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 6.35621 seconds.
    local lower bound updated to 0.261512
    local upper bound updated to 0.468595

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.44447 seconds.
    local lower bound updated to 0.459478
    local upper bound updated to 0.459478
The Primal step takes 7.80244 (S)
lower bound updated to 0.459478

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.523968
    local lower bound updated to 0.513141

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.523968
    local lower bound updated to 0.521423

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.521423
    local lower bound updated to 0.521423
The Dual step takes 0.2909 (S)
upper bound updated to 0.521423
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.4126 seconds.
    local lower bound updated to 0.328533
    local upper bound updated to 0.463839

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.74366 seconds.
    local lower bound updated to 0.459108
    local upper bound updated to 0.460556

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.81092 seconds.
    local lower bound updated to 0.45974
    local upper bound updated to 0.46003

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.77153 seconds.
    local lower bound updated to 0.46003
    local upper bound updated to 0.46003
The Primal step takes 24.7441 (S)
lower bound updated to 0.46003

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.495555
    local lower bound updated to 0.46673

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.479686
    local lower bound updated to 0.475715

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.475715
    local lower bound updated to 0.475715
The Dual step takes 0.590202 (S)
upper bound updated to 0.475715
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 40.7874 seconds.
    local lower bound updated to 0.375249
    local upper bound updated to 0.472731

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.41808 seconds.
    local lower bound updated to 0.383276
    local upper bound updated to 0.468401

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 17.2205 seconds.
    local lower bound updated to 0.460086
    local upper bound updated to 0.467315

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 20.0339 seconds.
    local lower bound updated to 0.463915
    local upper bound updated to 0.464555

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 6.57287 seconds.
    local lower bound updated to 0.463915
    local upper bound updated to 0.464029

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 14.9098 seconds.
    local lower bound updated to 0.464029
    local upper bound updated to 0.464029
The Primal step takes 100.955 (S)
lower bound updated to 0.464029

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.482162
    local lower bound updated to 0.464029

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.467257
    local lower bound updated to 0.464762

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.464762
    local lower bound updated to 0.464762
The Dual step takes 1.34891 (S)
upper bound updated to 0.464762
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0515 seconds.
    local lower bound updated to 0.396665
    local upper bound updated to 0.464762

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 21.4743 seconds.
    local lower bound updated to 0.447593
    local upper bound updated to 0.464678

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 24.5454 seconds.
    local lower bound updated to 0.460782
    local upper bound updated to 0.464479

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 18.003 seconds.
    local lower bound updated to 0.462784
    local upper bound updated to 0.464029

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 19.9178 seconds.
    local lower bound updated to 0.464029
    local upper bound updated to 0.464029
The Primal step takes 144.005 (S)
lower bound updated to 0.464029

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.474642
    local lower bound updated to 0.464029

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.465138
    local lower bound updated to 0.464396

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.464396
    local lower bound updated to 0.464396
The Dual step takes 2.94698 (S)
upper bound updated to 0.464396
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0114 seconds.
    local lower bound updated to 0.404408
    local upper bound updated to 0.464396

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 29.4604 seconds.
    local lower bound updated to 0.462884
    local upper bound updated to 0.464394

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 31.1725 seconds.
    local lower bound updated to 0.463957
    local upper bound updated to 0.464394

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 34.0745 seconds.
    local lower bound updated to 0.4641
    local upper bound updated to 0.464369

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 36.6749 seconds.
    local lower bound updated to 0.464369
    local upper bound updated to 0.464369
The Primal step takes 191.408 (S)
lower bound updated to 0.464369

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.475588
    local lower bound updated to 0.464369

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.475588
    local lower bound updated to 0.46437

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.46437
    local lower bound updated to 0.46437
The Dual step takes 4.62793 (S)
upper bound updated to 0.46437
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.043 seconds.
    local lower bound updated to 0.408572
    local upper bound updated to 0.46437

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 36.5419 seconds.
    local lower bound updated to 0.464054
    local upper bound updated to 0.464369

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 41.6147 seconds.
    local lower bound updated to 0.464369
    local upper bound updated to 0.464369
The time obtain the optimal randomized assortment is 616.929 (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_68818.log"
The computation time limit for a lower bound is 85378
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 128 physical cores, 128 logical processors, using up to 4 threads
Optimize a model with 2022 rows, 1546 columns and 6671 nonzeros
Model fingerprint: 0x611a552f
Variable types: 1481 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [6e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 437 rows and 807 columns
Presolve time: 0.03s
Presolved: 1585 rows, 739 columns, 6125 nonzeros
Variable types: 676 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.6203529
Found heuristic solution: objective 0.5729532
Found heuristic solution: objective 0.5473751

Root relaxation: objective 2.712820e-01, 212 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    0.27128    0   20    0.54738    0.27128  50.4%     -    0s
     0     0    0.27447    0   27    0.54738    0.27447  49.9%     -    0s
H    0     0                       0.5419724    0.27447  49.4%     -    0s
H    0     0                       0.5322094    0.27447  48.4%     -    0s
     0     0    0.33888    0   26    0.53221    0.33888  36.3%     -    0s
     0     0    0.33909    0   26    0.53221    0.33909  36.3%     -    0s
H    0     0                       0.5175198    0.35717  31.0%     -    0s
H    0     0                       0.5138460    0.35717  30.5%     -    0s
     0     0    0.35717    0   27    0.51385    0.35717  30.5%     -    0s
H    0     0                       0.4738771    0.35717  24.6%     -    0s
     0     0    0.35930    0   27    0.47388    0.35930  24.2%     -    0s
H    0     0                       0.4663573    0.35930  23.0%     -    0s
     0     0    0.36738    0   28    0.46636    0.36738  21.2%     -    0s
H    0     0                       0.4658612    0.36917  20.8%     -    0s
     0     0    0.36917    0   28    0.46586    0.36917  20.8%     -    0s
     0     0    0.37133    0   29    0.46586    0.37133  20.3%     -    0s
H    0     0                       0.4643688    0.37133  20.0%     -    1s
     0     2    0.37133    0   29    0.46437    0.37133  20.0%     -    1s
H  402   146                       0.4643688    0.38644  16.8%  22.7    3s
   793   289    0.42879   11   14    0.46437    0.39403  15.1%  20.8    6s
  1986   645    0.41398   10   16    0.46437    0.40283  13.3%  18.7   11s
  3037   912     cutoff   17         0.46437    0.40656  12.4%  18.3   15s
  3581  1007    0.43421   21   14    0.46437    0.40758  12.2%  19.9   20s
H 3585   959                       0.4643688    0.40758  12.2%  19.9   20s
H 3590   913                       0.4643688    0.40758  12.2%  19.9   20s
H 3623   867                       0.4643688    0.40758  12.2%  19.9   20s
H 3765   821                       0.4643688    0.40770  12.2%  20.2   22s
  5330   497    0.44964   23    6    0.46437    0.42712  8.02%  20.8   25s
  6831   477    0.45153   21   14    0.46437    0.43501  6.32%  21.0   30s
  8155   406    0.45761   22    6    0.46437    0.44102  5.03%  21.0   35s
  9590   229     cutoff   26         0.46437    0.44800  3.52%  20.8   40s

Cutting planes:
  Gomory: 1
  Implied bound: 169
  MIR: 120
  Flow cover: 343
  RLT: 38
  Relax-and-lift: 49

Explored 10276 nodes (213157 simplex iterations) in 41.10 seconds (23.89 work units)
Thread count was 4 (of 128 available processors)

Solution count 10: 0.464369 0.464369 0.465861 ... 0.547375

Optimal solution found (tolerance 1.00e-04)
Best objective 4.643687694408e-01, best bound 4.643687694408e-01, gap 0.0000%
The objective bound is 0.464369 while the objective upper bound is 0.464369

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.30 (ave)

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