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 1.22418 seconds.
    local lower bound updated to 0.239132
    local upper bound updated to 0.45959

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.728458 seconds.
    local lower bound updated to 0.45959
    local upper bound updated to 0.45959
The Primal step takes 1.95515 (S)
lower bound updated to 0.45959

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.553957
    local lower bound updated to 0.546246

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.553957
    local lower bound updated to 0.553717

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.553717
    local lower bound updated to 0.553717
The Dual step takes 0.105638 (S)
upper bound updated to 0.553717
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 8.13445 seconds.
    local lower bound updated to 0.359844
    local upper bound updated to 0.509026

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.518717 seconds.
    local lower bound updated to 0.399461
    local upper bound updated to 0.48266

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.72224 seconds.
    local lower bound updated to 0.462903
    local upper bound updated to 0.471799

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.49113 seconds.
    local lower bound updated to 0.467788
    local upper bound updated to 0.471412

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.82665 seconds.
    local lower bound updated to 0.470456
    local upper bound updated to 0.47101

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.52922 seconds.
    local lower bound updated to 0.470665
    local upper bound updated to 0.470968

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 7.95895 seconds.
    local lower bound updated to 0.470744
    local upper bound updated to 0.470859

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 8.14058 seconds.
    local lower bound updated to 0.470859
    local upper bound updated to 0.470859
The Primal step takes 51.3443 (S)
lower bound updated to 0.470859

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.540662
    local lower bound updated to 0.496967

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.536294
    local lower bound updated to 0.506358

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.517626
    local lower bound updated to 0.510674

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.517626
    local lower bound updated to 0.511716

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.515953
    local lower bound updated to 0.512136

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.513016
    local lower bound updated to 0.512452

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.512452
    local lower bound updated to 0.512452
The Dual step takes 1.29372 (S)
upper bound updated to 0.512452
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 22.6064 seconds.
    local lower bound updated to 0.399164
    local upper bound updated to 0.480077

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 13.4265 seconds.
    local lower bound updated to 0.469022
    local upper bound updated to 0.479373

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 45.1759 seconds.
    local lower bound updated to 0.469022
    local upper bound updated to 0.477288

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 31.0021 seconds.
    local lower bound updated to 0.469022
    local upper bound updated to 0.475959

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 22.6069 seconds.
    local lower bound updated to 0.469022
    local upper bound updated to 0.474725

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 29.6233 seconds.
    local lower bound updated to 0.469022
    local upper bound updated to 0.474511

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 45.942 seconds.
    local lower bound updated to 0.471882
    local upper bound updated to 0.473908

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 22.7919 seconds.
    local lower bound updated to 0.472981
    local upper bound updated to 0.473854

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 23.7738 seconds.
    local lower bound updated to 0.472981
    local upper bound updated to 0.473466

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 26.1012 seconds.
    local lower bound updated to 0.473124
    local upper bound updated to 0.473357

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 34.8276 seconds.
    local lower bound updated to 0.473217
    local upper bound updated to 0.473339

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 30.4073 seconds.
    local lower bound updated to 0.473339
    local upper bound updated to 0.473339
The Primal step takes 348.357 (S)
lower bound updated to 0.473339

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.510171
    local lower bound updated to 0.488446

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.509495
    local lower bound updated to 0.490928

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.492433
    local lower bound updated to 0.491082

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.491514
    local lower bound updated to 0.491096

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.491096
    local lower bound updated to 0.491096
The Dual step takes 8.7466 (S)
upper bound updated to 0.491096
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 29.8156 seconds.
    local lower bound updated to 0.417008
    local upper bound updated to 0.480848

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.42179 seconds.
    local lower bound updated to 0.417008
    local upper bound updated to 0.480519

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 40.2215 seconds.
    local lower bound updated to 0.467856
    local upper bound updated to 0.479735

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 31.7717 seconds.
    local lower bound updated to 0.467856
    local upper bound updated to 0.479479

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0218 seconds.
    local lower bound updated to 0.47288
    local upper bound updated to 0.479111

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0229 seconds.
    local lower bound updated to 0.475973
    local upper bound updated to 0.478889

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0268 seconds.
    local lower bound updated to 0.476726
    local upper bound updated to 0.478764

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0299 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.478561

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0276 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.478505

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0306 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.478425

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 55.7386 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.478054

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 43.6557 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.478003

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 29.6168 seconds.
    local lower bound updated to 0.477487
    local upper bound updated to 0.477997

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 44.5218 seconds.
    local lower bound updated to 0.477509
    local upper bound updated to 0.477996

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 37.4987 seconds.
    local lower bound updated to 0.477804
    local upper bound updated to 0.477987

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 37.1022 seconds.
    local lower bound updated to 0.477864
    local upper bound updated to 0.477983

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 43.7481 seconds.
    local lower bound updated to 0.47788
    local upper bound updated to 0.477981

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 40.7868 seconds.
    local lower bound updated to 0.477981
    local upper bound updated to 0.477981
The Primal step takes 801.192 (S)
lower bound updated to 0.477981

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.499937
    local lower bound updated to 0.478195

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.499937
    local lower bound updated to 0.482252

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.491047
    local lower bound updated to 0.482966

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.490832
    local lower bound updated to 0.483201

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.487374
    local lower bound updated to 0.483672

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.487374
    local lower bound updated to 0.48402

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.487374
    local lower bound updated to 0.484243

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.484645
    local lower bound updated to 0.484253

    ++ RESTRICTED DUAL ITERATION 9 ++
    local upper bound updated to 0.484253
    local lower bound updated to 0.484253
The Dual step takes 34.3321 (S)
upper bound updated to 0.484253
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.024 seconds.
    local lower bound updated to 0.448803
    local upper bound updated to 0.484253

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0198 seconds.
    local lower bound updated to 0.482738
    local upper bound updated to 0.484096

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0207 seconds.
    local lower bound updated to 0.482932
    local upper bound updated to 0.48392

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 44.8072 seconds.
    local lower bound updated to 0.482932
    local upper bound updated to 0.483917

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.021 seconds.
    local lower bound updated to 0.48327
    local upper bound updated to 0.483872

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 46.8264 seconds.
    local lower bound updated to 0.483282
    local upper bound updated to 0.483803

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0193 seconds.
    local lower bound updated to 0.483282
    local upper bound updated to 0.48379

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0322 seconds.
    local lower bound updated to 0.483598
    local upper bound updated to 0.483775

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0178 seconds.
    local lower bound updated to 0.483673
    local upper bound updated to 0.483764

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.02 seconds.
    local lower bound updated to 0.48375
    local upper bound updated to 0.483763

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0285 seconds.
    local lower bound updated to 0.483763
    local upper bound updated to 0.483763
The Primal step takes 631.938 (S)
lower bound updated to 0.483763

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.499854
    local lower bound updated to 0.483763

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.483897
    local lower bound updated to 0.483764

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.483764
    local lower bound updated to 0.483764
The Dual step takes 11.0962 (S)
upper bound updated to 0.483764
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.017 seconds.
    local lower bound updated to 0.44714
    local upper bound updated to 0.483764

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0212 seconds.
    local lower bound updated to 0.483764
    local upper bound updated to 0.483764
The time obtain the optimal randomized assortment is 2010.42 (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_60.000000_69616.log"
The computation time limit for a lower bound is 83983
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 3760 rows, 3048 columns and 12096 nonzeros
Model fingerprint: 0x80c2bf76
Variable types: 2991 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e-01, 1e+00]
Presolve removed 1026 rows and 1886 columns
Presolve time: 0.03s
Presolved: 2734 rows, 1162 columns, 10581 nonzeros
Variable types: 1106 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.6187874
Found heuristic solution: objective 0.6047541
Found heuristic solution: objective 0.5475707

Root relaxation: objective 2.422152e-01, 286 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    0.24222    0   21    0.54757    0.24222  55.8%     -    0s
H    0     0                       0.5368006    0.26600  50.4%     -    0s
     0     0    0.26600    0   29    0.53680    0.26600  50.4%     -    0s
H    0     0                       0.5217599    0.33072  36.6%     -    0s
     0     0    0.33073    0   29    0.52176    0.33073  36.6%     -    0s
H    0     0                       0.4899976    0.33073  32.5%     -    0s
H    0     0                       0.4892685    0.33150  32.2%     -    0s
     0     0    0.33211    0   30    0.48927    0.33211  32.1%     -    0s
     0     0    0.36123    0   33    0.48927    0.36123  26.2%     -    0s
H    0     0                       0.4892363    0.36259  25.9%     -    0s
     0     0    0.36259    0   31    0.48924    0.36259  25.9%     -    0s
     0     0    0.37052    0   34    0.48924    0.37052  24.3%     -    0s
     0     0    0.37178    0   31    0.48924    0.37178  24.0%     -    0s
     0     0    0.37470    0   30    0.48924    0.37470  23.4%     -    0s
H    0     0                       0.4839447    0.37470  22.6%     -    2s
     0     2    0.37470    0   30    0.48394    0.37470  22.6%     -    2s
H  403   193                       0.4837636    0.40812  15.6%  41.0    4s
   594   270    0.42343    8   20    0.48376    0.40946  15.4%  40.1    5s
  2019   577    0.46122    7   17    0.48376    0.42560  12.0%  34.3   10s
  3786   808    0.45077   10   18    0.48376    0.43699  9.67%  32.5   15s
  4133   849    0.45728    7   35    0.48376    0.43768  9.53%  32.0   20s
  4495   892    0.43768   21   23    0.48376    0.43768  9.53%  34.5   26s
  5282   808    0.45641   21   18    0.48376    0.43768  9.53%  35.8   30s
H 5300   759                       0.4837636    0.43768  9.53%  35.8   30s
  5725   672    0.45845   24   21    0.48376    0.43768  9.53%  36.3   35s
  6862   555    0.48245   29    9    0.48376    0.44580  7.85%  38.0   41s
  7843   620    0.48234   26    6    0.48376    0.45051  6.87%  38.0   45s
H 8124   621                       0.4837636    0.45173  6.62%  38.1   46s
  9388   603    0.47136   24   18    0.48376    0.45702  5.53%  38.7   50s
 11601   463     cutoff   26         0.48376    0.46615  3.64%  38.0   55s
 14488    21    0.48299   29   10    0.48376    0.47821  1.15%  36.0   60s

Cutting planes:
  Gomory: 1
  Implied bound: 325
  MIR: 204
  Flow cover: 593
  RLT: 52
  Relax-and-lift: 114

Explored 14669 nodes (528489 simplex iterations) in 60.04 seconds (53.19 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.483764 0.483945 0.489236 ... 0.618787

Optimal solution found (tolerance 1.00e-04)
Best objective 4.837635648755e-01, best bound 4.837635648755e-01, gap 0.0000%
The objective bound is 0.483764 while the objective upper bound is 0.483764

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.53 (ave)

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