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 1.22756 seconds.
    local lower bound updated to 0.260893
    local upper bound updated to 0.495763

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.38016 seconds.
    local lower bound updated to 0.483597
    local upper bound updated to 0.483597
The Primal step takes 2.61107 (S)
lower bound updated to 0.483597

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.633628
    local lower bound updated to 0.624643

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.628042
    local lower bound updated to 0.628042
The Dual step takes 0.069913 (S)
upper bound updated to 0.628042
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.56236 seconds.
    local lower bound updated to 0.357043
    local upper bound updated to 0.507216

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.38789 seconds.
    local lower bound updated to 0.480799
    local upper bound updated to 0.490449

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.88663 seconds.
    local lower bound updated to 0.489016
    local upper bound updated to 0.49044

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.91511 seconds.
    local lower bound updated to 0.490159
    local upper bound updated to 0.490171

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.27656 seconds.
    local lower bound updated to 0.490171
    local upper bound updated to 0.490171
The Primal step takes 16.0431 (S)
lower bound updated to 0.490171

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.581542
    local lower bound updated to 0.525039

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.542189
    local lower bound updated to 0.534513

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.540183
    local lower bound updated to 0.534958

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.537727
    local lower bound updated to 0.535391

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.535391
    local lower bound updated to 0.535391
The Dual step takes 1.14239 (S)
upper bound updated to 0.535391
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 43.5492 seconds.
    local lower bound updated to 0.414048
    local upper bound updated to 0.510699

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.7565 seconds.
    local lower bound updated to 0.485247
    local upper bound updated to 0.504514

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 40.0501 seconds.
    local lower bound updated to 0.498053
    local upper bound updated to 0.500692

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 17.5153 seconds.
    local lower bound updated to 0.498053
    local upper bound updated to 0.500006

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 24.2799 seconds.
    local lower bound updated to 0.498053
    local upper bound updated to 0.49868

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.013 seconds.
    local lower bound updated to 0.498053
    local upper bound updated to 0.498455

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0176 seconds.
    local lower bound updated to 0.498383
    local upper bound updated to 0.498451

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0192 seconds.
    local lower bound updated to 0.498451
    local upper bound updated to 0.498451
The Primal step takes 321.239 (S)
lower bound updated to 0.498451

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.534014
    local lower bound updated to 0.498451

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.519017
    local lower bound updated to 0.508733

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.5151
    local lower bound updated to 0.509818

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.513924
    local lower bound updated to 0.51028

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.51028
    local lower bound updated to 0.51028
The Dual step takes 5.01664 (S)
upper bound updated to 0.51028
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0194 seconds.
    local lower bound updated to 0.443824
    local upper bound updated to 0.51028

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0232 seconds.
    local lower bound updated to 0.498962
    local upper bound updated to 0.509372

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 39.0191 seconds.
    local lower bound updated to 0.498962
    local upper bound updated to 0.509099

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0326 seconds.
    local lower bound updated to 0.504675
    local upper bound updated to 0.507717

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0188 seconds.
    local lower bound updated to 0.505924
    local upper bound updated to 0.507483

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0282 seconds.
    local lower bound updated to 0.505924
    local upper bound updated to 0.507148

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0314 seconds.
    local lower bound updated to 0.505924
    local upper bound updated to 0.507011

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0187 seconds.
    local lower bound updated to 0.505924
    local upper bound updated to 0.506722

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0168 seconds.
    local lower bound updated to 0.506264
    local upper bound updated to 0.506678

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0212 seconds.
    local lower bound updated to 0.506531
    local upper bound updated to 0.506673

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0153 seconds.
    local lower bound updated to 0.506576
    local upper bound updated to 0.506669

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0228 seconds.
    local lower bound updated to 0.506645
    local upper bound updated to 0.506667

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0289 seconds.
    local lower bound updated to 0.506667
    local upper bound updated to 0.506667
The Primal step takes 759.387 (S)
lower bound updated to 0.506667

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.540122
    local lower bound updated to 0.506667

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.512688
    local lower bound updated to 0.507185

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.507524
    local lower bound updated to 0.5072

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.5072
    local lower bound updated to 0.5072
The Dual step takes 11.5372 (S)
upper bound updated to 0.5072
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.021 seconds.
    local lower bound updated to 0.450359
    local upper bound updated to 0.5072

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0186 seconds.
    local lower bound updated to 0.506903
    local upper bound updated to 0.507195

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0328 seconds.
    local lower bound updated to 0.506903
    local upper bound updated to 0.507169

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0361 seconds.
    local lower bound updated to 0.506967
    local upper bound updated to 0.507102

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0211 seconds.
    local lower bound updated to 0.506969
    local upper bound updated to 0.507091

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.024 seconds.
    local lower bound updated to 0.507074
    local upper bound updated to 0.507088

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0208 seconds.
    local lower bound updated to 0.507088
    local upper bound updated to 0.507088
The Primal step takes 420.235 (S)
lower bound updated to 0.507088

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.534184
    local lower bound updated to 0.507088

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.507088
    local lower bound updated to 0.507088
The Dual step takes 8.35416 (S)
upper bound updated to 0.507088
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0191 seconds.
    local lower bound updated to 0.450359
    local upper bound updated to 0.507088

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0191 seconds.
    local lower bound updated to 0.507088
    local upper bound updated to 0.507088
The time obtain the optimal randomized assortment is 1665.69 (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_17_4_60.000000_65718.log"
The computation time limit for a lower bound is 84329
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 2798 rows, 2138 columns and 9300 nonzeros
Model fingerprint: 0xa08b38b0
Variable types: 2073 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 658 rows and 1182 columns
Presolve time: 0.03s
Presolved: 2140 rows, 956 columns, 8490 nonzeros
Variable types: 894 continuous, 62 integer (62 binary)
Found heuristic solution: objective 0.6170065
Found heuristic solution: objective 0.5924340
Found heuristic solution: objective 0.5831832

Root relaxation: objective 3.609388e-01, 251 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    0.36094    0   22    0.58318    0.36094  38.1%     -    0s
H    0     0                       0.5695498    0.36538  35.8%     -    0s
     0     0    0.36538    0   26    0.56955    0.36538  35.8%     -    0s
H    0     0                       0.5629168    0.36538  35.1%     -    0s
H    0     0                       0.5600335    0.39890  28.8%     -    0s
     0     0    0.39890    0   30    0.56003    0.39890  28.8%     -    0s
H    0     0                       0.5203120    0.39890  23.3%     -    0s
     0     0    0.40020    0   30    0.52031    0.40020  23.1%     -    0s
     0     0    0.41770    0   31    0.52031    0.41770  19.7%     -    0s
H    0     0                       0.5146518    0.41868  18.6%     -    0s
H    0     0                       0.5136932    0.41868  18.5%     -    0s
     0     0    0.41868    0   31    0.51369    0.41868  18.5%     -    0s
     0     0    0.42368    0   33    0.51369    0.42368  17.5%     -    0s
H    0     0                       0.5123021    0.42368  17.3%     -    0s
     0     0    0.42417    0   35    0.51230    0.42417  17.2%     -    0s
     0     0    0.42484    0   32    0.51230    0.42484  17.1%     -    0s
H    0     0                       0.5113462    0.42484  16.9%     -    1s
H    0     0                       0.5070881    0.42484  16.2%     -    3s
     0     2    0.42484    0   32    0.50709    0.42484  16.2%     -    3s
    99    80    0.47077    7   19    0.50709    0.43345  14.5%  49.8    6s
   899   386    0.49339   12   15    0.50709    0.45616  10.0%  36.0   11s
  1216   473    0.50369   15   10    0.50709    0.45870  9.54%  35.6   15s
  1472   559    0.48137    6   20    0.50709    0.46081  9.13%  34.9   20s
  2090   763    0.50211   23   32    0.50709    0.46321  8.65%  33.1   26s
  2110   776    0.47519    9   33    0.50709    0.46321  8.65%  32.8   30s
H 2423   777                       0.5070881    0.46321  8.65%  36.5   32s
  2498   785    0.47669   20   21    0.50709    0.46321  8.65%  36.7   35s
  3437   679    0.50419   29   10    0.50709    0.46586  8.13%  37.8   40s
  3776   673     cutoff   29         0.50709    0.46895  7.52%  37.7   45s
  4576   713    0.48903   27   18    0.50709    0.47231  6.86%  38.1   50s
  5147   799    0.50481   24   15    0.50709    0.47419  6.49%  38.3   55s
  5528   841    0.49993   28   12    0.50709    0.47548  6.23%  38.0   60s
  5939   880    0.49889   27   12    0.50709    0.47700  5.93%  37.9   65s
  6715  1001    0.49446   24   12    0.50709    0.47869  5.60%  37.5   72s
  7554  1080    0.49187   23   12    0.50709    0.47988  5.37%  36.9   75s
  8536  1186    0.50444   23   10    0.50709    0.48218  4.91%  36.3   81s
  9684  1283    0.48877   21   14    0.50709    0.48367  4.62%  35.4   85s
 10799  1315    0.48973   25   12    0.50709    0.48487  4.38%  34.8   90s
 10921  1372     cutoff   28         0.50709    0.48492  4.37%  34.7   96s
 13133  1421    0.49222   23   14    0.50709    0.48743  3.88%  33.8  101s
 14319  1426    0.50101   26   14    0.50709    0.48909  3.55%  33.3  105s
 15305  1409    0.50378   28   10    0.50709    0.48973  3.42%  32.9  111s
 16759  1397 infeasible   24         0.50709    0.49086  3.20%  32.4  115s
 17959  1372    0.50229   25   14    0.50709    0.49171  3.03%  32.0  121s
 18982  1330    0.50092   31   11    0.50709    0.49260  2.86%  31.7  125s
 20617  1210     cutoff   24         0.50709    0.49343  2.69%  31.3  131s
 22099  1140     cutoff   32         0.50709    0.49527  2.33%  30.8  137s
 22951  1071    0.49909   27   12    0.50709    0.49595  2.20%  30.6  142s
 24022   853     cutoff   26         0.50709    0.49696  2.00%  30.3  146s
 26609   412 infeasible   23         0.50709    0.49991  1.41%  29.6  151s
 27385    57     cutoff   30         0.50709    0.50152  1.10%  29.4  155s

Cutting planes:
  Gomory: 1
  Implied bound: 222
  MIR: 154
  Flow cover: 502
  RLT: 95
  Relax-and-lift: 78

Explored 27756 nodes (814617 simplex iterations) in 156.00 seconds (126.32 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.507088 0.511346 0.512302 ... 0.583183

Optimal solution found (tolerance 1.00e-04)
Best objective 5.070881262696e-01, best bound 5.070881262696e-01, gap 0.0000%
The objective bound is 0.507088 while the objective upper bound is 0.507088

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.47 (ave)

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