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 0.54045 seconds.
    local lower bound updated to 0.275613
    local upper bound updated to 0.545726

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.524101 seconds.
    local lower bound updated to 0.510984
    local upper bound updated to 0.510984
The Primal step takes 1.06745 (S)
lower bound updated to 0.510984

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.582581
    local lower bound updated to 0.566033

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.582581
    local lower bound updated to 0.56847

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.571372
    local lower bound updated to 0.569562

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.569562
    local lower bound updated to 0.569562
The Dual step takes 0.298406 (S)
upper bound updated to 0.569562
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.403498 seconds.
    local lower bound updated to 0.351378
    local upper bound updated to 0.538732

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.715623 seconds.
    local lower bound updated to 0.488463
    local upper bound updated to 0.52984

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.12017 seconds.
    local lower bound updated to 0.51054
    local upper bound updated to 0.519536

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.34136 seconds.
    local lower bound updated to 0.514021
    local upper bound updated to 0.515197

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.80234 seconds.
    local lower bound updated to 0.514021
    local upper bound updated to 0.51484

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.32652 seconds.
    local lower bound updated to 0.51484
    local upper bound updated to 0.51484
The Primal step takes 7.72165 (S)
lower bound updated to 0.51484

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.578186
    local lower bound updated to 0.532848

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.555771
    local lower bound updated to 0.547925

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.553218
    local lower bound updated to 0.54949

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.54949
    local lower bound updated to 0.54949
The Dual step takes 0.416847 (S)
upper bound updated to 0.54949
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.34396 seconds.
    local lower bound updated to 0.423095
    local upper bound updated to 0.535042

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.65273 seconds.
    local lower bound updated to 0.478457
    local upper bound updated to 0.534589

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 17.8443 seconds.
    local lower bound updated to 0.507772
    local upper bound updated to 0.534134

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.21889 seconds.
    local lower bound updated to 0.507772
    local upper bound updated to 0.533818

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 15.5323 seconds.
    local lower bound updated to 0.511992
    local upper bound updated to 0.532132

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 17.37 seconds.
    local lower bound updated to 0.515166
    local upper bound updated to 0.530726

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 15.3625 seconds.
    local lower bound updated to 0.523773
    local upper bound updated to 0.529654

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 18.5086 seconds.
    local lower bound updated to 0.524497
    local upper bound updated to 0.529417

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 23.8057 seconds.
    local lower bound updated to 0.525253
    local upper bound updated to 0.529034

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 18.4768 seconds.
    local lower bound updated to 0.526507
    local upper bound updated to 0.52776

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 11.9556 seconds.
    local lower bound updated to 0.526507
    local upper bound updated to 0.527684

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 19.8363 seconds.
    local lower bound updated to 0.52722
    local upper bound updated to 0.52764

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 18.3827 seconds.
    local lower bound updated to 0.52764
    local upper bound updated to 0.52764
The Primal step takes 187.336 (S)
lower bound updated to 0.52764

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.558077
    local lower bound updated to 0.537215

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.545274
    local lower bound updated to 0.537881

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.545274
    local lower bound updated to 0.537885

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.545274
    local lower bound updated to 0.539354

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.542611
    local lower bound updated to 0.539427

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.54066
    local lower bound updated to 0.539502

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.539502
    local lower bound updated to 0.539502
The Dual step takes 2.24035 (S)
upper bound updated to 0.539502
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.3635 seconds.
    local lower bound updated to 0.471388
    local upper bound updated to 0.538678

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.0797 seconds.
    local lower bound updated to 0.517245
    local upper bound updated to 0.536283

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 28.3988 seconds.
    local lower bound updated to 0.523554
    local upper bound updated to 0.535875

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.82345 seconds.
    local lower bound updated to 0.523554
    local upper bound updated to 0.534698

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 24.1749 seconds.
    local lower bound updated to 0.532523
    local upper bound updated to 0.534414

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 41.8384 seconds.
    local lower bound updated to 0.532817
    local upper bound updated to 0.533987

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 44.5484 seconds.
    local lower bound updated to 0.532817
    local upper bound updated to 0.533742

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 49.1876 seconds.
    local lower bound updated to 0.532817
    local upper bound updated to 0.533681

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 37.6375 seconds.
    local lower bound updated to 0.533373
    local upper bound updated to 0.533652

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 44.5503 seconds.
    local lower bound updated to 0.533373
    local upper bound updated to 0.533643

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 46.0114 seconds.
    local lower bound updated to 0.533452
    local upper bound updated to 0.533637

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 31.2227 seconds.
    local lower bound updated to 0.533452
    local upper bound updated to 0.533634

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 44.3586 seconds.
    local lower bound updated to 0.533624
    local upper bound updated to 0.533633
The Primal step takes 429.273 (S)
lower bound updated to 0.533624

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.549009
    local lower bound updated to 0.533633

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.539121
    local lower bound updated to 0.533696

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.535422
    local lower bound updated to 0.533701

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.534382
    local lower bound updated to 0.533705

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.534072
    local lower bound updated to 0.533712

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.533712
    local lower bound updated to 0.533712
The Dual step takes 12.749 (S)
upper bound updated to 0.533712
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 44.7826 seconds.
    local lower bound updated to 0.480226
    local upper bound updated to 0.533712

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 64.5185 seconds.
    local lower bound updated to 0.533293
    local upper bound updated to 0.533644

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 53.2236 seconds.
    local lower bound updated to 0.533644
    local upper bound updated to 0.533644
The Primal step takes 162.544 (S)
lower bound updated to 0.533644

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.549084
    local lower bound updated to 0.533644

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.536445
    local lower bound updated to 0.533679

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.533679
    local lower bound updated to 0.533679
The Dual step takes 7.705 (S)
upper bound updated to 0.533679
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 31.0795 seconds.
    local lower bound updated to 0.479422
    local upper bound updated to 0.533679

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 67.1139 seconds.
    local lower bound updated to 0.53347
    local upper bound updated to 0.533674

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 58.0684 seconds.
    local lower bound updated to 0.533536
    local upper bound updated to 0.533672

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 62.9391 seconds.
    local lower bound updated to 0.533592
    local upper bound updated to 0.533668

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 65.5322 seconds.
    local lower bound updated to 0.533668
    local upper bound updated to 0.533668
The Primal step takes 284.77 (S)
lower bound updated to 0.533668

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.548423
    local lower bound updated to 0.533668

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.533668
    local lower bound updated to 0.533668
The Dual step takes 4.7872 (S)
upper bound updated to 0.533668
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 28.1213 seconds.
    local lower bound updated to 0.479422
    local upper bound updated to 0.533668

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 62.124 seconds.
    local lower bound updated to 0.533668
    local upper bound updated to 0.533668
The time obtain the optimal randomized assortment is 1191.17 (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_205316.log"
The computation time limit for a lower bound is 84805
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 3120 rows, 2528 columns and 9977 nonzeros
Model fingerprint: 0x357fa102
Variable types: 2471 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 910 rows and 1568 columns
Presolve time: 0.03s
Presolved: 2210 rows, 960 columns, 8529 nonzeros
Variable types: 905 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6844616
Found heuristic solution: objective 0.6154691
Found heuristic solution: objective 0.6122020

Root relaxation: objective 2.671971e-01, 268 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    0.26720    0   24    0.61220    0.26720  56.4%     -    0s
H    0     0                       0.5813170    0.26720  54.0%     -    0s
H    0     0                       0.5811919    0.30094  48.2%     -    0s
H    0     0                       0.5804913    0.30094  48.2%     -    0s
     0     0    0.30094    0   27    0.58049    0.30094  48.2%     -    0s
     0     0    0.30181    0   27    0.58049    0.30181  48.0%     -    0s
     0     0    0.37854    0   28    0.58049    0.37854  34.8%     -    0s
H    0     0                       0.5627789    0.37854  32.7%     -    0s
     0     0    0.37859    0   28    0.56278    0.37859  32.7%     -    0s
     0     0    0.39351    0   29    0.56278    0.39351  30.1%     -    0s
H    0     0                       0.5496479    0.39351  28.4%     -    0s
H    0     0                       0.5464019    0.39582  27.6%     -    0s
     0     0    0.39582    0   31    0.54640    0.39582  27.6%     -    0s
     0     0    0.41225    0   28    0.54640    0.41225  24.6%     -    0s
H    0     0                       0.5425184    0.41374  23.7%     -    0s
     0     0    0.41374    0   27    0.54252    0.41374  23.7%     -    0s
     0     0    0.41932    0   28    0.54252    0.41932  22.7%     -    0s
H    0     0                       0.5356197    0.41932  21.7%     -    1s
H    0     0                       0.5336678    0.41932  21.4%     -    2s
     0     2    0.41932    0   28    0.53367    0.41932  21.4%     -    2s
   204   134    0.47062    7   20    0.53367    0.44836  16.0%  38.2    5s
  1096   484    0.49274   10   16    0.53367    0.47234  11.5%  29.7   11s
  2066   805    0.49941   10   30    0.53367    0.48135  9.80%  26.5   15s
  2489   876    0.48210   23   21    0.53367    0.48135  9.80%  29.5   20s
H 2516   826                       0.5336678    0.48135  9.80%  29.4   20s
  3855   748    0.50908   22   17    0.53367    0.49300  7.62%  28.8   25s
  4987   837    0.52786   28   10    0.53367    0.49844  6.60%  28.3   30s
  6816  1112    0.52049   24   10    0.53367    0.50373  5.61%  27.6   35s
  8004  1241    0.51903   31   12    0.53367    0.50638  5.11%  27.2   41s
  9325  1285    0.51980   25   17    0.53367    0.50919  4.59%  26.8   45s
H10205  1296                       0.5336678    0.51045  4.35%  26.6   47s
H11039  1272                       0.5336678    0.51190  4.08%  26.4   49s
 11040  1260 infeasible   29         0.53367    0.51199  4.06%  26.4   50s
H11166  1260                       0.5336678    0.51204  4.05%  26.4   50s
 12987  1089    0.52749   27   12    0.53367    0.51502  3.49%  26.0   55s
H13200  1089                       0.5336678    0.51502  3.49%  25.9   55s
 15300   787     cutoff   28         0.53367    0.51820  2.90%  25.3   60s

Cutting planes:
  Implied bound: 243
  MIR: 177
  Flow cover: 464
  RLT: 73
  Relax-and-lift: 81

Explored 17953 nodes (441330 simplex iterations) in 64.71 seconds (50.84 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.533668 0.533668 0.53562 ... 0.581317

Optimal solution found (tolerance 1.00e-04)
Best objective 5.336677874960e-01, best bound 5.336677874960e-01, gap 0.0000%
The objective bound is 0.533668 while the objective upper bound is 0.533668

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.30 (ave)

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