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 0.436477 seconds.
    local lower bound updated to 0.234912
    local upper bound updated to 0.464767

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.04586 seconds.
    local lower bound updated to 0.46228
    local upper bound updated to 0.46228
The Primal step takes 3.48503 (S)
lower bound updated to 0.46228

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.632069
    local lower bound updated to 0.622494

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.622494
    local lower bound updated to 0.622494
The Dual step takes 0.0693173 (S)
upper bound updated to 0.622494
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.532113 seconds.
    local lower bound updated to 0.316721
    local upper bound updated to 0.477191

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.70031 seconds.
    local lower bound updated to 0.467657
    local upper bound updated to 0.468259

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.51286 seconds.
    local lower bound updated to 0.467657
    local upper bound updated to 0.468153

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.99442 seconds.
    local lower bound updated to 0.467657
    local upper bound updated to 0.468066

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.65146 seconds.
    local lower bound updated to 0.468066
    local upper bound updated to 0.468066
The Primal step takes 17.4019 (S)
lower bound updated to 0.468066

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.552048
    local lower bound updated to 0.489534

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.528284
    local lower bound updated to 0.51871

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.528284
    local lower bound updated to 0.521639

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.528284
    local lower bound updated to 0.524256

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.524256
    local lower bound updated to 0.524256
The Dual step takes 1.38735 (S)
upper bound updated to 0.524256
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.74276 seconds.
    local lower bound updated to 0.404161
    local upper bound updated to 0.485231

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.3877 seconds.
    local lower bound updated to 0.477141
    local upper bound updated to 0.484911

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.3204 seconds.
    local lower bound updated to 0.477141
    local upper bound updated to 0.482926

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.43016 seconds.
    local lower bound updated to 0.477141
    local upper bound updated to 0.480546

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 24.3672 seconds.
    local lower bound updated to 0.478742
    local upper bound updated to 0.48022

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 29.44 seconds.
    local lower bound updated to 0.479319
    local upper bound updated to 0.479858

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 13.8097 seconds.
    local lower bound updated to 0.479319
    local upper bound updated to 0.479714

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 28.5451 seconds.
    local lower bound updated to 0.479319
    local upper bound updated to 0.47968

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 29.5433 seconds.
    local lower bound updated to 0.47968
    local upper bound updated to 0.47968
The Primal step takes 171.619 (S)
lower bound updated to 0.47968

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.531519
    local lower bound updated to 0.487169

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518311
    local lower bound updated to 0.495832

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.506988
    local lower bound updated to 0.498184

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.504574
    local lower bound updated to 0.498823

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.503632
    local lower bound updated to 0.500042

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.500811
    local lower bound updated to 0.500072

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.500072
    local lower bound updated to 0.500072
The Dual step takes 7.29479 (S)
upper bound updated to 0.500072
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 20.4636 seconds.
    local lower bound updated to 0.44297
    local upper bound updated to 0.500072

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.018 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.499642

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0244 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.496393

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0232 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.49522

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0175 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.494875

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0198 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.494592

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.016 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.493718

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0187 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.493339

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0188 seconds.
    local lower bound updated to 0.490331
    local upper bound updated to 0.492911

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0231 seconds.
    local lower bound updated to 0.491265
    local upper bound updated to 0.492817

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.026 seconds.
    local lower bound updated to 0.491265
    local upper bound updated to 0.492662

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0168 seconds.
    local lower bound updated to 0.491998
    local upper bound updated to 0.492609

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0159 seconds.
    local lower bound updated to 0.492063
    local upper bound updated to 0.492572

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.0265 seconds.
    local lower bound updated to 0.492435
    local upper bound updated to 0.492537

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0308 seconds.
    local lower bound updated to 0.492537
    local upper bound updated to 0.492537
The Primal step takes 860.857 (S)
lower bound updated to 0.492537

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.518762
    local lower bound updated to 0.492537

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.496294
    local lower bound updated to 0.49332

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.494934
    local lower bound updated to 0.493485

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.493485
    local lower bound updated to 0.493485
The Dual step takes 19.1236 (S)
upper bound updated to 0.493485
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 34.5842 seconds.
    local lower bound updated to 0.449236
    local upper bound updated to 0.493485

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0264 seconds.
    local lower bound updated to 0.492878
    local upper bound updated to 0.493389

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0288 seconds.
    local lower bound updated to 0.492905
    local upper bound updated to 0.493302

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0216 seconds.
    local lower bound updated to 0.492905
    local upper bound updated to 0.493284

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0269 seconds.
    local lower bound updated to 0.493079
    local upper bound updated to 0.493264

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0276 seconds.
    local lower bound updated to 0.493187
    local upper bound updated to 0.493257

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0202 seconds.
    local lower bound updated to 0.493257
    local upper bound updated to 0.493257
The Primal step takes 394.792 (S)
lower bound updated to 0.493257

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.514251
    local lower bound updated to 0.493257

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.498328
    local lower bound updated to 0.493266

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.493266
    local lower bound updated to 0.493266
The Dual step takes 20.9589 (S)
upper bound updated to 0.493266
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 24.0824 seconds.
    local lower bound updated to 0.449156
    local upper bound updated to 0.493266

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0317 seconds.
    local lower bound updated to 0.493159
    local upper bound updated to 0.493257

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0205 seconds.
    local lower bound updated to 0.493257
    local upper bound updated to 0.493257
The time obtain the optimal randomized assortment is 1641.15 (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_60118.log"
The computation time limit for a lower bound is 84349
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 3186 rows, 2434 columns and 10486 nonzeros
Model fingerprint: 0x5c77d86c
Variable types: 2369 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [3e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 761 rows and 1361 columns
Presolve time: 0.03s
Presolved: 2425 rows, 1073 columns, 9548 nonzeros
Variable types: 1010 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.6673723
Found heuristic solution: objective 0.6661016
Found heuristic solution: objective 0.6081073
Found heuristic solution: objective 0.5944722

Root relaxation: objective 3.795330e-01, 281 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    0.37953    0   20    0.59447    0.37953  36.2%     -    0s
H    0     0                       0.5847830    0.37953  35.1%     -    0s
H    0     0                       0.5824642    0.38505  33.9%     -    0s
H    0     0                       0.5824285    0.38505  33.9%     -    0s
     0     0    0.38505    0   33    0.58243    0.38505  33.9%     -    0s
H    0     0                       0.5581253    0.38505  31.0%     -    0s
     0     0    0.42299    0   29    0.55813    0.42299  24.2%     -    0s
H    0     0                       0.5185375    0.42299  18.4%     -    0s
     0     0    0.42303    0   29    0.51854    0.42303  18.4%     -    0s
H    0     0                       0.5161454    0.43201  16.3%     -    0s
     0     0    0.43201    0   31    0.51615    0.43201  16.3%     -    0s
H    0     0                       0.5056285    0.43201  14.6%     -    0s
     0     0    0.43233    0   31    0.50563    0.43233  14.5%     -    0s
     0     0    0.43604    0   30    0.50563    0.43604  13.8%     -    0s
H    0     0                       0.4988793    0.43604  12.6%     -    0s
     0     0    0.43692    0   31    0.49888    0.43692  12.4%     -    0s
     0     0    0.43775    0   31    0.49888    0.43775  12.3%     -    0s
H    0     0                       0.4944648    0.43775  11.5%     -    2s
     0     2    0.43775    0   31    0.49446    0.43775  11.5%     -    2s
H   69    61                       0.4934641    0.44659  9.50%  68.1    3s
   199   127    0.47372    4   26    0.49346    0.44802  9.21%  52.5    5s
H  200   127                       0.4932569    0.44802  9.17%  52.2    5s
H  435   241                       0.4932569    0.45164  8.44%  44.8    6s
   790   377    0.48093   12   12    0.49326    0.45687  7.38%  41.1   10s
  1676   636    0.48706   15   13    0.49326    0.46086  6.57%  36.5   15s
  2179   749    0.48276   11   12    0.49326    0.46228  6.28%  35.5   20s
  3043   927    0.48783   18   15    0.49326    0.46369  5.99%  33.2   25s
  3313  1006    0.48883   20   31    0.49326    0.46424  5.88%  32.8   31s
  3797  1086    0.46424   17   24    0.49326    0.46424  5.88%  35.4   35s
  4746  1095    0.48706   30   12    0.49326    0.46424  5.88%  36.2   40s
  6624  1102    0.47424   23   19    0.49326    0.46771  5.18%  35.9   45s
  7497  1277    0.47539   21   21    0.49326    0.46911  4.90%  35.5   50s
  8959  1607    0.47557   23   16    0.49326    0.47126  4.46%  34.8   57s
  9544  1694     cutoff   25         0.49326    0.47178  4.35%  34.7   60s
 10456  1750    0.48529   24   12    0.49326    0.47274  4.16%  34.4   65s
 11922  1927    0.47948   24   12    0.49326    0.47395  3.91%  34.1   71s
 12848  1973     cutoff   27         0.49326    0.47481  3.74%  34.1   75s
 14569  2037    0.48491   25    8    0.49326    0.47573  3.55%  33.7   81s
 16425  2039     cutoff   23         0.49326    0.47734  3.23%  33.2   86s
 17938  1977    0.48393   25   17    0.49326    0.47835  3.02%  33.0   91s
 19263  1883    0.49051   33    4    0.49326    0.47962  2.77%  32.8   96s
 21167  1667    0.48703   23   16    0.49326    0.48094  2.50%  32.4  100s
 23762  1102     cutoff   21         0.49326    0.48278  2.12%  31.9  105s

Cutting planes:
  Implied bound: 284
  MIR: 152
  Flow cover: 479
  RLT: 74
  Relax-and-lift: 117

Explored 26679 nodes (831754 simplex iterations) in 108.90 seconds (89.54 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.493257 0.493464 0.494465 ... 0.582464

Optimal solution found (tolerance 1.00e-04)
Best objective 4.932569395893e-01, best bound 4.932569395893e-01, gap 0.0000%
The objective bound is 0.493257 while the objective upper bound is 0.493257

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.58 (ave)

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