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 0.235236 seconds.
    local lower bound updated to 0.280204
    local upper bound updated to 0.530452

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.520905 seconds.
    local lower bound updated to 0.529775
    local upper bound updated to 0.529775
The Primal step takes 0.758227 (S)
lower bound updated to 0.529775

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.599283
    local lower bound updated to 0.599283
The Dual step takes 0.0112288 (S)
upper bound updated to 0.599283
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.525576 seconds.
    local lower bound updated to 0.31948
    local upper bound updated to 0.533134

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.811847 seconds.
    local lower bound updated to 0.525951
    local upper bound updated to 0.529775

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.718219 seconds.
    local lower bound updated to 0.529775
    local upper bound updated to 0.529775
The Primal step takes 2.06084 (S)
lower bound updated to 0.529775

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.565787
    local lower bound updated to 0.55376

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.55376
    local lower bound updated to 0.55376
The Dual step takes 0.0869815 (S)
upper bound updated to 0.55376
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.687234 seconds.
    local lower bound updated to 0.363032
    local upper bound updated to 0.530658

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.818393 seconds.
    local lower bound updated to 0.530068
    local upper bound updated to 0.530543

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.853067 seconds.
    local lower bound updated to 0.530514
    local upper bound updated to 0.53052
The Primal step takes 2.36527 (S)
lower bound updated to 0.530514

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.553656
    local lower bound updated to 0.533079

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.533671
    local lower bound updated to 0.533201

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.533231
    local lower bound updated to 0.53323
The Dual step takes 0.197657 (S)
upper bound updated to 0.533231
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.16279 seconds.
    local lower bound updated to 0.435023
    local upper bound updated to 0.53323

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.600592 seconds.
    local lower bound updated to 0.516337
    local upper bound updated to 0.53144

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.1134 seconds.
    local lower bound updated to 0.531384
    local upper bound updated to 0.531429

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.28082 seconds.
    local lower bound updated to 0.53142
    local upper bound updated to 0.531424
The Primal step takes 4.17018 (S)
lower bound updated to 0.53142

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.543414
    local lower bound updated to 0.531424

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.533084
    local lower bound updated to 0.531433

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.531524
    local lower bound updated to 0.531435

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.531435
    local lower bound updated to 0.531435
The Dual step takes 0.614522 (S)
upper bound updated to 0.531435
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.81406 seconds.
    local lower bound updated to 0.443155
    local upper bound updated to 0.531435

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.91993 seconds.
    local lower bound updated to 0.531431
    local upper bound updated to 0.531435
The Primal step takes 3.74284 (S)
lower bound updated to 0.531431

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.539892
    local lower bound updated to 0.531435

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.531435
    local lower bound updated to 0.531435
The Dual step takes 0.49371 (S)
upper bound updated to 0.531435
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.84705 seconds.
    local lower bound updated to 0.443155
    local upper bound updated to 0.531435

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.43662 seconds.
    local lower bound updated to 0.531434
    local upper bound updated to 0.531435
The time obtain the optimal randomized assortment is 18.7936 (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_201014.log"
The computation time limit for a lower bound is 85978
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 1212 rows, 1058 columns and 3788 nonzeros
Model fingerprint: 0x601286b6
Variable types: 1009 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [2e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 351 rows and 677 columns
Presolve time: 0.02s
Presolved: 861 rows, 381 columns, 3265 nonzeros
Variable types: 334 continuous, 47 integer (47 binary)
Found heuristic solution: objective 0.7082251
Found heuristic solution: objective 0.6145089

Root relaxation: objective 2.170937e-01, 139 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    0.21709    0   16    0.61451    0.21709  64.7%     -    0s
H    0     0                       0.5756273    0.21709  62.3%     -    0s
     0     0    0.23534    0   21    0.57563    0.23534  59.1%     -    0s
H    0     0                       0.5739902    0.23534  59.0%     -    0s
H    0     0                       0.5733754    0.30447  46.9%     -    0s
     0     0    0.30447    0   23    0.57338    0.30447  46.9%     -    0s
H    0     0                       0.5350457    0.30447  43.1%     -    0s
     0     0    0.31240    0   23    0.53505    0.31240  41.6%     -    0s
H    0     0                       0.5345167    0.37095  30.6%     -    0s
     0     0    0.37095    0   20    0.53452    0.37095  30.6%     -    0s
     0     0    0.37133    0   22    0.53452    0.37133  30.5%     -    0s
H    0     0                       0.5334585    0.37133  30.4%     -    0s
H    0     0                       0.5334578    0.37133  30.4%     -    0s
     0     0    0.40228    0   21    0.53346    0.40228  24.6%     -    0s
     0     0    0.40358    0   22    0.53346    0.40358  24.3%     -    0s
     0     0    0.42256    0   21    0.53346    0.42256  20.8%     -    0s
H    0     0                       0.5314346    0.42256  20.5%     -    0s
     0     2    0.42256    0   21    0.53143    0.42256  20.5%     -    0s
H   98    52                       0.5314342    0.44723  15.8%  13.4    0s

Cutting planes:
  Gomory: 1
  Implied bound: 128
  MIR: 25
  Flow cover: 82
  RLT: 12
  Relax-and-lift: 47

Explored 1617 nodes (19298 simplex iterations) in 2.39 seconds (1.29 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.531434 0.531435 0.533458 ... 0.614509

Optimal solution found (tolerance 1.00e-04)
Best objective 5.314342319859e-01, best bound 5.314342319859e-01, gap 0.0000%
The objective bound is 0.531434 while the objective upper bound is 0.531434

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

        Job resource usage summary 

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

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