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 0.34119 seconds.
    local lower bound updated to 0.275283
    local upper bound updated to 0.5273

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.4183 seconds.
    local lower bound updated to 0.520009
    local upper bound updated to 0.520009
The Primal step takes 0.761626 (S)
lower bound updated to 0.520009

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.645397
    local lower bound updated to 0.639176

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.639176
    local lower bound updated to 0.639176
The Dual step takes 0.0286377 (S)
upper bound updated to 0.639176
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.51995 seconds.
    local lower bound updated to 0.36901
    local upper bound updated to 0.547312

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.36796 seconds.
    local lower bound updated to 0.499797
    local upper bound updated to 0.54377

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.60674 seconds.
    local lower bound updated to 0.527897
    local upper bound updated to 0.541052

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.3544 seconds.
    local lower bound updated to 0.536643
    local upper bound updated to 0.537585

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 7.98189 seconds.
    local lower bound updated to 0.536643
    local upper bound updated to 0.53685

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.64877 seconds.
    local lower bound updated to 0.53685
    local upper bound updated to 0.53685
The Primal step takes 32.4904 (S)
lower bound updated to 0.53685

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.602818
    local lower bound updated to 0.56674

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.5878
    local lower bound updated to 0.57941

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.581959
    local lower bound updated to 0.579709

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.579812
    local lower bound updated to 0.579746

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.579746
    local lower bound updated to 0.579746
The Dual step takes 0.725729 (S)
upper bound updated to 0.579746
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 44.7702 seconds.
    local lower bound updated to 0.483906
    local upper bound updated to 0.577907

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 8.538 seconds.
    local lower bound updated to 0.534074
    local upper bound updated to 0.571793

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.26321 seconds.
    local lower bound updated to 0.543051
    local upper bound updated to 0.566854

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 36.5436 seconds.
    local lower bound updated to 0.555046
    local upper bound updated to 0.561703

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 23.7692 seconds.
    local lower bound updated to 0.555046
    local upper bound updated to 0.560681

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 20.3797 seconds.
    local lower bound updated to 0.555046
    local upper bound updated to 0.559508

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 28.1326 seconds.
    local lower bound updated to 0.555046
    local upper bound updated to 0.558671

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 31.7892 seconds.
    local lower bound updated to 0.555222
    local upper bound updated to 0.557155

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 21.9937 seconds.
    local lower bound updated to 0.555222
    local upper bound updated to 0.556542

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 28.0063 seconds.
    local lower bound updated to 0.55591
    local upper bound updated to 0.55651

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 33.9586 seconds.
    local lower bound updated to 0.556309
    local upper bound updated to 0.556495

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 35.5437 seconds.
    local lower bound updated to 0.556332
    local upper bound updated to 0.556484

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 35.8816 seconds.
    local lower bound updated to 0.556484
    local upper bound updated to 0.556484
The Primal step takes 352.614 (S)
lower bound updated to 0.556484

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.581233
    local lower bound updated to 0.560059

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.577205
    local lower bound updated to 0.562845

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.574024
    local lower bound updated to 0.566629

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.570521
    local lower bound updated to 0.566655

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.567946
    local lower bound updated to 0.566726

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.566796
    local lower bound updated to 0.566731

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.566731
    local lower bound updated to 0.566731
The Dual step takes 8.94587 (S)
upper bound updated to 0.566731
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 110.083 seconds.
    local lower bound updated to 0.513373
    local upper bound updated to 0.565687

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 29.7778 seconds.
    local lower bound updated to 0.542077
    local upper bound updated to 0.563549

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 89.7464 seconds.
    local lower bound updated to 0.557083
    local upper bound updated to 0.561393

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.023 seconds.
    local lower bound updated to 0.559621
    local upper bound updated to 0.561197

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.483 seconds.
    local lower bound updated to 0.560178
    local upper bound updated to 0.561161

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 94.4404 seconds.
    local lower bound updated to 0.56056
    local upper bound updated to 0.561091

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 119.698 seconds.
    local lower bound updated to 0.560987
    local upper bound updated to 0.561067

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 115.105 seconds.
    local lower bound updated to 0.561032
    local upper bound updated to 0.561062

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 108.298 seconds.
    local lower bound updated to 0.561062
    local upper bound updated to 0.561062
The Primal step takes 967.71 (S)
lower bound updated to 0.561062

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.572887
    local lower bound updated to 0.561062

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.570511
    local lower bound updated to 0.562749

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.566487
    local lower bound updated to 0.563291

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.564156
    local lower bound updated to 0.563399

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.563399
    local lower bound updated to 0.563399
The Dual step takes 10.7056 (S)
upper bound updated to 0.563399
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 104.854 seconds.
    local lower bound updated to 0.519812
    local upper bound updated to 0.563084

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 122.926 seconds.
    local lower bound updated to 0.557114
    local upper bound updated to 0.562557

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.560434
    local upper bound updated to 0.562524

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.560434
    local upper bound updated to 0.562441

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.560551
    local upper bound updated to 0.562226

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.032 seconds.
    local lower bound updated to 0.5617
    local upper bound updated to 0.562202

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.561718
    local upper bound updated to 0.562132

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.5618
    local upper bound updated to 0.562075

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.5618
    local upper bound updated to 0.562064

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.561951
    local upper bound updated to 0.562046

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.562012
    local upper bound updated to 0.562046

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.562046
    local upper bound updated to 0.562046
The Primal step takes 2228.2 (S)
lower bound updated to 0.562046

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.570528
    local lower bound updated to 0.562067

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.562842
    local lower bound updated to 0.562069

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.562069
    local lower bound updated to 0.562069
The Dual step takes 11.515 (S)
upper bound updated to 0.562069
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.525001
    local upper bound updated to 0.562069

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.562069
    local upper bound updated to 0.562069
The Primal step takes 400.07 (S)
lower bound updated to 0.562069

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.57051
    local lower bound updated to 0.562069

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.562069
    local lower bound updated to 0.562069
The Dual step takes 7.89798 (S)
upper bound updated to 0.562069
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.525001
    local upper bound updated to 0.562069

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.033 seconds.
    local lower bound updated to 0.562069
    local upper bound updated to 0.562069
The time obtain the optimal randomized assortment is 4421.75 (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_200.000000_206516.log"
The computation time limit for a lower bound is 81573
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 2960 rows, 2398 columns and 9489 nonzeros
Model fingerprint: 0xda6badfb
Variable types: 2341 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 758 rows and 1458 columns
Presolve time: 0.04s
Presolved: 2202 rows, 940 columns, 8596 nonzeros
Variable types: 885 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6346139
Found heuristic solution: objective 0.6318905
Found heuristic solution: objective 0.5933621

Root relaxation: objective 4.107927e-01, 317 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    0.41079    0   22    0.59336    0.41079  30.8%     -    0s
     0     0    0.41637    0   25    0.59336    0.41637  29.8%     -    0s
H    0     0                       0.5854635    0.41637  28.9%     -    0s
     0     0    0.47239    0   28    0.58546    0.47239  19.3%     -    0s
     0     0    0.47273    0   28    0.58546    0.47273  19.3%     -    0s
H    0     0                       0.5769748    0.48465  16.0%     -    0s
     0     0    0.48465    0   27    0.57697    0.48465  16.0%     -    0s
H    0     0                       0.5748746    0.48465  15.7%     -    0s
     0     0    0.48617    0   28    0.57487    0.48617  15.4%     -    0s
     0     0    0.48978    0   30    0.57487    0.48978  14.8%     -    0s
     0     0    0.48992    0   28    0.57487    0.48992  14.8%     -    0s
     0     0    0.49079    0   28    0.57487    0.49079  14.6%     -    0s
H    0     0                       0.5637241    0.49079  12.9%     -    2s
     0     2    0.49079    0   28    0.56372    0.49079  12.9%     -    2s
H  114    98                       0.5634897    0.49297  12.5%  42.4    3s
H  220   151                       0.5630111    0.49297  12.4%  32.9    3s
H  330   193                       0.5627471    0.50039  11.1%  31.2    3s
H  400   233                       0.5624807    0.50039  11.0%  30.4    4s
H  408   233                       0.5620687    0.50039  11.0%  30.2    4s
   493   271    0.52215   10   17    0.56207    0.50666  9.86%  29.9    5s
  1644   687    0.54506    9   17    0.56207    0.51377  8.59%  25.6   10s
  2081   786    0.51549   15   29    0.56207    0.51549  8.29%  26.0   15s
  2781   982    0.52005   21   21    0.56207    0.51549  8.29%  28.1   20s
  3479  1042    0.54289   27   13    0.56207    0.51946  7.58%  28.3   25s
  4832  1127    0.55024   28   14    0.56207    0.52373  6.82%  28.4   30s
  5395  1298    0.54416   28   12    0.56207    0.52524  6.55%  28.2   35s
  6502  1666    0.54150   23   17    0.56207    0.52699  6.24%  28.1   41s
  7392  1838    0.55315   28   16    0.56207    0.52797  6.07%  27.9   46s
  8564  2192    0.56088   31    8    0.56207    0.52919  5.85%  27.8   50s
  9832  2492    0.55196   25   14    0.56207    0.53060  5.60%  27.5   56s
 10806  2784    0.54980   27   18    0.56207    0.53145  5.45%  27.4   60s
 12898  2974    0.55104   26   13    0.56207    0.53266  5.23%  26.8   65s
 14196  3253    0.55002   28   19    0.56207    0.53343  5.10%  26.6   71s
 15635  3528    0.55087   30   14    0.56207    0.53408  4.98%  26.4   75s
 17841  3861    0.55021   25   15    0.56207    0.53498  4.82%  26.1   80s
 19276  4007    0.55921   28   10    0.56207    0.53567  4.70%  26.0   85s
 21674  4362     cutoff   28         0.56207    0.53663  4.53%  25.8   92s
 22615  4570    0.54861   35   12    0.56207    0.53703  4.45%  25.6   95s
 24704  4791     cutoff   27         0.56207    0.53781  4.32%  25.5  100s
 26686  4960    0.54935   32   10    0.56207    0.53843  4.21%  25.3  105s
 28649  5176    0.55882   34   10    0.56207    0.53911  4.08%  25.1  111s
 30635  5280     cutoff   35         0.56207    0.53968  3.98%  25.0  115s
 32270  5359     cutoff   32         0.56207    0.54016  3.90%  24.9  122s
H32663  5359                       0.5620687    0.54018  3.89%  24.9  122s
 32814  5408    0.55626   29   12    0.56207    0.54033  3.87%  24.9  125s
H32903  5408                       0.5620687    0.54036  3.86%  24.9  125s
H33104  5408                       0.5620686    0.54036  3.86%  24.9  125s
 35077  5538     cutoff   28         0.56207    0.54094  3.76%  24.7  130s
 36722  5595     cutoff   35         0.56207    0.54136  3.68%  24.6  135s
H37221  5605                       0.5620686    0.54154  3.65%  24.6  136s
 38834  5653    0.55037   32   10    0.56207    0.54184  3.60%  24.5  140s
 41423  5763    0.55931   37   10    0.56207    0.54251  3.48%  24.4  147s
 42914  5770    0.54793   34   10    0.56207    0.54288  3.41%  24.4  150s
 44555  5792     cutoff   36         0.56207    0.54328  3.34%  24.3  156s
H44736  5792                       0.5620686    0.54329  3.34%  24.3  156s
 45927  5827     cutoff   28         0.56207    0.54356  3.29%  24.2  161s
 47476  5844    0.56196   34   10    0.56207    0.54393  3.23%  24.1  167s
 48859  5887     cutoff   30         0.56207    0.54434  3.15%  24.1  171s
 49889  5897    0.56106   33    9    0.56207    0.54452  3.12%  24.1  176s
 51101  5891    0.56118   28   12    0.56207    0.54470  3.09%  24.0  180s
 52846  5887    0.54862   29   17    0.56207    0.54509  3.02%  24.0  185s
 55646  5895     cutoff   32         0.56207    0.54574  2.91%  23.9  190s
 57663  5884    0.56073   34    8    0.56207    0.54607  2.85%  23.8  195s
 59463  5831     cutoff   39         0.56207    0.54642  2.78%  23.8  200s
 61423  5800     cutoff   35         0.56207    0.54682  2.71%  23.7  205s
 63199  5744    0.55361   34   10    0.56207    0.54717  2.65%  23.7  210s
 64979  5664    0.55440   31   10    0.56207    0.54756  2.58%  23.6  216s
 66808  5537    0.55757   32   10    0.56207    0.54789  2.52%  23.6  220s
 68144  5447    0.55251   30   12    0.56207    0.54817  2.47%  23.5  225s
 69776  5345    0.56146   30   11    0.56207    0.54850  2.41%  23.5  230s
 72335  5144    0.55174   29   14    0.56207    0.54904  2.32%  23.4  236s
 74631  4866     cutoff   29         0.56207    0.54958  2.22%  23.4  241s
 76593  4718    0.55425   31   10    0.56207    0.54999  2.15%  23.3  246s
H76725  4717                       0.5620686    0.55001  2.14%  23.3  247s
H76728  4717                       0.5620686    0.55001  2.14%  23.3  247s
 77251  4543    0.55143   29   15    0.56207    0.55021  2.11%  23.3  250s
 79755  4265     cutoff   37         0.56207    0.55079  2.01%  23.2  255s
 81274  3973     cutoff   29         0.56207    0.55125  1.92%  23.2  261s
 83393  3625 infeasible   31         0.56207    0.55185  1.82%  23.1  265s
 86377  3116     cutoff   34         0.56207    0.55274  1.66%  23.1  270s
 88035  2665    0.56071   33   10    0.56207    0.55350  1.52%  23.0  275s
 90917  1963    0.55758   33   10    0.56207    0.55483  1.29%  22.9  280s
 92307  1516    0.56021   37    4    0.56207    0.55551  1.17%  22.9  285s

Cutting planes:
  Gomory: 1
  Implied bound: 263
  MIR: 160
  Flow cover: 511
  RLT: 93
  Relax-and-lift: 52

Explored 95829 nodes (2171197 simplex iterations) in 289.00 seconds (229.29 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.562069 0.562069 0.562069 ... 0.585463

Optimal solution found (tolerance 1.00e-04)
Best objective 5.620686610816e-01, best bound 5.620686610816e-01, gap 0.0000%
The objective bound is 0.562069 while the objective upper bound is 0.562069

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

        Job resource usage summary 

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

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