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 0.899893 seconds.
    local lower bound updated to 0.434885
    local upper bound updated to 0.614256

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.63925 seconds.
    local lower bound updated to 0.614256
    local upper bound updated to 0.614256
The Primal step takes 4.54121 (S)
lower bound updated to 0.614256

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.695437
    local lower bound updated to 0.689715

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.689715
    local lower bound updated to 0.689715
The Dual step takes 0.0554897 (S)
upper bound updated to 0.689715
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.946124 seconds.
    local lower bound updated to 0.491537
    local upper bound updated to 0.617788

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.2384 seconds.
    local lower bound updated to 0.616379
    local upper bound updated to 0.617385

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.47903 seconds.
    local lower bound updated to 0.616447
    local upper bound updated to 0.616619

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.84107 seconds.
    local lower bound updated to 0.616618
    local upper bound updated to 0.616619
The Primal step takes 16.5121 (S)
lower bound updated to 0.616618

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.654946
    local lower bound updated to 0.622917

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.648296
    local lower bound updated to 0.644489

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.648254
    local lower bound updated to 0.645489

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.645954
    local lower bound updated to 0.645673

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.645673
    local lower bound updated to 0.645673
The Dual step takes 1.1784 (S)
upper bound updated to 0.645673
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.89789 seconds.
    local lower bound updated to 0.560176
    local upper bound updated to 0.633999

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 24.1472 seconds.
    local lower bound updated to 0.618945
    local upper bound updated to 0.631594

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 24.8272 seconds.
    local lower bound updated to 0.624523
    local upper bound updated to 0.631292

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 68.064 seconds.
    local lower bound updated to 0.629429
    local upper bound updated to 0.630762

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 48.2709 seconds.
    local lower bound updated to 0.629435
    local upper bound updated to 0.630648

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 89.1318 seconds.
    local lower bound updated to 0.630483
    local upper bound updated to 0.630579

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 86.1543 seconds.
    local lower bound updated to 0.630579
    local upper bound updated to 0.630579
The Primal step takes 347.52 (S)
lower bound updated to 0.630579

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.663252
    local lower bound updated to 0.638257

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.644373
    local lower bound updated to 0.638978

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.644373
    local lower bound updated to 0.642079

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.644373
    local lower bound updated to 0.642573

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.642573
    local lower bound updated to 0.642573
The Dual step takes 3.99441 (S)
upper bound updated to 0.642573
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 58.2602 seconds.
    local lower bound updated to 0.592231
    local upper bound updated to 0.639175

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 144.16 seconds.
    local lower bound updated to 0.633043
    local upper bound updated to 0.63852

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.023 seconds.
    local lower bound updated to 0.633302
    local upper bound updated to 0.638283

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 102.175 seconds.
    local lower bound updated to 0.633302
    local upper bound updated to 0.637623

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.024 seconds.
    local lower bound updated to 0.63589
    local upper bound updated to 0.637384

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.636432
    local upper bound updated to 0.637291

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.636432
    local upper bound updated to 0.637211

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.028 seconds.
    local lower bound updated to 0.636432
    local upper bound updated to 0.636955

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.027 seconds.
    local lower bound updated to 0.636432
    local upper bound updated to 0.636944

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.636619
    local upper bound updated to 0.63692

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.027 seconds.
    local lower bound updated to 0.636653
    local upper bound updated to 0.636883

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 200.019 seconds.
    local lower bound updated to 0.636653
    local upper bound updated to 0.636879

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 200.027 seconds.
    local lower bound updated to 0.636703
    local upper bound updated to 0.636871

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.636803
    local upper bound updated to 0.636864

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.636856
    local upper bound updated to 0.636863
The Primal step takes 2705 (S)
lower bound updated to 0.636856

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.655598
    local lower bound updated to 0.636863

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.639309
    local lower bound updated to 0.636863

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.637258
    local lower bound updated to 0.636865

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.637258
    local lower bound updated to 0.636868

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.636868
    local lower bound updated to 0.636868
The Dual step takes 12.999 (S)
upper bound updated to 0.636868
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.019 seconds.
    local lower bound updated to 0.603564
    local upper bound updated to 0.636868

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.636842
    local upper bound updated to 0.636867

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.025 seconds.
    local lower bound updated to 0.636867
    local upper bound updated to 0.636867
The Primal step takes 600.104 (S)
lower bound updated to 0.636867

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.65572
    local lower bound updated to 0.636867

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.636867
    local lower bound updated to 0.636867
The Dual step takes 7.71336 (S)
upper bound updated to 0.636867
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.603564
    local upper bound updated to 0.636867

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.024 seconds.
    local lower bound updated to 0.636867
    local upper bound updated to 0.636867
The time obtain the optimal randomized assortment is 4099.69 (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_205416.log"
The computation time limit for a lower bound is 81892
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 2480 rows, 2008 columns and 7936 nonzeros
Model fingerprint: 0xee5ea484
Variable types: 1951 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [5e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 639 rows and 1216 columns
Presolve time: 0.02s
Presolved: 1841 rows, 792 columns, 7105 nonzeros
Variable types: 741 continuous, 51 integer (51 binary)
Found heuristic solution: objective 0.6978242
Found heuristic solution: objective 0.6525582

Root relaxation: objective 4.676492e-01, 213 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    0.46765    0   27    0.65256    0.46765  28.3%     -    0s
     0     0    0.48409    0   26    0.65256    0.48409  25.8%     -    0s
H    0     0                       0.6520237    0.48409  25.8%     -    0s
H    0     0                       0.6505475    0.53687  17.5%     -    0s
H    0     0                       0.6490127    0.53687  17.3%     -    0s
     0     0    0.53692    0   24    0.64901    0.53692  17.3%     -    0s
H    0     0                       0.6417960    0.53692  16.3%     -    0s
     0     0    0.53708    0   24    0.64180    0.53708  16.3%     -    0s
     0     0    0.54478    0   27    0.64180    0.54478  15.1%     -    0s
     0     0    0.54635    0   25    0.64180    0.54635  14.9%     -    0s
     0     0    0.55276    0   29    0.64180    0.55276  13.9%     -    0s
     0     0    0.55328    0   30    0.64180    0.55328  13.8%     -    0s
     0     0    0.55489    0   26    0.64180    0.55489  13.5%     -    0s
H    0     0                       0.6377585    0.55489  13.0%     -    1s
     0     2    0.55489    0   26    0.63776    0.55489  13.0%     -    1s
H  234   133                       0.6373796    0.57006  10.6%  31.5    2s
H  320   170                       0.6368672    0.57083  10.4%  33.2    2s
H  352   191                       0.6368671    0.57087  10.4%  33.2    2s
H  633   331                       0.6368671    0.57399  9.87%  31.4    2s
H  862   413                       0.6368671    0.57589  9.57%  29.6    4s
   891   442    0.58094    8   25    0.63687    0.57589  9.57%  29.3    6s
  2117   957    0.61063   13   30    0.63687    0.58155  8.69%  27.8   11s
  2895  1062    0.59040   21   19    0.63687    0.58512  8.13%  31.0   15s
  4477  1046    0.61587   30   15    0.63687    0.59093  7.21%  31.2   20s
  5484  1099    0.63317   30    8    0.63687    0.59297  6.89%  31.2   26s
  5986  1242    0.61070   25   13    0.63687    0.59373  6.77%  31.4   30s
  6696  1444    0.60769   25   12    0.63687    0.59470  6.62%  31.2   35s
  7392  1618    0.60903   26   15    0.63687    0.59561  6.48%  31.2   40s
  8241  1826     cutoff   34         0.63687    0.59648  6.34%  31.2   46s
  8845  1980    0.62198   31   15    0.63687    0.59696  6.27%  31.2   50s
  9539  2188    0.63359   32    8    0.63687    0.59741  6.20%  31.4   56s
 10734  2550     cutoff   39         0.63687    0.59825  6.06%  31.5   60s
 12639  2917     cutoff   34         0.63687    0.59956  5.86%  31.6   65s
 14056  3150    0.61982   31   15    0.63687    0.60044  5.72%  31.7   70s
 15334  3389     cutoff   31         0.63687    0.60116  5.61%  31.8   76s
 16406  3679    0.63553   30    8    0.63687    0.60170  5.52%  31.8   80s
 17647  3943     cutoff   30         0.63687    0.60260  5.38%  31.8   85s
 19745  4257     cutoff   34         0.63687    0.60350  5.24%  32.0   91s
 20852  4431    0.62133   34   15    0.63687    0.60374  5.20%  31.9   96s
 21460  4586    0.63483   30   11    0.63687    0.60415  5.14%  31.9  102s
 22301  4724    0.63619   28    9    0.63687    0.60445  5.09%  32.0  105s
 24436  4920    0.60959   28   18    0.63687    0.60519  4.97%  32.1  111s
 25321  5088    0.63638   33   11    0.63687    0.60544  4.94%  32.1  115s
 26928  5385     cutoff   34         0.63687    0.60590  4.86%  32.1  122s
 28481  5484    0.63537   34    7    0.63687    0.60647  4.77%  32.1  127s
 28892  5535     cutoff   34         0.63687    0.60657  4.76%  32.2  130s
 30996  5805    0.62774   32   13    0.63687    0.60720  4.66%  32.1  136s
 32387  5952     cutoff   37         0.63687    0.60752  4.61%  32.0  141s
 33110  6059    0.63184   33    8    0.63687    0.60780  4.56%  32.0  146s
 34296  6179    0.61872   31   12    0.63687    0.60804  4.53%  32.0  150s
 35778  6327    0.63428   33    8    0.63687    0.60844  4.46%  32.0  156s
 36394  6365    0.63351   32    8    0.63687    0.60860  4.44%  32.0  161s
 37609  6549    0.61358   28   13    0.63687    0.60884  4.40%  32.0  166s
 38912  6683 infeasible   29         0.63687    0.60917  4.35%  31.9  170s
 40674  6840    0.63219   32    9    0.63687    0.60954  4.29%  31.9  176s
 41999  6940    0.62178   29   11    0.63687    0.60983  4.25%  31.9  181s
 43150  7085    0.62192   33   10    0.63687    0.61010  4.20%  31.9  186s
 44690  7204    0.62383   29   14    0.63687    0.61038  4.16%  31.8  191s
 45825  7339    0.62577   30   12    0.63687    0.61063  4.12%  31.8  195s
 47458  7514 infeasible   33         0.63687    0.61087  4.08%  31.7  201s
 48752  7561    0.62218   31   12    0.63687    0.61120  4.03%  31.7  205s
 49682  7617    0.62092   33   16    0.63687    0.61131  4.01%  31.7  210s
 50710  7746    0.63672   31    7    0.63687    0.61143  3.99%  31.7  216s
 51875  7799     cutoff   28         0.63687    0.61164  3.96%  31.7  221s
 52932  7897    0.63673   31    8    0.63687    0.61178  3.94%  31.7  225s
 54842  8049     cutoff   33         0.63687    0.61218  3.88%  31.7  230s
 56423  8147    0.61620   29   13    0.63687    0.61250  3.83%  31.6  236s
 57774  8215     cutoff   29         0.63687    0.61274  3.79%  31.7  241s
 59045  8283    0.61877   26   14    0.63687    0.61290  3.76%  31.6  247s
 60348  8355     cutoff   34         0.63687    0.61319  3.72%  31.6  251s
 61010  8400    0.63654   34    9    0.63687    0.61325  3.71%  31.6  255s
 62649  8481    0.62609   30   11    0.63687    0.61350  3.67%  31.6  261s
 63705  8527    0.62850   27    9    0.63687    0.61367  3.64%  31.6  266s
 64737  8584    0.63060   34   13    0.63687    0.61379  3.62%  31.6  271s
 66939  8645    0.62940   35   10    0.63687    0.61410  3.58%  31.5  275s
 68397  8699 infeasible   34         0.63687    0.61430  3.54%  31.5  281s
 70671  8753     cutoff   31         0.63687    0.61469  3.48%  31.5  286s
 72078  8784    0.63053   37   12    0.63687    0.61487  3.45%  31.5  290s
 73691  8839    0.62547   33   13    0.63687    0.61509  3.42%  31.5  295s
 75357  8868     cutoff   35         0.63687    0.61530  3.39%  31.5  300s
 77541  8890 infeasible   33         0.63687    0.61560  3.34%  31.4  305s
 79206  8889     cutoff   35         0.63687    0.61582  3.30%  31.4  310s
 80763  8889 infeasible   35         0.63687    0.61607  3.27%  31.3  316s
 81772  8883    0.63095   35   13    0.63687    0.61619  3.25%  31.3  320s
 83118  8888     cutoff   35         0.63687    0.61635  3.22%  31.3  326s
 85213  8854 infeasible   30         0.63687    0.61662  3.18%  31.3  331s
 86683  8833    0.62278   32   11    0.63687    0.61689  3.14%  31.2  336s
 87539  8825    0.63441   33    7    0.63687    0.61700  3.12%  31.2  340s
 89329  8807     cutoff   31         0.63687    0.61728  3.08%  31.2  346s
 90768  8789    0.62704   31    8    0.63687    0.61745  3.05%  31.2  350s
 93256  8685     cutoff   37         0.63687    0.61780  2.99%  31.2  355s
 95430  8616     cutoff   34         0.63687    0.61807  2.95%  31.2  360s
 97020  8569    0.63014   34   13    0.63687    0.61828  2.92%  31.1  366s
 98741  8520     cutoff   32         0.63687    0.61857  2.87%  31.1  372s
 99705  8476    0.62625   29   10    0.63687    0.61874  2.85%  31.1  375s
 102143  8375     cutoff   31         0.63687    0.61908  2.79%  31.1  381s
 103792  8297    0.62779   32   11    0.63687    0.61919  2.78%  31.1  385s
 105109  8195     cutoff   33         0.63687    0.61949  2.73%  31.1  391s
 105909  8130    0.62464   31   13    0.63687    0.61958  2.71%  31.1  395s
 107932  7982    0.63006   29   11    0.63687    0.61987  2.67%  31.0  400s
 109594  7881    0.62451   33   14    0.63687    0.62012  2.63%  31.0  405s
 111179  7735    0.63000   31    9    0.63687    0.62027  2.61%  31.0  410s
 113156  7616    0.63546   34    4    0.63687    0.62063  2.55%  31.0  415s
 114695  7455     cutoff   31         0.63687    0.62090  2.51%  31.0  420s
 116662  7261    0.63056   31   11    0.63687    0.62119  2.46%  30.9  425s
 118667  7042    0.63064   30   11    0.63687    0.62148  2.42%  30.9  431s
 119774  6969    0.63682   30    9    0.63687    0.62173  2.38%  30.9  435s
 121351  6769     cutoff   31         0.63687    0.62191  2.35%  30.8  440s
H121666  6769                       0.6368671    0.62192  2.35%  30.8  440s
H121801  6727                       0.6368671    0.62204  2.33%  30.8  442s
 122474  6611    0.63648   36    8    0.63687    0.62218  2.31%  30.8  445s
 124087  6373 infeasible   34         0.63687    0.62248  2.26%  30.8  450s
 126209  5990     cutoff   29         0.63687    0.62282  2.21%  30.8  455s
 128404  5648    0.62892   30   10    0.63687    0.62324  2.14%  30.7  461s
 129735  5453    0.63465   28    6    0.63687    0.62355  2.09%  30.7  465s
 131662  5062     cutoff   32         0.63687    0.62397  2.02%  30.7  470s
 134003  4674    0.63301   32    9    0.63687    0.62454  1.94%  30.6  475s
 135780  4246     cutoff   38         0.63687    0.62494  1.87%  30.6  480s
H136400  4126                       0.6368671    0.62509  1.85%  30.6  481s
H136826  4074                       0.6368671    0.62513  1.84%  30.6  483s
 137075  3963    0.62984   34   11    0.63687    0.62517  1.84%  30.6  485s
H137200  3963                       0.6368671    0.62517  1.84%  30.6  485s
 139534  3143    0.62923   34   13    0.63687    0.62630  1.66%  30.5  490s
 141775  2482     cutoff   35         0.63687    0.62731  1.50%  30.5  495s
H143863  1934                       0.6368671    0.62878  1.27%  30.4  498s
 144312  1355    0.63193   33   11    0.63687    0.62902  1.23%  30.4  501s

Cutting planes:
  Gomory: 2
  Implied bound: 208
  MIR: 136
  Flow cover: 399
  RLT: 95
  Relax-and-lift: 74

Explored 147025 nodes (4444717 simplex iterations) in 504.74 seconds (445.75 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.636867 0.636867 0.637758 ... 0.697824

Optimal solution found (tolerance 1.00e-04)
Best objective 6.368671593001e-01, best bound 6.368670952693e-01, gap 0.0000%
The objective bound is 0.636867 while the objective upper bound is 0.636867

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.71 (ave)

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