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 0.0856433 seconds.
    local lower bound updated to 0.244221
    local upper bound updated to 0.488092

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.294578 seconds.
    local lower bound updated to 0.487159
    local upper bound updated to 0.487159
The Primal step takes 0.383215 (S)
lower bound updated to 0.487159

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.598418
    local lower bound updated to 0.598256

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.598418
    local lower bound updated to 0.598383

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.598418
    local lower bound updated to 0.598386

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.598386
    local lower bound updated to 0.598386
The Dual step takes 0.0588389 (S)
upper bound updated to 0.598386
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.63924 seconds.
    local lower bound updated to 0.380974
    local upper bound updated to 0.556327

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.562001 seconds.
    local lower bound updated to 0.41905
    local upper bound updated to 0.50347

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.65388 seconds.
    local lower bound updated to 0.490155
    local upper bound updated to 0.494981

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.957349 seconds.
    local lower bound updated to 0.49043
    local upper bound updated to 0.49403

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.19182 seconds.
    local lower bound updated to 0.493923
    local upper bound updated to 0.493942

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.21559 seconds.
    local lower bound updated to 0.493942
    local upper bound updated to 0.493942
The Primal step takes 5.24037 (S)
lower bound updated to 0.493942

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.56127
    local lower bound updated to 0.521221

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.56127
    local lower bound updated to 0.547271

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.55924
    local lower bound updated to 0.548293

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.557975
    local lower bound updated to 0.548476

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.548476
    local lower bound updated to 0.548476
The Dual step takes 0.843563 (S)
upper bound updated to 0.548476
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.62788 seconds.
    local lower bound updated to 0.428317
    local upper bound updated to 0.528316

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.18451 seconds.
    local lower bound updated to 0.497802
    local upper bound updated to 0.513115

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.74833 seconds.
    local lower bound updated to 0.50366
    local upper bound updated to 0.512993

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.88534 seconds.
    local lower bound updated to 0.50366
    local upper bound updated to 0.512612

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.44456 seconds.
    local lower bound updated to 0.508261
    local upper bound updated to 0.511523

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.72167 seconds.
    local lower bound updated to 0.508487
    local upper bound updated to 0.511443

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 1.56181 seconds.
    local lower bound updated to 0.508966
    local upper bound updated to 0.510282

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.74838 seconds.
    local lower bound updated to 0.508966
    local upper bound updated to 0.509882

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 1.52811 seconds.
    local lower bound updated to 0.508966
    local upper bound updated to 0.509695

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 1.69077 seconds.
    local lower bound updated to 0.509378
    local upper bound updated to 0.509694

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 1.68219 seconds.
    local lower bound updated to 0.509407
    local upper bound updated to 0.509638

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 1.46631 seconds.
    local lower bound updated to 0.509638
    local upper bound updated to 0.509638
The Primal step takes 20.3574 (S)
lower bound updated to 0.509638

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.540372
    local lower bound updated to 0.5139

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.540372
    local lower bound updated to 0.517352

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.529509
    local lower bound updated to 0.518437

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.529056
    local lower bound updated to 0.521301

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.529056
    local lower bound updated to 0.522594

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.525932
    local lower bound updated to 0.523981

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.525121
    local lower bound updated to 0.524022

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.524022
    local lower bound updated to 0.524022
The Dual step takes 3.60227 (S)
upper bound updated to 0.524022
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.66168 seconds.
    local lower bound updated to 0.449203
    local upper bound updated to 0.524022

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.5478 seconds.
    local lower bound updated to 0.449203
    local upper bound updated to 0.520696

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.54713 seconds.
    local lower bound updated to 0.496354
    local upper bound updated to 0.520055

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.61518 seconds.
    local lower bound updated to 0.511192
    local upper bound updated to 0.519668

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 6.25422 seconds.
    local lower bound updated to 0.514203
    local upper bound updated to 0.519345

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.27222 seconds.
    local lower bound updated to 0.514473
    local upper bound updated to 0.519134

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.30598 seconds.
    local lower bound updated to 0.515154
    local upper bound updated to 0.518901

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.78447 seconds.
    local lower bound updated to 0.516313
    local upper bound updated to 0.518767

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 5.49706 seconds.
    local lower bound updated to 0.517963
    local upper bound updated to 0.518731

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 6.01755 seconds.
    local lower bound updated to 0.517963
    local upper bound updated to 0.51865

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 8.94765 seconds.
    local lower bound updated to 0.518324
    local upper bound updated to 0.51864

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 5.82698 seconds.
    local lower bound updated to 0.518426
    local upper bound updated to 0.518603

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 7.61588 seconds.
    local lower bound updated to 0.518426
    local upper bound updated to 0.518598

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 8.3641 seconds.
    local lower bound updated to 0.518426
    local upper bound updated to 0.518594

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 6.94299 seconds.
    local lower bound updated to 0.518557
    local upper bound updated to 0.518591

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 9.17831 seconds.
    local lower bound updated to 0.518591
    local upper bound updated to 0.518591
The Primal step takes 91.5379 (S)
lower bound updated to 0.518591

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.550769
    local lower bound updated to 0.518666

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.52405
    local lower bound updated to 0.519228

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.522501
    local lower bound updated to 0.519348

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.520585
    local lower bound updated to 0.51943

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.51943
    local lower bound updated to 0.51943
The Dual step takes 17.4306 (S)
upper bound updated to 0.51943
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 6.79272 seconds.
    local lower bound updated to 0.468253
    local upper bound updated to 0.51943

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.19778 seconds.
    local lower bound updated to 0.504183
    local upper bound updated to 0.519166

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.12536 seconds.
    local lower bound updated to 0.509924
    local upper bound updated to 0.519128

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.3032 seconds.
    local lower bound updated to 0.516118
    local upper bound updated to 0.519091

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.2451 seconds.
    local lower bound updated to 0.517498
    local upper bound updated to 0.519071

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 11.4737 seconds.
    local lower bound updated to 0.518227
    local upper bound updated to 0.519057

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 10.3328 seconds.
    local lower bound updated to 0.518227
    local upper bound updated to 0.518966

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 9.19022 seconds.
    local lower bound updated to 0.518227
    local upper bound updated to 0.518961

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 10.5528 seconds.
    local lower bound updated to 0.518344
    local upper bound updated to 0.518888

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 7.91655 seconds.
    local lower bound updated to 0.518344
    local upper bound updated to 0.518884

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 7.59589 seconds.
    local lower bound updated to 0.518523
    local upper bound updated to 0.518881

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 11.1135 seconds.
    local lower bound updated to 0.518714
    local upper bound updated to 0.518881

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 9.03451 seconds.
    local lower bound updated to 0.518806
    local upper bound updated to 0.51888

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 9.18486 seconds.
    local lower bound updated to 0.518806
    local upper bound updated to 0.518879

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 10.8851 seconds.
    local lower bound updated to 0.518806
    local upper bound updated to 0.518879

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 11.6494 seconds.
    local lower bound updated to 0.518874
    local upper bound updated to 0.518879
The Primal step takes 144.777 (S)
lower bound updated to 0.518874

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.554844
    local lower bound updated to 0.518879

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.523141
    local lower bound updated to 0.518889

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.518889
    local lower bound updated to 0.518889
The Dual step takes 17.71 (S)
upper bound updated to 0.518889
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.07435 seconds.
    local lower bound updated to 0.466439
    local upper bound updated to 0.518889

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 13.1659 seconds.
    local lower bound updated to 0.517942
    local upper bound updated to 0.518888

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 11.5317 seconds.
    local lower bound updated to 0.517956
    local upper bound updated to 0.518879

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.2029 seconds.
    local lower bound updated to 0.518855
    local upper bound updated to 0.518879

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.0016 seconds.
    local lower bound updated to 0.518879
    local upper bound updated to 0.518879
The Primal step takes 53.0397 (S)
lower bound updated to 0.518879

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.555471
    local lower bound updated to 0.518879

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518879
    local lower bound updated to 0.518879
The Dual step takes 13.2747 (S)
upper bound updated to 0.518879
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.00851 seconds.
    local lower bound updated to 0.466439
    local upper bound updated to 0.518879

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.4261 seconds.
    local lower bound updated to 0.518879
    local upper bound updated to 0.518879
The time obtain the optimal randomized assortment is 384.716 (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_208714.log"
The computation time limit for a lower bound is 85613
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 2724 rows, 2402 columns and 8458 nonzeros
Model fingerprint: 0xde4b0489
Variable types: 2353 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [4e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e-01, 1e+00]
Presolve removed 920 rows and 1644 columns
Presolve time: 0.04s
Presolved: 1804 rows, 758 columns, 6869 nonzeros
Variable types: 710 continuous, 48 integer (48 binary)
Found heuristic solution: objective 0.6432565
Found heuristic solution: objective 0.5991549
Found heuristic solution: objective 0.5807403

Root relaxation: objective 2.508719e-01, 270 iterations, 0.01 seconds (0.00 work units)

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

     0     0    0.25087    0   23    0.58074    0.25087  56.8%     -    0s
H    0     0                       0.5527757    0.25087  54.6%     -    0s
H    0     0                       0.5458879    0.25087  54.0%     -    0s
H    0     0                       0.5418199    0.25087  53.7%     -    0s
H    0     0                       0.5400028    0.35483  34.3%     -    0s
     0     0    0.35483    0   22    0.54000    0.35483  34.3%     -    0s
H    0     0                       0.5222113    0.35483  32.1%     -    0s
     0     0    0.36487    0   22    0.52221    0.36487  30.1%     -    0s
     0     0    0.39506    0   20    0.52221    0.39506  24.3%     -    0s
     0     0    0.39800    0   21    0.52221    0.39800  23.8%     -    0s
     0     0    0.39900    0   21    0.52221    0.39900  23.6%     -    0s
     0     0    0.39900    0   22    0.52221    0.39900  23.6%     -    0s
     0     0    0.39900    0   22    0.52221    0.39900  23.6%     -    0s
     0     0    0.39900    0   22    0.52221    0.39900  23.6%     -    0s
     0     0    0.39900    0   23    0.52221    0.39900  23.6%     -    0s
H    0     0                       0.5188787    0.39900  23.1%     -    2s
     0     2    0.39900    0   23    0.51888    0.39900  23.1%     -    2s
   650   157    0.50919   12   11    0.51888    0.47829  7.82%  26.3    5s
  1491   200    0.51644   13    8    0.51888    0.49704  4.21%  22.2   10s

Cutting planes:
  Gomory: 1
  Implied bound: 275
  MIR: 73
  Flow cover: 252
  RLT: 31
  Relax-and-lift: 127

Explored 2906 nodes (60002 simplex iterations) in 11.41 seconds (5.31 work units)
Thread count was 4 (of 40 available processors)

Solution count 9: 0.518879 0.522211 0.540003 ... 0.643256

Optimal solution found (tolerance 1.00e-04)
Best objective 5.188786955806e-01, best bound 5.188786955806e-01, gap 0.0000%
The objective bound is 0.518879 while the objective upper bound is 0.518879

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

        Job resource usage summary 

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

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