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 0.162151 seconds.
    local lower bound updated to 0.173883
    local upper bound updated to 0.343685

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.122411 seconds.
    local lower bound updated to 0.338603
    local upper bound updated to 0.338603
The Primal step takes 0.287346 (S)
lower bound updated to 0.338603

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.414973
    local lower bound updated to 0.414009

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.414973
    local lower bound updated to 0.414806

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.414806
    local lower bound updated to 0.414806
The Dual step takes 0.0386612 (S)
upper bound updated to 0.414806
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.476234 seconds.
    local lower bound updated to 0.257663
    local upper bound updated to 0.38271

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.259551 seconds.
    local lower bound updated to 0.257663
    local upper bound updated to 0.372601

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.618692 seconds.
    local lower bound updated to 0.346005
    local upper bound updated to 0.349831

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.35014 seconds.
    local lower bound updated to 0.348407
    local upper bound updated to 0.3496

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.00584 seconds.
    local lower bound updated to 0.349347
    local upper bound updated to 0.349392

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.25376 seconds.
    local lower bound updated to 0.349392
    local upper bound updated to 0.349392
The Primal step takes 4.97763 (S)
lower bound updated to 0.349392

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.424148
    local lower bound updated to 0.366471

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.404277
    local lower bound updated to 0.377584

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.404277
    local lower bound updated to 0.394607

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.404277
    local lower bound updated to 0.395415

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.404277
    local lower bound updated to 0.396397

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.399928
    local lower bound updated to 0.396662

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.396787
    local lower bound updated to 0.396673

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.396673
    local lower bound updated to 0.396673
The Dual step takes 0.582337 (S)
upper bound updated to 0.396673
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.960572 seconds.
    local lower bound updated to 0.30476
    local upper bound updated to 0.395733

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.778639 seconds.
    local lower bound updated to 0.326244
    local upper bound updated to 0.376448

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.07818 seconds.
    local lower bound updated to 0.367143
    local upper bound updated to 0.375905

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.61152 seconds.
    local lower bound updated to 0.367143
    local upper bound updated to 0.375871

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.8754 seconds.
    local lower bound updated to 0.373843
    local upper bound updated to 0.375769

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.59446 seconds.
    local lower bound updated to 0.373896
    local upper bound updated to 0.375474

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 11.5919 seconds.
    local lower bound updated to 0.375277
    local upper bound updated to 0.375441

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 13.0972 seconds.
    local lower bound updated to 0.375321
    local upper bound updated to 0.375426

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 17.1652 seconds.
    local lower bound updated to 0.375321
    local upper bound updated to 0.375425

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 8.55611 seconds.
    local lower bound updated to 0.37538
    local upper bound updated to 0.375404

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 13.2176 seconds.
    local lower bound updated to 0.375404
    local upper bound updated to 0.375404
The Primal step takes 92.5758 (S)
lower bound updated to 0.375404

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.432222
    local lower bound updated to 0.375404

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.406423
    local lower bound updated to 0.382008

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.406423
    local lower bound updated to 0.386891

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.406423
    local lower bound updated to 0.387693

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.406423
    local lower bound updated to 0.388491

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.402794
    local lower bound updated to 0.388862

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.392784
    local lower bound updated to 0.389015

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.389015
    local lower bound updated to 0.389015
The Dual step takes 2.03662 (S)
upper bound updated to 0.389015
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.06379 seconds.
    local lower bound updated to 0.334199
    local upper bound updated to 0.383694

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.02662 seconds.
    local lower bound updated to 0.35703
    local upper bound updated to 0.381305

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.59276 seconds.
    local lower bound updated to 0.377595
    local upper bound updated to 0.380679

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.69617 seconds.
    local lower bound updated to 0.37912
    local upper bound updated to 0.380509

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.84779 seconds.
    local lower bound updated to 0.379156
    local upper bound updated to 0.380213

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.2786 seconds.
    local lower bound updated to 0.379156
    local upper bound updated to 0.380182

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.79624 seconds.
    local lower bound updated to 0.379223
    local upper bound updated to 0.380134

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 8.85714 seconds.
    local lower bound updated to 0.379588
    local upper bound updated to 0.380118

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 8.85771 seconds.
    local lower bound updated to 0.379588
    local upper bound updated to 0.380094

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 13.8551 seconds.
    local lower bound updated to 0.380094
    local upper bound updated to 0.380094
The Primal step takes 71.9511 (S)
lower bound updated to 0.380094

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.417909
    local lower bound updated to 0.380094

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.38803
    local lower bound updated to 0.381152

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.387141
    local lower bound updated to 0.381971

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.382361
    local lower bound updated to 0.381982

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.381982
    local lower bound updated to 0.381982
The Dual step takes 3.23608 (S)
upper bound updated to 0.381982
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.4186 seconds.
    local lower bound updated to 0.341132
    local upper bound updated to 0.381982

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 8.61265 seconds.
    local lower bound updated to 0.379284
    local upper bound updated to 0.381759

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.4245 seconds.
    local lower bound updated to 0.38015
    local upper bound updated to 0.381655

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.911 seconds.
    local lower bound updated to 0.380909
    local upper bound updated to 0.381475

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 13.2612 seconds.
    local lower bound updated to 0.381059
    local upper bound updated to 0.381403

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 11.439 seconds.
    local lower bound updated to 0.381345
    local upper bound updated to 0.3814

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 13.2154 seconds.
    local lower bound updated to 0.381357
    local upper bound updated to 0.381392

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 14.6658 seconds.
    local lower bound updated to 0.381392
    local upper bound updated to 0.381392
The Primal step takes 90.0195 (S)
lower bound updated to 0.381392

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.41772
    local lower bound updated to 0.381392

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.387524
    local lower bound updated to 0.381392

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.381559
    local lower bound updated to 0.381394

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.381394
    local lower bound updated to 0.381394
The Dual step takes 5.29868 (S)
upper bound updated to 0.381394
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.66086 seconds.
    local lower bound updated to 0.34441
    local upper bound updated to 0.381394

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.2116 seconds.
    local lower bound updated to 0.381394
    local upper bound updated to 0.381394
The time obtain the optimal randomized assortment is 291.894 (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_13_4_200.000000_206714.log"
The computation time limit for a lower bound is 85707
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 20 physical cores, 40 logical processors, using up to 4 threads
Optimize a model with 2850 rows, 2514 columns and 8832 nonzeros
Model fingerprint: 0x12aeb990
Variable types: 2465 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [3e-09, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 966 rows and 1723 columns
Presolve time: 0.03s
Presolved: 1884 rows, 791 columns, 7048 nonzeros
Variable types: 744 continuous, 47 integer (47 binary)
Found heuristic solution: objective 0.4116049
Found heuristic solution: objective 0.4013868
Found heuristic solution: objective 0.4000106

Root relaxation: objective 1.911631e-01, 259 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    0.19116    0   16    0.40001    0.19116  52.2%     -    0s
     0     0    0.25828    0   23    0.40001    0.25828  35.4%     -    0s
H    0     0                       0.3875323    0.25828  33.4%     -    0s
     0     0    0.28637    0   22    0.38753    0.28637  26.1%     -    0s
H    0     0                       0.3867089    0.28637  25.9%     -    0s
H    0     0                       0.3864979    0.29080  24.8%     -    0s
     0     0    0.29080    0   22    0.38650    0.29080  24.8%     -    0s
     0     0    0.29660    0   24    0.38650    0.29660  23.3%     -    0s
     0     0    0.29711    0   23    0.38650    0.29711  23.1%     -    0s
     0     0    0.29711    0   25    0.38650    0.29711  23.1%     -    0s
H    0     0                       0.3830864    0.29711  22.4%     -    0s
     0     0    0.29711    0   25    0.38309    0.29711  22.4%     -    0s
     0     0    0.29711    0   25    0.38309    0.29711  22.4%     -    0s
H    0     0                       0.3813944    0.29711  22.1%     -    1s
     0     2    0.29711    0   25    0.38139    0.29711  22.1%     -    1s
H  217    49                       0.3813944    0.33340  12.6%  44.0    2s
H  380    64                       0.3813944    0.34331  10.0%  40.5    2s
  1348   156    0.36895   15    8    0.38139    0.36153  5.21%  33.6    5s
  3235   203    0.37839   14    8    0.38139    0.37183  2.51%  28.0   10s
H 5074    22                       0.3813944    0.37938  0.53%  25.2   13s

Cutting planes:
  Gomory: 1
  Implied bound: 303
  MIR: 112
  Flow cover: 237
  RLT: 29
  Relax-and-lift: 139

Explored 5110 nodes (130483 simplex iterations) in 13.27 seconds (7.95 work units)
Thread count was 4 (of 40 available processors)

Solution count 8: 0.381394 0.383086 0.386498 ... 0.411605
No other solutions better than 0.381394

Optimal solution found (tolerance 1.00e-04)
Best objective 3.813944039180e-01, best bound 3.813944039180e-01, gap 0.0000%
The objective bound is 0.381394 while the objective upper bound is 0.381394

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.08 (ave)

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