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 1.11065 seconds.
    local lower bound updated to 0.219485
    local upper bound updated to 0.422497

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.624707 seconds.
    local lower bound updated to 0.412507
    local upper bound updated to 0.412507
The Primal step takes 1.73808 (S)
lower bound updated to 0.412507

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.541993
    local lower bound updated to 0.492631

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.507969
    local lower bound updated to 0.506645

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.507969
    local lower bound updated to 0.507228

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.507228
    local lower bound updated to 0.507228
The Dual step takes 0.140166 (S)
upper bound updated to 0.507228
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.89367 seconds.
    local lower bound updated to 0.299297
    local upper bound updated to 0.422022

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.16215 seconds.
    local lower bound updated to 0.413199
    local upper bound updated to 0.416025

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.76414 seconds.
    local lower bound updated to 0.413199
    local upper bound updated to 0.415393

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.35226 seconds.
    local lower bound updated to 0.414373
    local upper bound updated to 0.415142

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.01365 seconds.
    local lower bound updated to 0.414373
    local upper bound updated to 0.414963

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.95822 seconds.
    local lower bound updated to 0.414373
    local upper bound updated to 0.414667

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.11805 seconds.
    local lower bound updated to 0.414373
    local upper bound updated to 0.414582

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 2.10106 seconds.
    local lower bound updated to 0.414582
    local upper bound updated to 0.414582
The Primal step takes 19.3842 (S)
lower bound updated to 0.414582

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.469377
    local lower bound updated to 0.421793

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.449815
    local lower bound updated to 0.441882

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.449815
    local lower bound updated to 0.442524

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.449815
    local lower bound updated to 0.447663

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.447663
    local lower bound updated to 0.447663
The Dual step takes 2.03979 (S)
upper bound updated to 0.447663
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.7645 seconds.
    local lower bound updated to 0.354662
    local upper bound updated to 0.434438

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.22532 seconds.
    local lower bound updated to 0.388784
    local upper bound updated to 0.433823

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 38.268 seconds.
    local lower bound updated to 0.427306
    local upper bound updated to 0.432614

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 33.1099 seconds.
    local lower bound updated to 0.429513
    local upper bound updated to 0.432047

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0166 seconds.
    local lower bound updated to 0.429513
    local upper bound updated to 0.431888

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 48.4231 seconds.
    local lower bound updated to 0.429712
    local upper bound updated to 0.431615

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 42.3258 seconds.
    local lower bound updated to 0.429712
    local upper bound updated to 0.430365

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 12.9688 seconds.
    local lower bound updated to 0.429712
    local upper bound updated to 0.43034

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 33.3803 seconds.
    local lower bound updated to 0.429712
    local upper bound updated to 0.430272

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 31.2446 seconds.
    local lower bound updated to 0.429712
    local upper bound updated to 0.430154

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 29.3536 seconds.
    local lower bound updated to 0.430046
    local upper bound updated to 0.430144

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 33.6626 seconds.
    local lower bound updated to 0.430046
    local upper bound updated to 0.430124

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 30.9214 seconds.
    local lower bound updated to 0.430124
    local upper bound updated to 0.430124
The Primal step takes 405.728 (S)
lower bound updated to 0.430124

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.456825
    local lower bound updated to 0.432829

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.456825
    local lower bound updated to 0.437301

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.445586
    local lower bound updated to 0.440585

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.445586
    local lower bound updated to 0.4412

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.4412
    local lower bound updated to 0.4412
The Dual step takes 7.66681 (S)
upper bound updated to 0.4412
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 26.8649 seconds.
    local lower bound updated to 0.381549
    local upper bound updated to 0.4412

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0171 seconds.
    local lower bound updated to 0.434973
    local upper bound updated to 0.441029

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0229 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439986

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 28.2357 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439899

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0173 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439499

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0187 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439393

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0179 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439347

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0147 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.439319

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0165 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.43883

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0227 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.438828

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0175 seconds.
    local lower bound updated to 0.43851
    local upper bound updated to 0.438825

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0162 seconds.
    local lower bound updated to 0.438732
    local upper bound updated to 0.438824

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0199 seconds.
    local lower bound updated to 0.438732
    local upper bound updated to 0.438824

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 48.1695 seconds.
    local lower bound updated to 0.438735
    local upper bound updated to 0.438812

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0215 seconds.
    local lower bound updated to 0.438812
    local upper bound updated to 0.438812
The Primal step takes 823.586 (S)
lower bound updated to 0.438812

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.453559
    local lower bound updated to 0.438812

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.453559
    local lower bound updated to 0.438856

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.444326
    local lower bound updated to 0.439057

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.439057
    local lower bound updated to 0.439057
The Dual step takes 14.3944 (S)
upper bound updated to 0.439057
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 24.1361 seconds.
    local lower bound updated to 0.384825
    local upper bound updated to 0.439057

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.018 seconds.
    local lower bound updated to 0.438526
    local upper bound updated to 0.439032

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0154 seconds.
    local lower bound updated to 0.438948
    local upper bound updated to 0.439026

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0172 seconds.
    local lower bound updated to 0.438948
    local upper bound updated to 0.439025

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0207 seconds.
    local lower bound updated to 0.439025
    local upper bound updated to 0.439025
The Primal step takes 264.245 (S)
lower bound updated to 0.439025

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.452093
    local lower bound updated to 0.439025

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.439025
    local lower bound updated to 0.439025
The Dual step takes 8.70417 (S)
upper bound updated to 0.439025
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 23.9317 seconds.
    local lower bound updated to 0.384825
    local upper bound updated to 0.439025

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0282 seconds.
    local lower bound updated to 0.439025
    local upper bound updated to 0.439025
The time obtain the optimal randomized assortment is 1631.6 (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_68118.log"
The computation time limit for a lower bound is 84363
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 2992 rows, 2286 columns and 9852 nonzeros
Model fingerprint: 0x8839d026
Variable types: 2221 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        [2e-01, 1e+00]
Presolve removed 699 rows and 1265 columns
Presolve time: 0.04s
Presolved: 2293 rows, 1021 columns, 8983 nonzeros
Variable types: 957 continuous, 64 integer (64 binary)
Found heuristic solution: objective 0.5537088
Found heuristic solution: objective 0.5047385

Root relaxation: objective 3.424914e-01, 242 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    0.34249    0   23    0.50474    0.34249  32.1%     -    0s
     0     0    0.34652    0   29    0.50474    0.34652  31.3%     -    0s
H    0     0                       0.4526230    0.34652  23.4%     -    0s
     0     0    0.34652    0   29    0.45262    0.34652  23.4%     -    0s
     0     0    0.37210    0   32    0.45262    0.37210  17.8%     -    0s
     0     0    0.37247    0   33    0.45262    0.37247  17.7%     -    0s
     0     0    0.38221    0   28    0.45262    0.38221  15.6%     -    0s
H    0     0                       0.4460476    0.38221  14.3%     -    0s
     0     0    0.38324    0   27    0.44605    0.38324  14.1%     -    0s
     0     0    0.38561    0   28    0.44605    0.38561  13.5%     -    0s
     0     0    0.38627    0   32    0.44605    0.38627  13.4%     -    0s
H    0     0                       0.4414433    0.38627  12.5%     -    0s
     0     0    0.38666    0   26    0.44144    0.38666  12.4%     -    0s
H    0     0                       0.4396277    0.38666  12.0%     -    2s
     0     2    0.38666    0   26    0.43963    0.38666  12.0%     -    2s
H   59    47                       0.4390504    0.39958  8.99%  88.5    3s
H  103    75                       0.4390250    0.39958  8.98%  72.8    4s
   200   116     cutoff   12         0.43903    0.40099  8.66%  59.9    6s
H  360   167                       0.4390250    0.40546  7.65%  54.9    6s
   595   258    0.42639   11   10    0.43903    0.40799  7.07%  50.5   10s
  1374   416     cutoff   13         0.43903    0.41266  6.01%  46.0   16s
  2069   530 infeasible   10         0.43903    0.41524  5.42%  43.7   20s
  2942   677     cutoff   13         0.43903    0.41658  5.11%  40.4   25s
  3897   765    0.42512   13   13    0.43903    0.41835  4.71%  39.3   31s
H 4201   804                       0.4390250    0.41872  4.63%  38.9   32s
  4436   805    0.42206   12   26    0.43903    0.41934  4.48%  38.3   35s
H 4734   833                       0.4390250    0.41934  4.48%  40.1   39s
  4761   835     cutoff   29         0.43903    0.41934  4.48%  40.1   40s
  5874   630    0.43638   24   12    0.43903    0.41934  4.48%  40.4   45s
  7495   504    0.43049   24   15    0.43903    0.42098  4.11%  39.9   50s
  8945   588     cutoff   27         0.43903    0.42308  3.63%  39.3   55s
  9685   661    0.43739   28    8    0.43903    0.42397  3.43%  39.2   60s
 11066   667    0.43302   25    9    0.43903    0.42591  2.99%  38.6   65s
 12893   586     cutoff   29         0.43903    0.42846  2.41%  38.1   70s
 15191   276     cutoff   31         0.43903    0.43192  1.62%  37.1   75s

Cutting planes:
  Gomory: 1
  Implied bound: 267
  MIR: 174
  Flow cover: 434
  RLT: 48
  Relax-and-lift: 126

Explored 16161 nodes (592392 simplex iterations) in 75.99 seconds (65.90 work units)
Thread count was 4 (of 48 available processors)

Solution count 8: 0.439025 0.43905 0.439628 ... 0.553709

Optimal solution found (tolerance 1.00e-04)
Best objective 4.390250179484e-01, best bound 4.390250179484e-01, gap 0.0000%
The objective bound is 0.439025 while the objective upper bound is 0.439025

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.38 (ave)

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