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 0.551202 seconds.
    local lower bound updated to 0.270071
    local upper bound updated to 0.509345

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.71694 seconds.
    local lower bound updated to 0.509345
    local upper bound updated to 0.509345
The Primal step takes 2.26971 (S)
lower bound updated to 0.509345

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.646017
    local lower bound updated to 0.646017
The Dual step takes 0.0178618 (S)
upper bound updated to 0.646017
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.21933 seconds.
    local lower bound updated to 0.34218
    local upper bound updated to 0.537283

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 7.1693 seconds.
    local lower bound updated to 0.518693
    local upper bound updated to 0.526162

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.71451 seconds.
    local lower bound updated to 0.518693
    local upper bound updated to 0.521145

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.50171 seconds.
    local lower bound updated to 0.519905
    local upper bound updated to 0.520382

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.53859 seconds.
    local lower bound updated to 0.520382
    local upper bound updated to 0.520382
The Primal step takes 25.1505 (S)
lower bound updated to 0.520382

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.598316
    local lower bound updated to 0.571669

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.578029
    local lower bound updated to 0.574344

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.574344
    local lower bound updated to 0.574344
The Dual step takes 0.215888 (S)
upper bound updated to 0.574344
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 76.507 seconds.
    local lower bound updated to 0.439612
    local upper bound updated to 0.549737

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.618345 seconds.
    local lower bound updated to 0.439612
    local upper bound updated to 0.53971

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.80009 seconds.
    local lower bound updated to 0.507884
    local upper bound updated to 0.526537

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.62532 seconds.
    local lower bound updated to 0.523471
    local upper bound updated to 0.525186

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.8092 seconds.
    local lower bound updated to 0.523997
    local upper bound updated to 0.524894

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 12.0172 seconds.
    local lower bound updated to 0.524894
    local upper bound updated to 0.524894
The Primal step takes 116.389 (S)
lower bound updated to 0.524894

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.561165
    local lower bound updated to 0.530696

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.55569
    local lower bound updated to 0.531681

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.546711
    local lower bound updated to 0.541402

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.545816
    local lower bound updated to 0.542167

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.545816
    local lower bound updated to 0.542748

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.542865
    local lower bound updated to 0.542749

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.542749
    local lower bound updated to 0.542749
The Dual step takes 3.91257 (S)
upper bound updated to 0.542749
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.487982
    local upper bound updated to 0.54147

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.42748 seconds.
    local lower bound updated to 0.487982
    local upper bound updated to 0.529754

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 24.3601 seconds.
    local lower bound updated to 0.519856
    local upper bound updated to 0.529265

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 39.2666 seconds.
    local lower bound updated to 0.52448
    local upper bound updated to 0.528981

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 38.3603 seconds.
    local lower bound updated to 0.525539
    local upper bound updated to 0.528893

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.4205 seconds.
    local lower bound updated to 0.525539
    local upper bound updated to 0.528862

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 40.3329 seconds.
    local lower bound updated to 0.526315
    local upper bound updated to 0.528536

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 50.2946 seconds.
    local lower bound updated to 0.526569
    local upper bound updated to 0.528452

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 40.529 seconds.
    local lower bound updated to 0.527085
    local upper bound updated to 0.528143

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 40.5328 seconds.
    local lower bound updated to 0.527762
    local upper bound updated to 0.52812

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 35.1231 seconds.
    local lower bound updated to 0.52812
    local upper bound updated to 0.52812
The Primal step takes 470.707 (S)
lower bound updated to 0.52812

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.548647
    local lower bound updated to 0.528321

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.542545
    local lower bound updated to 0.53006

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.536323
    local lower bound updated to 0.53047

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.533756
    local lower bound updated to 0.530888

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.532615
    local lower bound updated to 0.531003

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.531473
    local lower bound updated to 0.531039

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.531447
    local lower bound updated to 0.531039

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.531039
    local lower bound updated to 0.531039
The Dual step takes 14.7817 (S)
upper bound updated to 0.531039
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.501339
    local upper bound updated to 0.531039

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.019 seconds.
    local lower bound updated to 0.526166
    local upper bound updated to 0.530942

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.019 seconds.
    local lower bound updated to 0.528387
    local upper bound updated to 0.530858

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.022 seconds.
    local lower bound updated to 0.530048
    local upper bound updated to 0.530797

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.530048
    local upper bound updated to 0.530768

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.530197
    local upper bound updated to 0.530646

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.530197
    local upper bound updated to 0.530639

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.530197
    local upper bound updated to 0.530591

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 100.025 seconds.
    local lower bound updated to 0.530197
    local upper bound updated to 0.530589

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.530343
    local upper bound updated to 0.530547

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 100.019 seconds.
    local lower bound updated to 0.530343
    local upper bound updated to 0.530544

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 100.022 seconds.
    local lower bound updated to 0.530343
    local upper bound updated to 0.530505

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.530419
    local upper bound updated to 0.530491

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.530468
    local upper bound updated to 0.53049

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 100.019 seconds.
    local lower bound updated to 0.530468
    local upper bound updated to 0.530489

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.530477
    local upper bound updated to 0.530488

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 100.016 seconds.
    local lower bound updated to 0.530488
    local upper bound updated to 0.530488
The Primal step takes 1700.42 (S)
lower bound updated to 0.530488

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.536601
    local lower bound updated to 0.530488

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.530488
    local lower bound updated to 0.530488
The Dual step takes 8.40996 (S)
upper bound updated to 0.530488
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.017 seconds.
    local lower bound updated to 0.501339
    local upper bound updated to 0.530488

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.018 seconds.
    local lower bound updated to 0.530488
    local upper bound updated to 0.530488
The time obtain the optimal randomized assortment is 2542.32 (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_109416.log"
The computation time limit for a lower bound is 83452
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 2960 rows, 2398 columns and 9490 nonzeros
Model fingerprint: 0x0bc81ce3
Variable types: 2341 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 828 rows and 1480 columns
Presolve time: 0.02s
Presolved: 2132 rows, 918 columns, 8264 nonzeros
Variable types: 862 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.5998193

Root relaxation: objective 2.961744e-01, 274 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    0.29617    0   26    0.59982    0.29617  50.6%     -    0s
H    0     0                       0.5935086    0.29617  50.1%     -    0s
H    0     0                       0.5906969    0.30300  48.7%     -    0s
H    0     0                       0.5899976    0.30300  48.6%     -    0s
H    0     0                       0.5841854    0.30300  48.1%     -    0s
     0     0    0.30300    0   30    0.58419    0.30300  48.1%     -    0s
H    0     0                       0.5723589    0.30300  47.1%     -    0s
H    0     0                       0.5679604    0.30300  46.7%     -    0s
     0     0    0.30300    0   30    0.56796    0.30300  46.7%     -    0s
     0     0    0.34652    0   28    0.56796    0.34652  39.0%     -    0s
H    0     0                       0.5338532    0.34652  35.1%     -    0s
     0     0    0.34652    0   28    0.53385    0.34652  35.1%     -    0s
     0     0    0.37172    0   29    0.53385    0.37172  30.4%     -    0s
     0     0    0.38198    0   30    0.53385    0.38198  28.4%     -    0s
     0     0    0.39329    0   31    0.53385    0.39329  26.3%     -    0s
     0     0    0.39488    0   35    0.53385    0.39488  26.0%     -    0s
     0     0    0.39689    0   35    0.53385    0.39689  25.7%     -    0s
H    0     0                       0.5305689    0.39689  25.2%     -    2s
     0     2    0.39689    0   35    0.53057    0.39689  25.2%     -    2s
H   13    16                       0.5305142    0.40917  22.9%  98.2    2s
H   48    53                       0.5305035    0.40917  22.9%  57.8    2s
H  661   343                       0.5304877    0.43427  18.1%  29.9    4s
   696   363     cutoff   18         0.53049    0.43663  17.7%  29.3    5s
  1971   764     cutoff   13         0.53049    0.45021  15.1%  24.1   10s
  2800   887    0.51031   21   12    0.53049    0.45586  14.1%  30.2   16s
  3499   882    0.51260   20   14    0.53049    0.46480  12.4%  31.3   21s
  4284   826    0.49930   19   19    0.53049    0.46929  11.5%  31.9   25s
  5475  1110    0.51280   21   18    0.53049    0.47444  10.6%  31.7   30s
  6615  1347     cutoff   24         0.53049    0.47727  10.0%  31.7   36s
  7746  1506    0.51211   20   14    0.53049    0.48092  9.34%  31.5   40s
  8192  1608    0.49423   20   18    0.53049    0.48175  9.19%  31.5   45s
  9493  1938    0.51388   27   13    0.53049    0.48385  8.79%  31.0   50s
 11785  2251    0.50781   22   18    0.53049    0.48767  8.07%  30.7   56s
 12904  2417    0.50732   20   20    0.53049    0.48876  7.87%  30.5   61s
 15443  2518    0.51312   25   14    0.53049    0.49198  7.26%  29.9   66s
 17286  2599    0.50610   21   12    0.53049    0.49406  6.87%  29.8   70s
 18540  2677     cutoff   24         0.53049    0.49561  6.57%  29.8   75s
 19521  2697 infeasible   31         0.53049    0.49693  6.33%  29.7   80s
 22053  2734     cutoff   21         0.53049    0.49880  5.97%  29.6   85s
 24434  2749    0.52400   28   14    0.53049    0.50161  5.44%  29.4   90s
 26053  2750    0.51336   23   14    0.53049    0.50286  5.21%  29.3   95s
 28392  2707 infeasible   29         0.53049    0.50500  4.80%  29.2  101s
 29909  2649     cutoff   27         0.53049    0.50633  4.55%  29.1  106s
 32107  2565    0.52659   22   15    0.53049    0.50791  4.26%  28.9  110s
 33586  2528 infeasible   23         0.53049    0.50928  4.00%  28.7  115s
 35999  2461 infeasible   23         0.53049    0.51100  3.67%  28.4  121s
 38496  2337    0.51617   22   18    0.53049    0.51285  3.32%  28.1  125s
 41903  2137    0.52513   21   16    0.53049    0.51507  2.91%  27.6  130s
 44934  2042     cutoff   28         0.53049    0.51681  2.58%  27.1  135s
 47090  1925    0.52495   23   12    0.53049    0.51820  2.32%  26.8  140s
 49132  1792     cutoff   26         0.53049    0.51935  2.10%  26.4  145s
 53790  1460     cutoff   28         0.53049    0.52155  1.69%  25.6  150s
 57737  1020    0.52619   27    6    0.53049    0.52357  1.30%  25.0  155s

Cutting planes:
  Gomory: 2
  Implied bound: 196
  MIR: 181
  Flow cover: 572
  RLT: 123
  Relax-and-lift: 57

Explored 62130 nodes (1506065 simplex iterations) in 158.63 seconds (157.61 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.530488 0.530504 0.530514 ... 0.590697

Optimal solution found (tolerance 1.00e-04)
Best objective 5.304877288034e-01, best bound 5.304877288034e-01, gap 0.0000%
The objective bound is 0.530488 while the objective upper bound is 0.530488

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.71 (ave)

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