0    0.42858    0   27    0.49742    0.42858  13.8%     -    0s
H    0     0                       0.4957530    0.42858  13.5%     -    0s
H    0     0                       0.4954093    0.42906  13.4%     -    0s
     0     0    0.42906    0   28    0.49541    0.42906  13.4%     -    0s
     0     0    0.42999    0   28    0.49541    0.42999  13.2%     -    0s
H    0     0                       0.4935792    0.42999  12.9%     -    0s
H    0     0                       0.4882820    0.42999  11.9%     -    3s
     0     2    0.42999    0   28    0.48828    0.42999  11.9%     -    3s
   347   174    0.48250   12   19    0.48828    0.44160  9.56%  33.8    5s
  1664   725    0.46275   17   10    0.48828    0.44849  8.15%  27.1   10s
  2150   886    0.45957   10   28    0.48828    0.44970  7.90%  25.8   16s
  2199   927    0.45311   21   20    0.48828    0.44970  7.90%  28.2   21s
  2696   985    0.46630   26   12    0.48828    0.44970  7.90%  29.5   26s
  3999   972     cutoff   30         0.48828    0.45337  7.15%  31.5   31s
  4275   980    0.46358   26   14    0.48828    0.45431  6.96%  31.4   36s
  4855  1040    0.48190   29   17    0.48828    0.45512  6.79%  31.5   40s
  6058  1407    0.46827   30   14    0.48828    0.45712  6.38%  32.2   45s
  6665  1595     cutoff   34         0.48828    0.45785  6.23%  32.2   50s
H 6944  1615                       0.4882820    0.45814  6.17%  32.3   52s
  7160  1750    0.46402   24   15    0.48828    0.45829  6.14%  32.2   55s
H 7465  1750                       0.4882820    0.45869  6.06%  32.2   55s
  8012  1902    0.47160   27   19    0.48828    0.45937  5.92%  31.8   60s
H 8191  1902                       0.4882820    0.45938  5.92%  31.7   60s
  8839  2169    0.47927   32    4    0.48828    0.45983  5.83%  31.5   66s
  9697  2373     cutoff   33         0.48828    0.46055  5.68%  31.4   71s
 10663  2652     cutoff   33         0.48828    0.46092  5.60%  31.2   76s
 11978  2910     cutoff   38         0.48828    0.46163  5.46%  31.1   82s
 12453  2992     cutoff   23         0.48828    0.46186  5.41%  31.0   85s
 13455  3183    0.48245   27   15    0.48828    0.46217  5.35%  31.0   90s
 14396  3490    0.47767   33   16    0.48828    0.46258  5.26%  30.8   95s
 15981  3636     cutoff   34         0.48828    0.46352  5.07%  30.6  100s
 17340  3991     cutoff   28         0.48828    0.46400  4.97%  30.5  107s
 17952  4016    0.47267   31   14    0.48828    0.46445  4.88%  30.4  110s
 19078  4367    0.48523   35    8    0.48828    0.46469  4.83%  30.2  116s
 20624  4542    0.48469   31   12    0.48828    0.46515  4.74%  30.0  121s
 21658  4760    0.47136   30   11    0.48828    0.46546  4.67%  29.8  128s
 22623  4871    0.47677   26   16    0.48828    0.46584  4.60%  29.8  130s
 23846  5075    0.47821   31   12    0.48828    0.46637  4.49%  29.6  135s
 25713  5279     cutoff   35         0.48828    0.46683  4.39%  29.3  142s
 26065  5335    0.47397   30   12    0.48828    0.46690  4.38%  29.3  145s
H26692  5436                       0.4882820    0.46696  4.37%  29.2  148s
 27231  5507     cutoff   35         0.48828    0.46710  4.34%  29.1  151s
 28259  5612    0.47955   28   14    0.48828    0.46738  4.28%  29.1  157s
 29100  5697    0.48174   34   14    0.48828    0.46756  4.24%  29.1  161s
 29817  5878    0.47182   32   15    0.48828    0.46771  4.21%  29.0  166s
 30687  5998    0.48332   36   10    0.48828    0.46794  4.17%  28.9  172s
 31443  6069     cutoff   35         0.48828    0.46807  4.14%  28.9  175s
 32873  6155    0.47575   33   10    0.48828    0.46839  4.07%  28.7  180s
 33954  6271    0.48805   33    6    0.48828    0.46863  4.02%  28.7  185s
 35671  6451    0.48235   33   14    0.48828    0.46893  3.96%  28.6  192s
 36262  6510    0.47707   31   16    0.48828    0.46902  3.95%  28.5  195s
 37490  6616     cutoff   30         0.48828    0.46931  3.89%  28.5  201s
 38826  6725    0.48570   33   10    0.48828    0.46950  3.85%  28.4  206s
 40347  6832    0.47741   35   14    0.48828    0.46979  3.79%  28.3  211s
 41555  6908     cutoff   32         0.48828    0.47001  3.74%  28.2  215s
 43050  6974    0.47500   31   18    0.48828    0.47029  3.68%  28.2  220s
 44496  7040    0.48492   36    6    0.48828    0.47048  3.65%  28.1  226s
 45442  7148    0.47470   30   12    0.48828    0.47070  3.60%  28.1  232s
 46687  7199     cutoff   37         0.48828    0.47086  3.57%  28.0  236s
 47825  7227    0.48660   34   12    0.48828    0.47105  3.53%  27.9  240s
 48815  7270     cutoff   33         0.48828    0.47121  3.50%  27.9  246s
 50007  7315    0.48310   38   14    0.48828    0.47133  3.47%  27.8  251s
 51322  7391    0.48792   37    8    0.48828    0.47160  3.42%  27.7  256s
 52845  7445    0.47841   28   16    0.48828    0.47182  3.37%  27.6  261s
 53697  7450    0.47884   33   12    0.48828    0.47195  3.34%  27.6  268s
 54339  7475     cutoff   31         0.48828    0.47197  3.34%  27.5  270s
 55677  7514    0.47436   32   14    0.48828    0.47226  3.28%  27.5  275s
 56851  7534     cutoff   36         0.48828    0.47236  3.26%  27.5  280s
 58059  7566     cutoff   26         0.48828    0.47257  3.22%  27.4  286s
 59047  7619    0.48411   27    8    0.48828    0.47275  3.18%  27.4  290s
 60769  7585    0.47642   33   14    0.48828    0.47295  3.14%  27.3  296s
 61536  7605     cutoff   29         0.48828    0.47306  3.12%  27.3  301s
 62890  7607    0.48375   36    8    0.48828    0.47331  3.07%  27.2  306s
 63999  7587    0.48555   32   10    0.48828    0.47344  3.04%  27.2  311s
 65377  7584    0.48692   32    6    0.48828    0.47362  3.00%  27.2  316s
 66670  7552 infeasible   37         0.48828    0.47378  2.97%  27.1  322s
 67322  7562    0.48601   34   10    0.48828    0.47382  2.96%  27.1  327s
 67831  7561    0.48245   33   12    0.48828    0.47394  2.94%  27.1  330s
 68971  7548    0.48450   33   10    0.48828    0.47410  2.90%  27.1  335s
 70068  7528    0.47670   31   12    0.48828    0.47420  2.88%  27.0  341s
 71459  7490    0.47583   30   16    0.48828    0.47434  2.86%  27.0  345s
 73050  7441    0.48385   38   18    0.48828    0.47457  2.81%  26.9  350s
 74989  7408    0.48453   29   10    0.48828    0.47484  2.75%  26.9  357s
 76156  7350    0.47881   30   12    0.48828    0.47495  2.73%  26.8  361s
 78103  7304    0.47894   31   15    0.48828    0.47515  2.69%  26.8  365s
 78575  7249    0.48157   35   14    0.48828    0.47525  2.67%  26.8  370s
 80344  7163     cutoff   39         0.48828    0.47544  2.63%  26.7  375s
 81388  7096 infeasible   35         0.48828    0.47560  2.60%  26.7  380s
 83445  6999    0.48629   30   12    0.48828    0.47586  2.54%  26.6  387s
 84172  6955    0.48502   30   10    0.48828    0.47602  2.51%  26.6  391s
 85155  6871     cutoff   37         0.48828    0.47607  2.50%  26.6  395s
 87215  6732     cutoff   32         0.48828    0.47632  2.45%  26.5  401s
 88339  6630    0.48358   34   14    0.48828    0.47649  2.41%  26.5  405s
H88730  6630                       0.4882820    0.47650  2.41%  26.5  405s
 89845  6515     cutoff   32         0.48828    0.47673  2.37%  26.5  413s
 90349  6479    0.47829   35   14    0.48828    0.47679  2.35%  26.5  415s
 91758  6357     cutoff   30         0.48828    0.47694  2.32%  26.4  420s
 93143  6251    0.48553   36   10    0.48828    0.47718  2.27%  26.4  426s
 94158  6158     cutoff   32         0.48828    0.47730  2.25%  26.4  432s
 94985  6044    0.48686   38   10    0.48828    0.47739  2.23%  26.4  436s
 96189  5902     cutoff   32         0.48828    0.47761  2.19%  26.4  440s
 97652  5754     cutoff   35         0.48828    0.47779  2.15%  26.3  445s
 98342  5677    0.48344   35   12    0.48828    0.47788  2.13%  26.3  450s
 99206  5539    0.48322   35   12    0.48828    0.47807  2.09%  26.3  455s
 100987  5347    0.48515   31   12    0.48828    0.47832  2.04%  26.2  460s
 103170  5071     cutoff   36         0.48828    0.47872  1.96%  26.2  467s
 103594  4950     cutoff   34         0.48828    0.47878  1.95%  26.2  470s
 105465  4607     cutoff   35         0.48828    0.47919  1.86%  26.1  476s
 107291  4406     cutoff   35         0.48828    0.47949  1.80%  26.1  482s
 107731  4296    0.48250   34   12    0.48828    0.47954  1.79%  26.1  485s
 109492  3907     cutoff   34         0.48828    0.47998  1.70%  26.0  491s
 110228  3723    0.48456   33   10    0.48828    0.48015  1.67%  26.0  495s
 111706  3323     cutoff   35         0.48828    0.48053  1.59%  26.0  500s
 113145  3008 infeasible   37         0.48828    0.48089  1.51%  26.0  505s
 114986  2649     cutoff   32         0.48828    0.48148  1.39%  25.9  512s
 115570  2413     cutoff   35         0.48828    0.48163  1.36%  25.9  516s
 116153  2128     cutoff   35         0.48828    0.48199  1.29%  25.9  520s
 118280  1384     cutoff   34         0.48828    0.48339  1.00%  25.8  526s
 119647   179     cutoff   30         0.48828    0.48522  0.63%  25.7  530s

Cutting planes:
  Implied bound: 290
  MIR: 203
  Flow cover: 518
  RLT: 74
  Relax-and-lift: 86

Explored 120613 nodes (3086585 simplex iterations) in 530.92 seconds (502.83 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.488282 0.488282 0.488282 ... 0.528795

Optimal solution found (tolerance 1.00e-04)
Best objective 4.882820475961e-01, best bound 4.882820330770e-01, gap 0.0000%
The objective bound is 0.488282 while the objective upper bound is 0.488282

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        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.46 (ave)

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