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 0.266609 seconds.
    local lower bound updated to 0.204502
    local upper bound updated to 0.39882

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.286255 seconds.
    local lower bound updated to 0.385643
    local upper bound updated to 0.385643
The Primal step takes 0.555527 (S)
lower bound updated to 0.385643

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.570621
    local lower bound updated to 0.540978

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.550715
    local lower bound updated to 0.550715
The Dual step takes 0.0433687 (S)
upper bound updated to 0.550715
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.76615 seconds.
    local lower bound updated to 0.283779
    local upper bound updated to 0.40484

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.498446 seconds.
    local lower bound updated to 0.391191
    local upper bound updated to 0.395634

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.478577 seconds.
    local lower bound updated to 0.391191
    local upper bound updated to 0.395264

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.622714 seconds.
    local lower bound updated to 0.391191
    local upper bound updated to 0.392729

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.608556 seconds.
    local lower bound updated to 0.392729
    local upper bound updated to 0.392729
The Primal step takes 2.98332 (S)
lower bound updated to 0.392729

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.454219
    local lower bound updated to 0.40489

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.4308
    local lower bound updated to 0.417692

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.429822
    local lower bound updated to 0.422027

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.422027
    local lower bound updated to 0.422027
The Dual step takes 0.52057 (S)
upper bound updated to 0.422027
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.97742 seconds.
    local lower bound updated to 0.337629
    local upper bound updated to 0.416403

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.42246 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.407323

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.29114 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.406072

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.5704 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.405123

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.14995 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.404811

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.67652 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.404733

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.41437 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.404631

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.25067 seconds.
    local lower bound updated to 0.403965
    local upper bound updated to 0.404497

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 1.86899 seconds.
    local lower bound updated to 0.404497
    local upper bound updated to 0.404497
The Primal step takes 13.6494 (S)
lower bound updated to 0.404497

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.446531
    local lower bound updated to 0.405452

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.413438
    local lower bound updated to 0.407126

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.411994
    local lower bound updated to 0.407398

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.407398
    local lower bound updated to 0.407398
The Dual step takes 4.77773 (S)
upper bound updated to 0.407398
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.56258 seconds.
    local lower bound updated to 0.350122
    local upper bound updated to 0.407398

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.51307 seconds.
    local lower bound updated to 0.400866
    local upper bound updated to 0.407248

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.75123 seconds.
    local lower bound updated to 0.402181
    local upper bound updated to 0.406847

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.84059 seconds.
    local lower bound updated to 0.403288
    local upper bound updated to 0.406746

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.88407 seconds.
    local lower bound updated to 0.404056
    local upper bound updated to 0.406502

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.33173 seconds.
    local lower bound updated to 0.404056
    local upper bound updated to 0.406402

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.30762 seconds.
    local lower bound updated to 0.405932
    local upper bound updated to 0.406376

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 4.11201 seconds.
    local lower bound updated to 0.406019
    local upper bound updated to 0.406359

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 3.52416 seconds.
    local lower bound updated to 0.406359
    local upper bound updated to 0.406359
The Primal step takes 35.8708 (S)
lower bound updated to 0.406359

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.433745
    local lower bound updated to 0.406639

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.410289
    local lower bound updated to 0.406873

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.407463
    local lower bound updated to 0.406886

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.407376
    local lower bound updated to 0.406937

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.406937
    local lower bound updated to 0.406937
The Dual step takes 10.3302 (S)
upper bound updated to 0.406937
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.88284 seconds.
    local lower bound updated to 0.363672
    local upper bound updated to 0.406937

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.47425 seconds.
    local lower bound updated to 0.402896
    local upper bound updated to 0.406579

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.30686 seconds.
    local lower bound updated to 0.404034
    local upper bound updated to 0.406367

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.37546 seconds.
    local lower bound updated to 0.405878
    local upper bound updated to 0.406359

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.53651 seconds.
    local lower bound updated to 0.406359
    local upper bound updated to 0.406359
The Primal step takes 24.6055 (S)
lower bound updated to 0.406359

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.429925
    local lower bound updated to 0.406359

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.407462
    local lower bound updated to 0.406359

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.406359
    local lower bound updated to 0.406359
The Dual step takes 9.31465 (S)
upper bound updated to 0.406359
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.74475 seconds.
    local lower bound updated to 0.368382
    local upper bound updated to 0.406359

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.52903 seconds.
    local lower bound updated to 0.406359
    local upper bound updated to 0.406359
The time obtain the optimal randomized assortment is 113.939 (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_106016.log"
The computation time limit for a lower bound is 85884
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 2640 rows, 2138 columns and 8435 nonzeros
Model fingerprint: 0x279a5dc1
Variable types: 2081 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e-01, 1e+00]
Presolve removed 731 rows and 1317 columns
Presolve time: 0.02s
Presolved: 1909 rows, 821 columns, 7367 nonzeros
Variable types: 766 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5365709
Found heuristic solution: objective 0.5306374
Found heuristic solution: objective 0.4695472

Root relaxation: objective 3.116759e-01, 163 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    0.31168    0   15    0.46955    0.31168  33.6%     -    0s
H    0     0                       0.4312749    0.31829  26.2%     -    0s
H    0     0                       0.4289881    0.31829  25.8%     -    0s
     0     0    0.31829    0   23    0.42899    0.31829  25.8%     -    0s
     0     0    0.31829    0   23    0.42899    0.31829  25.8%     -    0s
     0     0    0.33456    0   22    0.42899    0.33456  22.0%     -    0s
H    0     0                       0.4183392    0.33456  20.0%     -    0s
     0     0    0.33469    0   23    0.41834    0.33469  20.0%     -    0s
     0     0    0.34351    0   23    0.41834    0.34351  17.9%     -    0s
H    0     0                       0.4158259    0.34351  17.4%     -    0s
     0     0    0.34421    0   23    0.41583    0.34421  17.2%     -    0s
     0     0    0.35183    0   22    0.41583    0.35183  15.4%     -    0s
H    0     0                       0.4155814    0.35238  15.2%     -    0s
     0     0    0.35238    0   24    0.41558    0.35238  15.2%     -    0s
     0     0    0.35434    0   21    0.41558    0.35434  14.7%     -    0s
H    0     0                       0.4063587    0.35434  12.8%     -    0s
     0     2    0.35434    0   21    0.40636    0.35434  12.8%     -    1s
  1690    39    0.39639   11   12    0.40636    0.39422  2.99%  32.0    5s

Cutting planes:
  Implied bound: 270
  MIR: 87
  Flow cover: 256
  RLT: 16
  Relax-and-lift: 140

Explored 1844 nodes (60022 simplex iterations) in 5.46 seconds (4.15 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.406359 0.415581 0.415826 ... 0.536571

Optimal solution found (tolerance 1.00e-04)
Best objective 4.063587154008e-01, best bound 4.063587154008e-01, gap 0.0000%
The objective bound is 0.406359 while the objective upper bound is 0.406359

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.11 (ave)

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