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 0.648935 seconds.
    local lower bound updated to 0.321118
    local upper bound updated to 0.528226

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.21317 seconds.
    local lower bound updated to 0.505783
    local upper bound updated to 0.505783
The Primal step takes 0.86388 (S)
lower bound updated to 0.505783

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.648746
    local lower bound updated to 0.607773

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.623612
    local lower bound updated to 0.620189

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.622929
    local lower bound updated to 0.621775

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.621775
    local lower bound updated to 0.621775
The Dual step takes 0.0727275 (S)
upper bound updated to 0.621775
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.76834 seconds.
    local lower bound updated to 0.419257
    local upper bound updated to 0.565172

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.87387 seconds.
    local lower bound updated to 0.517193
    local upper bound updated to 0.529905

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.721112 seconds.
    local lower bound updated to 0.517193
    local upper bound updated to 0.526742

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.60222 seconds.
    local lower bound updated to 0.517193
    local upper bound updated to 0.523452

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.74316 seconds.
    local lower bound updated to 0.517193
    local upper bound updated to 0.522739

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 5.5976 seconds.
    local lower bound updated to 0.518847
    local upper bound updated to 0.521469

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.36908 seconds.
    local lower bound updated to 0.518847
    local upper bound updated to 0.521317

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 4.59975 seconds.
    local lower bound updated to 0.520779
    local upper bound updated to 0.521292

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 3.93935 seconds.
    local lower bound updated to 0.520779
    local upper bound updated to 0.520943

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 6.08337 seconds.
    local lower bound updated to 0.520943
    local upper bound updated to 0.520943
The Primal step takes 35.314 (S)
lower bound updated to 0.520943

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.588226
    local lower bound updated to 0.528355

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.570305
    local lower bound updated to 0.548782

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.553262
    local lower bound updated to 0.549607

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.550518
    local lower bound updated to 0.549737

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.549737
    local lower bound updated to 0.549737
The Dual step takes 1.70194 (S)
upper bound updated to 0.549737
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 11.3629 seconds.
    local lower bound updated to 0.466439
    local upper bound updated to 0.537747

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.55627 seconds.
    local lower bound updated to 0.525911
    local upper bound updated to 0.531927

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 19.415 seconds.
    local lower bound updated to 0.525911
    local upper bound updated to 0.531853

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 28.3557 seconds.
    local lower bound updated to 0.526637
    local upper bound updated to 0.531655

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 25.7354 seconds.
    local lower bound updated to 0.5303
    local upper bound updated to 0.531582

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 19.9376 seconds.
    local lower bound updated to 0.530395
    local upper bound updated to 0.531351

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 24.9635 seconds.
    local lower bound updated to 0.530395
    local upper bound updated to 0.531194

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 23.0238 seconds.
    local lower bound updated to 0.530943
    local upper bound updated to 0.531185

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 21.0333 seconds.
    local lower bound updated to 0.531185
    local upper bound updated to 0.531185
The Primal step takes 180.406 (S)
lower bound updated to 0.531185

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.575693
    local lower bound updated to 0.531848

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.555074
    local lower bound updated to 0.537782

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.544402
    local lower bound updated to 0.539545

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.541264
    local lower bound updated to 0.539545

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.539545
    local lower bound updated to 0.539545
The Dual step takes 3.95991 (S)
upper bound updated to 0.539545
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.1022 seconds.
    local lower bound updated to 0.48604
    local upper bound updated to 0.539545

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.61414 seconds.
    local lower bound updated to 0.534566
    local upper bound updated to 0.538802

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 9.35168 seconds.
    local lower bound updated to 0.536021
    local upper bound updated to 0.538154

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.9555 seconds.
    local lower bound updated to 0.537798
    local upper bound updated to 0.538098

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.5433 seconds.
    local lower bound updated to 0.537815
    local upper bound updated to 0.537969

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.08805 seconds.
    local lower bound updated to 0.537815
    local upper bound updated to 0.537962

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 12.4837 seconds.
    local lower bound updated to 0.537815
    local upper bound updated to 0.537961

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 12.2141 seconds.
    local lower bound updated to 0.537924
    local upper bound updated to 0.537961

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 11.8883 seconds.
    local lower bound updated to 0.537961
    local upper bound updated to 0.537961
The Primal step takes 92.2725 (S)
lower bound updated to 0.537961

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.566438
    local lower bound updated to 0.537961

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.540586
    local lower bound updated to 0.538034

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.540586
    local lower bound updated to 0.538082

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.538082
    local lower bound updated to 0.538082
The Dual step takes 8.23452 (S)
upper bound updated to 0.538082
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.9058 seconds.
    local lower bound updated to 0.491411
    local upper bound updated to 0.538082

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.3547 seconds.
    local lower bound updated to 0.537981
    local upper bound updated to 0.53807

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 15.2234 seconds.
    local lower bound updated to 0.53807
    local upper bound updated to 0.53807
The Primal step takes 40.4958 (S)
lower bound updated to 0.53807

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.561408
    local lower bound updated to 0.53807

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.538114
    local lower bound updated to 0.53807

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.53807
    local lower bound updated to 0.53807
The Dual step takes 7.92694 (S)
upper bound updated to 0.53807
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 27.7067 seconds.
    local lower bound updated to 0.492412
    local upper bound updated to 0.53807

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 15.9982 seconds.
    local lower bound updated to 0.53807
    local upper bound updated to 0.53807
The time obtain the optimal randomized assortment is 414.962 (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_60.000000_65316.log"
The computation time limit for a lower bound is 85583
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 128 physical cores, 256 logical processors, using up to 4 threads
Optimize a model with 2640 rows, 2138 columns and 8467 nonzeros
Model fingerprint: 0x35ea79a1
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        [5e-01, 1e+00]
Presolve removed 731 rows and 1305 columns
Presolve time: 0.02s
Presolved: 1909 rows, 833 columns, 7338 nonzeros
Variable types: 777 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.6285629
Found heuristic solution: objective 0.5785306

Root relaxation: objective 4.339403e-01, 224 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    0.43394    0   16    0.57853    0.43394  25.0%     -    0s
H    0     0                       0.5650471    0.43394  23.2%     -    0s
H    0     0                       0.5380699    0.43830  18.5%     -    0s
     0     0    0.43830    0   23    0.53807    0.43830  18.5%     -    0s
     0     0    0.46050    0   30    0.53807    0.46050  14.4%     -    0s
     0     0    0.46051    0   30    0.53807    0.46051  14.4%     -    0s
     0     0    0.47216    0   27    0.53807    0.47216  12.2%     -    0s
     0     0    0.47244    0   27    0.53807    0.47244  12.2%     -    0s
     0     0    0.47673    0   28    0.53807    0.47673  11.4%     -    0s
     0     0    0.47685    0   27    0.53807    0.47685  11.4%     -    0s
     0     0    0.47892    0   26    0.53807    0.47892  11.0%     -    0s
     0     2    0.47892    0   26    0.53807    0.47892  11.0%     -    1s
   690   248     cutoff   12         0.53807    0.50281  6.55%  29.4    5s
  2954   411    0.53544   10   18    0.53807    0.51715  3.89%  25.5   10s
  5500     9     cutoff   11         0.53807    0.53116  1.28%  23.8   15s

Cutting planes:
  Gomory: 1
  Implied bound: 296
  MIR: 76
  Flow cover: 251
  RLT: 35
  Relax-and-lift: 158

Explored 5567 nodes (133778 simplex iterations) in 15.98 seconds (16.51 work units)
Thread count was 4 (of 256 available processors)

Solution count 4: 0.53807 0.565047 0.578531 0.628563 

Optimal solution found (tolerance 1.00e-04)
Best objective 5.380698790939e-01, best bound 5.380698790939e-01, gap 0.0000%
The objective bound is 0.53807 while the objective upper bound is 0.53807

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.61 (ave)

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