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 0.310618 seconds.
    local lower bound updated to 0.286322
    local upper bound updated to 0.48093

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.392982 seconds.
    local lower bound updated to 0.476155
    local upper bound updated to 0.476155
The Primal step takes 0.706073 (S)
lower bound updated to 0.476155

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.583402
    local lower bound updated to 0.573076

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.579597
    local lower bound updated to 0.579597
The Dual step takes 0.0682323 (S)
upper bound updated to 0.579597
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.466908 seconds.
    local lower bound updated to 0.356241
    local upper bound updated to 0.494391

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.80416 seconds.
    local lower bound updated to 0.483544
    local upper bound updated to 0.485804

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.6627 seconds.
    local lower bound updated to 0.483754
    local upper bound updated to 0.484054

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.43929 seconds.
    local lower bound updated to 0.483836
    local upper bound updated to 0.484036

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.35172 seconds.
    local lower bound updated to 0.484036
    local upper bound updated to 0.484036
The Primal step takes 8.73454 (S)
lower bound updated to 0.484036

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.562106
    local lower bound updated to 0.516346

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.562106
    local lower bound updated to 0.528049

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.546408
    local lower bound updated to 0.542019

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.546408
    local lower bound updated to 0.542175

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.544415
    local lower bound updated to 0.542537

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.542537
    local lower bound updated to 0.542537
The Dual step takes 0.620385 (S)
upper bound updated to 0.542537
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 12.0208 seconds.
    local lower bound updated to 0.462579
    local upper bound updated to 0.534609

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.35125 seconds.
    local lower bound updated to 0.492008
    local upper bound updated to 0.529938

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.39763 seconds.
    local lower bound updated to 0.505795
    local upper bound updated to 0.527253

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 25.0949 seconds.
    local lower bound updated to 0.524838
    local upper bound updated to 0.526796

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.3472 seconds.
    local lower bound updated to 0.524951
    local upper bound updated to 0.525748

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 15.222 seconds.
    local lower bound updated to 0.524951
    local upper bound updated to 0.525708

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 19.304 seconds.
    local lower bound updated to 0.524951
    local upper bound updated to 0.525647

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 22.2385 seconds.
    local lower bound updated to 0.524951
    local upper bound updated to 0.525598

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 14.164 seconds.
    local lower bound updated to 0.525353
    local upper bound updated to 0.525587

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 13.383 seconds.
    local lower bound updated to 0.525587
    local upper bound updated to 0.525587
The Primal step takes 138.562 (S)
lower bound updated to 0.525587

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.55005
    local lower bound updated to 0.525587

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.52978
    local lower bound updated to 0.526444

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.526444
    local lower bound updated to 0.526444
The Dual step takes 1.00186 (S)
upper bound updated to 0.526444
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 12.6139 seconds.
    local lower bound updated to 0.471862
    local upper bound updated to 0.526444

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 9.59881 seconds.
    local lower bound updated to 0.512627
    local upper bound updated to 0.526062

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 16.8185 seconds.
    local lower bound updated to 0.524782
    local upper bound updated to 0.526053

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 30.3744 seconds.
    local lower bound updated to 0.525529
    local upper bound updated to 0.526039

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 22.9633 seconds.
    local lower bound updated to 0.526039
    local upper bound updated to 0.526039
The Primal step takes 92.3924 (S)
lower bound updated to 0.526039

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.552977
    local lower bound updated to 0.526039

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.527751
    local lower bound updated to 0.526147

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.526962
    local lower bound updated to 0.526147

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.526147
    local lower bound updated to 0.526147
The Dual step takes 5.03253 (S)
upper bound updated to 0.526147
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.6744 seconds.
    local lower bound updated to 0.474542
    local upper bound updated to 0.526147

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 27.1719 seconds.
    local lower bound updated to 0.524333
    local upper bound updated to 0.526114

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 36.1141 seconds.
    local lower bound updated to 0.526114
    local upper bound updated to 0.526114
The Primal step takes 80.9758 (S)
lower bound updated to 0.526114

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.553304
    local lower bound updated to 0.526114

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.526114
    local lower bound updated to 0.526114
The Dual step takes 2.2398 (S)
upper bound updated to 0.526114
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.7822 seconds.
    local lower bound updated to 0.474542
    local upper bound updated to 0.526114

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 36.9478 seconds.
    local lower bound updated to 0.526114
    local upper bound updated to 0.526114
The time obtain the optimal randomized assortment is 385.074 (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_100.000000_105116.log"
The computation time limit for a lower bound is 85610
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 2160 rows, 1748 columns and 6902 nonzeros
Model fingerprint: 0xf327a869
Variable types: 1691 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        [4e-01, 1e+00]
Presolve removed 593 rows and 1073 columns
Presolve time: 0.02s
Presolved: 1567 rows, 675 columns, 6075 nonzeros
Variable types: 619 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.7039172
Found heuristic solution: objective 0.6838290
Found heuristic solution: objective 0.6442860

Root relaxation: objective 3.117789e-01, 206 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    0.31178    0   22    0.64429    0.31178  51.6%     -    0s
H    0     0                       0.5700921    0.31178  45.3%     -    0s
H    0     0                       0.5519421    0.31858  42.3%     -    0s
     0     0    0.31858    0   28    0.55194    0.31858  42.3%     -    0s
     0     0    0.31858    0   28    0.55194    0.31858  42.3%     -    0s
     0     0    0.39300    0   29    0.55194    0.39300  28.8%     -    0s
H    0     0                       0.5518654    0.39300  28.8%     -    0s
H    0     0                       0.5389333    0.39300  27.1%     -    0s
     0     0    0.39483    0   29    0.53893    0.39483  26.7%     -    0s
H    0     0                       0.5358024    0.40397  24.6%     -    0s
     0     0    0.40397    0   26    0.53580    0.40397  24.6%     -    0s
     0     0    0.40452    0   27    0.53580    0.40452  24.5%     -    0s
     0     0    0.41235    0   26    0.53580    0.41235  23.0%     -    0s
     0     0    0.41257    0   27    0.53580    0.41257  23.0%     -    0s
     0     0    0.41312    0   23    0.53580    0.41312  22.9%     -    0s
H    0     0                       0.5261139    0.41312  21.5%     -    1s
     0     2    0.41312    0   23    0.52611    0.41312  21.5%     -    1s
   986   379    0.48695    9   10    0.52611    0.45941  12.7%  24.6    5s
  3548   792    0.51236   10   15    0.52611    0.47903  8.95%  21.2   10s
  4169   851    0.50403   13   23    0.52611    0.48092  8.59%  21.0   15s
H 4374   882                       0.5261139    0.48092  8.59%  22.3   17s
  6568   600    0.51160   29   10    0.52611    0.48092  8.59%  24.0   20s
H 6730   596                       0.5261139    0.48092  8.59%  24.1   21s
H 7839   675                       0.5261139    0.48648  7.53%  24.1   23s
  8305   670    0.52123   29    8    0.52611    0.48801  7.24%  24.2   25s
H 9601   654                       0.5261139    0.49359  6.18%  24.1   28s
 10072   618    0.50822   25   10    0.52611    0.49618  5.69%  24.1   30s
H10100   618                       0.5261139    0.49618  5.69%  24.1   30s
 11367   398     cutoff   25         0.52611    0.50254  4.48%  24.0   35s

Cutting planes:
  Implied bound: 212
  MIR: 96
  Flow cover: 294
  RLT: 49
  Relax-and-lift: 84

Explored 12814 nodes (304387 simplex iterations) in 36.57 seconds (29.59 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.526114 0.526114 0.526114 ... 0.683829

Optimal solution found (tolerance 1.00e-04)
Best objective 5.261138776581e-01, best bound 5.261138776581e-01, gap 0.0000%
The objective bound is 0.526114 while the objective upper bound is 0.526114

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.50 (ave)

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