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 7.04311 seconds.
    local lower bound updated to 0.294201
    local upper bound updated to 0.582976

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.20926 seconds.
    local lower bound updated to 0.539376
    local upper bound updated to 0.539376
The Primal step takes 11.2555 (S)
lower bound updated to 0.539376

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.661835
    local lower bound updated to 0.645247

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.657285
    local lower bound updated to 0.655293

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.655293
    local lower bound updated to 0.655293
The Dual step takes 0.102218 (S)
upper bound updated to 0.655293
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.7092 seconds.
    local lower bound updated to 0.402117
    local upper bound updated to 0.577833

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 29.8413 seconds.
    local lower bound updated to 0.55894
    local upper bound updated to 0.571598

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 21.6785 seconds.
    local lower bound updated to 0.55894
    local upper bound updated to 0.571572

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 36.6584 seconds.
    local lower bound updated to 0.559077
    local upper bound updated to 0.564673

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 37.8029 seconds.
    local lower bound updated to 0.56189
    local upper bound updated to 0.56382

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 21.5641 seconds.
    local lower bound updated to 0.56189
    local upper bound updated to 0.563124

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 36.7347 seconds.
    local lower bound updated to 0.562797
    local upper bound updated to 0.563036

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 37.3498 seconds.
    local lower bound updated to 0.563036
    local upper bound updated to 0.563036
The Primal step takes 239.361 (S)
lower bound updated to 0.563036

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.637839
    local lower bound updated to 0.59071

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.617557
    local lower bound updated to 0.613051

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.613051
    local lower bound updated to 0.613051
The Dual step takes 0.826637 (S)
upper bound updated to 0.613051
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.022 seconds.
    local lower bound updated to 0.48606
    local upper bound updated to 0.600299

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.08401 seconds.
    local lower bound updated to 0.49017
    local upper bound updated to 0.587672

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 33.8672 seconds.
    local lower bound updated to 0.574654
    local upper bound updated to 0.580523

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 47.9812 seconds.
    local lower bound updated to 0.575646
    local upper bound updated to 0.580325

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 41.663 seconds.
    local lower bound updated to 0.575646
    local upper bound updated to 0.580262

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 57.6632 seconds.
    local lower bound updated to 0.575937
    local upper bound updated to 0.579059

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 62.094 seconds.
    local lower bound updated to 0.577907
    local upper bound updated to 0.578498

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 63.3954 seconds.
    local lower bound updated to 0.577907
    local upper bound updated to 0.578129

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 54.0038 seconds.
    local lower bound updated to 0.577907
    local upper bound updated to 0.578085

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 70.6215 seconds.
    local lower bound updated to 0.577907
    local upper bound updated to 0.578059

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 50.7279 seconds.
    local lower bound updated to 0.577907
    local upper bound updated to 0.578001

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 59.2832 seconds.
    local lower bound updated to 0.578001
    local upper bound updated to 0.578001
The Primal step takes 643.454 (S)
lower bound updated to 0.578001

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.61859
    local lower bound updated to 0.580951

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.613657
    local lower bound updated to 0.594994

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.594994
    local lower bound updated to 0.594994
The Dual step takes 6.02773 (S)
upper bound updated to 0.594994
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.015 seconds.
    local lower bound updated to 0.503698
    local upper bound updated to 0.583164

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 79.2841 seconds.
    local lower bound updated to 0.57454
    local upper bound updated to 0.582289

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.57454
    local upper bound updated to 0.581808

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.013 seconds.
    local lower bound updated to 0.577923
    local upper bound updated to 0.580955

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.577923
    local upper bound updated to 0.580864

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.578589
    local upper bound updated to 0.580538

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.578589
    local upper bound updated to 0.580378

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.578589
    local upper bound updated to 0.580345

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 100.025 seconds.
    local lower bound updated to 0.578619
    local upper bound updated to 0.580153

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.579845
    local upper bound updated to 0.580149

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 100.022 seconds.
    local lower bound updated to 0.579845
    local upper bound updated to 0.580086

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.579845
    local upper bound updated to 0.58001

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 100.029 seconds.
    local lower bound updated to 0.579851
    local upper bound updated to 0.579996

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.579996
    local upper bound updated to 0.579996
The Primal step takes 1379.61 (S)
lower bound updated to 0.579996

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.605642
    local lower bound updated to 0.58082

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.592809
    local lower bound updated to 0.583864

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.590794
    local lower bound updated to 0.584465

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.584466
    local lower bound updated to 0.584465
The Dual step takes 23.5752 (S)
upper bound updated to 0.584466
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.523565
    local upper bound updated to 0.584465

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 73.6231 seconds.
    local lower bound updated to 0.553033
    local upper bound updated to 0.58378

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.577455
    local upper bound updated to 0.582556

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.039 seconds.
    local lower bound updated to 0.5783
    local upper bound updated to 0.582042

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.025 seconds.
    local lower bound updated to 0.5783
    local upper bound updated to 0.581866

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.028 seconds.
    local lower bound updated to 0.580924
    local upper bound updated to 0.58174

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.03 seconds.
    local lower bound updated to 0.580924
    local upper bound updated to 0.581705

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.581303
    local upper bound updated to 0.581642

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.581303
    local upper bound updated to 0.581607

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.58131
    local upper bound updated to 0.581577

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.58131
    local upper bound updated to 0.581535

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 100.03 seconds.
    local lower bound updated to 0.581375
    local upper bound updated to 0.58151

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 100.028 seconds.
    local lower bound updated to 0.58151
    local upper bound updated to 0.58151
The Primal step takes 1274.03 (S)
lower bound updated to 0.58151

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.60748
    local lower bound updated to 0.58151

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.596125
    local lower bound updated to 0.581965

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.581965
    local lower bound updated to 0.581965
The Dual step takes 25.3496 (S)
upper bound updated to 0.581965
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.029 seconds.
    local lower bound updated to 0.527421
    local upper bound updated to 0.581965

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.581108
    local upper bound updated to 0.581735

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.581108
    local upper bound updated to 0.581656

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.031 seconds.
    local lower bound updated to 0.581258
    local upper bound updated to 0.58164

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.029 seconds.
    local lower bound updated to 0.581365
    local upper bound updated to 0.581574

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.581365
    local upper bound updated to 0.581561

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.58148
    local upper bound updated to 0.581554

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.581554
    local upper bound updated to 0.581554
The Primal step takes 800.261 (S)
lower bound updated to 0.581554

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.604475
    local lower bound updated to 0.581554

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.581554
    local lower bound updated to 0.581554
The Dual step takes 28.3537 (S)
upper bound updated to 0.581554
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.527421
    local upper bound updated to 0.581554

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.58152
    local upper bound updated to 0.581546

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.028 seconds.
    local lower bound updated to 0.58152
    local upper bound updated to 0.581543

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.027 seconds.
    local lower bound updated to 0.581543
    local upper bound updated to 0.581543
The time obtain the optimal randomized assortment is 4832.35 (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_100.000000_102118.log"
The computation time limit for a lower bound is 81139
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 2410 rows, 1842 columns and 7991 nonzeros
Model fingerprint: 0xaf43f4dd
Variable types: 1777 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 541 rows and 979 columns
Presolve time: 0.03s
Presolved: 1869 rows, 863 columns, 7227 nonzeros
Variable types: 800 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.7575560
Found heuristic solution: objective 0.7119618

Root relaxation: objective 3.588109e-01, 247 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    0.35881    0   22    0.71196    0.35881  49.6%     -    0s
H    0     0                       0.6353717    0.35881  43.5%     -    0s
H    0     0                       0.6027168    0.35881  40.5%     -    0s
H    0     0                       0.6000517    0.35881  40.2%     -    0s
H    0     0                       0.5889253    0.36806  37.5%     -    0s
     0     0    0.36806    0   34    0.58893    0.36806  37.5%     -    0s
     0     0    0.36806    0   34    0.58893    0.36806  37.5%     -    0s
     0     0    0.40241    0   32    0.58893    0.40241  31.7%     -    0s
     0     0    0.40396    0   33    0.58893    0.40396  31.4%     -    0s
     0     0    0.42526    0   31    0.58893    0.42526  27.8%     -    0s
H    0     0                       0.5832955    0.42526  27.1%     -    0s
     0     0    0.42671    0   31    0.58330    0.42671  26.8%     -    0s
     0     0    0.43109    0   32    0.58330    0.43109  26.1%     -    0s
     0     0    0.43226    0   32    0.58330    0.43226  25.9%     -    0s
     0     0    0.43362    0   34    0.58330    0.43362  25.7%     -    0s
H    0     0                       0.5824296    0.43362  25.5%     -    0s
     0     2    0.43362    0   34    0.58243    0.43362  25.5%     -    2s
   198   164    0.53613   14   19    0.58243    0.44914  22.9%  37.2    5s
H  200   164                       0.5817125    0.44914  22.8%  36.8    5s
H  452   279                       0.5815433    0.45870  21.1%  31.8    6s
   989   490     cutoff    9         0.58154    0.47584  18.2%  29.4   10s
  1971   791    0.53293   14   17    0.58154    0.48426  16.7%  25.9   15s
  2096   804    0.49199   12   32    0.58154    0.48535  16.5%  25.8   20s
  2999   937    0.55933   23   20    0.58154    0.48691  16.3%  29.9   25s
  4094  1011    0.52214   20   23    0.58154    0.49964  14.1%  30.5   30s
  4794  1109     cutoff   30         0.58154    0.50405  13.3%  30.1   35s
H 4822  1134                       0.5815433    0.50405  13.3%  30.1   36s
H 5431  1275                       0.5815433    0.50676  12.9%  30.1   38s
H 5488  1275                       0.5815433    0.50724  12.8%  30.1   38s
  5953  1503    0.57109   36   10    0.58154    0.50968  12.4%  29.9   40s
  6466  1644     cutoff   35         0.58154    0.51128  12.1%  29.5   46s
H 6674  1682                       0.5815433    0.51188  12.0%  29.5   47s
  7019  1840     cutoff   33         0.58154    0.51316  11.8%  29.5   50s
  7721  1957    0.57587   27   14    0.58154    0.51534  11.4%  29.4   55s
  8869  2182    0.57525   29   13    0.58154    0.51769  11.0%  28.9   60s
H 9199  2182                       0.5815433    0.51843  10.9%  28.7   60s
  9389  2283    0.54462   23   18    0.58154    0.51872  10.8%  28.7   65s
 10364  2419    0.53677   32   16    0.58154    0.52126  10.4%  28.4   71s
 11687  2584    0.54325   30   18    0.58154    0.52355  10.0%  28.2   77s
H11715  2584                       0.5815433    0.52360  10.0%  28.2   77s
 12216  2758    0.55936   31   15    0.58154    0.52482  9.75%  28.1   81s
 13254  2872    0.57954   27   14    0.58154    0.52632  9.50%  28.0   86s
 14178  3010    0.56650   25   18    0.58154    0.52748  9.30%  27.8   92s
 15210  3166    0.57151   30   14    0.58154    0.52931  8.98%  27.7   95s
 16694  3226     cutoff   28         0.58154    0.53155  8.60%  27.6  100s
 17563  3322     cutoff   29         0.58154    0.53276  8.39%  27.6  106s
 18734  3443     cutoff   28         0.58154    0.53446  8.10%  27.4  110s
 20438  3531    0.57329   32   15    0.58154    0.53644  7.76%  27.1  116s
 21564  3588    0.56613   30   22    0.58154    0.53785  7.51%  26.9  121s
 22962  3621    0.55386   29   18    0.58154    0.53941  7.25%  26.8  125s
 24281  3647    0.56242   32   18    0.58154    0.54120  6.94%  26.7  131s
 25639  3710    0.55318   28   18    0.58154    0.54216  6.77%  26.5  136s
 26393  3742    0.57265   29   20    0.58154    0.54289  6.65%  26.5  142s
 27474  3734    0.55704   24   19    0.58154    0.54368  6.51%  26.4  146s
 28503  3728    0.56842   34   17    0.58154    0.54488  6.30%  26.3  150s
 29626  3704    0.57511   26   18    0.58154    0.54595  6.12%  26.2  155s
 31263  3667     cutoff   28         0.58154    0.54749  5.86%  26.0  161s
H31790  3663                       0.5815433    0.54775  5.81%  26.0  164s
 31808  3658    0.57409   31    8    0.58154    0.54779  5.80%  26.0  166s
 33014  3600    0.56779   29   17    0.58154    0.54897  5.60%  25.9  171s
 34231  3538     cutoff   31         0.58154    0.55014  5.40%  25.8  175s
 35368  3498     cutoff   31         0.58154    0.55117  5.22%  25.6  180s
 36237  3428    0.57372   31   21    0.58154    0.55156  5.16%  25.6  186s
 37841  3262     cutoff   26         0.58154    0.55325  4.87%  25.4  192s
 39056  3230    0.57335   40   10    0.58154    0.55472  4.61%  25.3  196s
 40494  3139     cutoff   28         0.58154    0.55586  4.42%  25.1  201s
 41807  2931    0.56694   25   17    0.58154    0.55727  4.17%  24.9  206s
 43436  2797     cutoff   31         0.58154    0.55860  3.95%  24.8  210s
 44209  2649    0.57212   38   11    0.58154    0.55935  3.82%  24.7  215s
 46465  2451     cutoff   37         0.58154    0.56113  3.51%  24.3  221s
 48284  2277     cutoff   28         0.58154    0.56252  3.27%  24.1  226s
 49318  2079     cutoff   40         0.58154    0.56362  3.08%  23.9  230s
 51695  1769    0.57720   38    6    0.58154    0.56582  2.70%  23.6  236s
 53240  1429    0.57764   41    8    0.58154    0.56740  2.43%  23.4  240s
 56687   179     cutoff   29         0.58154    0.57346  1.39%  22.8  245s

Cutting planes:
  Gomory: 1
  Implied bound: 208
  MIR: 162
  Flow cover: 356
  RLT: 68
  Relax-and-lift: 89

Explored 57322 nodes (1299601 simplex iterations) in 246.10 seconds (190.83 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.581543 0.581543 0.581543 ... 0.635372

Optimal solution found (tolerance 1.00e-04)
Best objective 5.815433242849e-01, best bound 5.815432713378e-01, gap 0.0000%
The objective bound is 0.581543 while the objective upper bound is 0.581543

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.69 (ave)

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