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 0.667791 seconds.
    local lower bound updated to 0.230348
    local upper bound updated to 0.445793

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.294833 seconds.
    local lower bound updated to 0.414558
    local upper bound updated to 0.414558
The Primal step takes 0.965418 (S)
lower bound updated to 0.414558

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.552214
    local lower bound updated to 0.512368

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.526527
    local lower bound updated to 0.521791

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.526527
    local lower bound updated to 0.524081

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.524081
    local lower bound updated to 0.524081
The Dual step takes 0.17858 (S)
upper bound updated to 0.524081
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.577917 seconds.
    local lower bound updated to 0.3047
    local upper bound updated to 0.437395

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.868263 seconds.
    local lower bound updated to 0.41949
    local upper bound updated to 0.421277

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.637051 seconds.
    local lower bound updated to 0.41949
    local upper bound updated to 0.420253

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.864533 seconds.
    local lower bound updated to 0.419991
    local upper bound updated to 0.420219

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.770674 seconds.
    local lower bound updated to 0.420219
    local upper bound updated to 0.420219
The Primal step takes 3.73246 (S)
lower bound updated to 0.420219

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.472555
    local lower bound updated to 0.430444

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.469035
    local lower bound updated to 0.432491

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.449208
    local lower bound updated to 0.445427

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.449208
    local lower bound updated to 0.445552

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.449208
    local lower bound updated to 0.445634

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.449139
    local lower bound updated to 0.445673

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.449139
    local lower bound updated to 0.445957

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.446051
    local lower bound updated to 0.445979

    ++ RESTRICTED DUAL ITERATION 9 ++
    local upper bound updated to 0.445979
    local lower bound updated to 0.445979
The Dual step takes 5.87773 (S)
upper bound updated to 0.445979
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.22361 seconds.
    local lower bound updated to 0.355692
    local upper bound updated to 0.435883

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 28.0015 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.428739

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.95632 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.427327

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.4774 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.425804

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.32488 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.425714

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.27122 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.425158

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 6.88916 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.424884

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 15.5347 seconds.
    local lower bound updated to 0.42292
    local upper bound updated to 0.424248

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 18.6368 seconds.
    local lower bound updated to 0.424013
    local upper bound updated to 0.424227

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 15.199 seconds.
    local lower bound updated to 0.424227
    local upper bound updated to 0.424227
The Primal step takes 116.58 (S)
lower bound updated to 0.424227

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.442188
    local lower bound updated to 0.430978

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.43838
    local lower bound updated to 0.43129

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.432179
    local lower bound updated to 0.431313

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.431313
    local lower bound updated to 0.431313
The Dual step takes 10.0196 (S)
upper bound updated to 0.431313
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.85911 seconds.
    local lower bound updated to 0.363905
    local upper bound updated to 0.431313

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.5186 seconds.
    local lower bound updated to 0.427022
    local upper bound updated to 0.430642

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 17.6052 seconds.
    local lower bound updated to 0.427931
    local upper bound updated to 0.430466

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 16.3232 seconds.
    local lower bound updated to 0.429824
    local upper bound updated to 0.430352

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.4991 seconds.
    local lower bound updated to 0.429824
    local upper bound updated to 0.430326

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 18.5467 seconds.
    local lower bound updated to 0.429936
    local upper bound updated to 0.430269

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 14.9954 seconds.
    local lower bound updated to 0.429936
    local upper bound updated to 0.430243

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 20.7978 seconds.
    local lower bound updated to 0.430243
    local upper bound updated to 0.430243
The Primal step takes 123.207 (S)
lower bound updated to 0.430243

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.438261
    local lower bound updated to 0.430243

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.436662
    local lower bound updated to 0.430687

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.435707
    local lower bound updated to 0.430687

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.433964
    local lower bound updated to 0.430716

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.432945
    local lower bound updated to 0.430725

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.432551
    local lower bound updated to 0.430744

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.430744
    local lower bound updated to 0.430744
The Dual step takes 23.2591 (S)
upper bound updated to 0.430744
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.5676 seconds.
    local lower bound updated to 0.373463
    local upper bound updated to 0.430744

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 26.065 seconds.
    local lower bound updated to 0.430062
    local upper bound updated to 0.430707

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 18.5836 seconds.
    local lower bound updated to 0.430307
    local upper bound updated to 0.430588

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 24.511 seconds.
    local lower bound updated to 0.430391
    local upper bound updated to 0.430577

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 29.3085 seconds.
    local lower bound updated to 0.430479
    local upper bound updated to 0.43057

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 21.4974 seconds.
    local lower bound updated to 0.430522
    local upper bound updated to 0.430562

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 21.5215 seconds.
    local lower bound updated to 0.430522
    local upper bound updated to 0.430558

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 30.8308 seconds.
    local lower bound updated to 0.430522
    local upper bound updated to 0.430555

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 23.2082 seconds.
    local lower bound updated to 0.430555
    local upper bound updated to 0.430555
The Primal step takes 206.197 (S)
lower bound updated to 0.430555

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.436474
    local lower bound updated to 0.430555

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.433787
    local lower bound updated to 0.430674

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.430674
    local lower bound updated to 0.430674
The Dual step takes 20.6702 (S)
upper bound updated to 0.430674
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 11.6696 seconds.
    local lower bound updated to 0.376548
    local upper bound updated to 0.430674

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 27.9406 seconds.
    local lower bound updated to 0.430526
    local upper bound updated to 0.430658

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 35.1596 seconds.
    local lower bound updated to 0.430526
    local upper bound updated to 0.43063

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 27.3158 seconds.
    local lower bound updated to 0.430526
    local upper bound updated to 0.4306

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 18.0726 seconds.
    local lower bound updated to 0.4306
    local upper bound updated to 0.4306
The Primal step takes 120.22 (S)
lower bound updated to 0.4306

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.436013
    local lower bound updated to 0.4306

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.433003
    local lower bound updated to 0.4306

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.4306
    local lower bound updated to 0.4306
The Dual step takes 22.41 (S)
upper bound updated to 0.4306
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.90592 seconds.
    local lower bound updated to 0.376323
    local upper bound updated to 0.4306

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 38.9582 seconds.
    local lower bound updated to 0.4306
    local upper bound updated to 0.4306
The time obtain the optimal randomized assortment is 702.213 (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_100.000000_107218.log"
The computation time limit for a lower bound is 85292
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 4544 rows, 3470 columns and 14941 nonzeros
Model fingerprint: 0x68f97aa5
Variable types: 3405 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [3e-08, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 1066 rows and 1968 columns
Presolve time: 0.07s
Presolved: 3478 rows, 1502 columns, 13633 nonzeros
Variable types: 1438 continuous, 64 integer (64 binary)
Found heuristic solution: objective 0.6098052
Found heuristic solution: objective 0.5180669

Root relaxation: objective 3.598229e-01, 423 iterations, 0.02 seconds (0.01 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.35982    0   24    0.51807    0.35982  30.5%     -    0s
H    0     0                       0.5082268    0.35982  29.2%     -    0s
     0     0    0.36025    0   28    0.50823    0.36025  29.1%     -    0s
H    0     0                       0.5050463    0.37775  25.2%     -    0s
H    0     0                       0.4989266    0.37775  24.3%     -    0s
H    0     0                       0.4753497    0.37775  20.5%     -    0s
     0     0    0.37775    0   28    0.47535    0.37775  20.5%     -    0s
     0     0    0.37905    0   28    0.47535    0.37905  20.3%     -    0s
H    0     0                       0.4347390    0.38929  10.5%     -    1s
     0     0    0.38929    0   26    0.43474    0.38929  10.5%     -    1s
H    0     0                       0.4309202    0.38929  9.66%     -    1s
     0     0    0.38947    0   26    0.43092    0.38947  9.62%     -    1s
     0     0    0.39402    0   27    0.43092    0.39402  8.56%     -    1s
H    0     0                       0.4308702    0.39484  8.36%     -    1s
H    0     0                       0.4307212    0.39484  8.33%     -    1s
     0     0    0.39484    0   27    0.43072    0.39484  8.33%     -    1s
     0     0    0.39600    0   27    0.43072    0.39600  8.06%     -    1s
H    0     0                       0.4306001    0.39600  8.04%     -    4s
     0     2    0.39600    0   27    0.43060    0.39600  8.04%     -    4s
    11    16    0.40905    4   23    0.43060    0.39817  7.53%   143    5s
   395   126    0.41762    6   18    0.43060    0.40502  5.94%  43.2   10s
   697   183    0.42146   11   16    0.43060    0.40835  5.17%  38.9   15s
  1180   246    0.42915   12    4    0.43060    0.41239  4.23%  37.1   20s
  2066   311     cutoff   17         0.43060    0.41637  3.31%  36.1   25s
  3433   256     cutoff   16         0.43060    0.42056  2.33%  34.0   30s
  4691   156     cutoff   16         0.43060    0.42348  1.65%  32.3   36s

Cutting planes:
  Implied bound: 585
  MIR: 112
  Flow cover: 435
  RLT: 35
  Relax-and-lift: 268

Explored 5124 nodes (168318 simplex iterations) in 38.53 seconds (23.08 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.4306 0.430721 0.43087 ... 0.518067
No other solutions better than 0.4306

Optimal solution found (tolerance 1.00e-04)
Best objective 4.306000015452e-01, best bound 4.306000015452e-01, gap 0.0000%
The objective bound is 0.4306 while the objective upper bound is 0.4306

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.21 (ave)

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