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 4.45269 seconds.
    local lower bound updated to 0.287011
    local upper bound updated to 0.466316

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.4249 seconds.
    local lower bound updated to 0.450157
    local upper bound updated to 0.450157
The Primal step takes 5.87991 (S)
lower bound updated to 0.450157

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.587375
    local lower bound updated to 0.58378

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.58378
    local lower bound updated to 0.58378
The Dual step takes 0.0597259 (S)
upper bound updated to 0.58378
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.5037 seconds.
    local lower bound updated to 0.337003
    local upper bound updated to 0.4848

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 16.4158 seconds.
    local lower bound updated to 0.464905
    local upper bound updated to 0.467146

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 22.2063 seconds.
    local lower bound updated to 0.465313
    local upper bound updated to 0.466622

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 21.7571 seconds.
    local lower bound updated to 0.465343
    local upper bound updated to 0.465372

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 14.8818 seconds.
    local lower bound updated to 0.465372
    local upper bound updated to 0.465372
The Primal step takes 85.7732 (S)
lower bound updated to 0.465372

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.545531
    local lower bound updated to 0.530527

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.545531
    local lower bound updated to 0.534507

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.534507
    local lower bound updated to 0.534507
The Dual step takes 0.32265 (S)
upper bound updated to 0.534507
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.024 seconds.
    local lower bound updated to 0.407283
    local upper bound updated to 0.490746

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 13.7881 seconds.
    local lower bound updated to 0.459167
    local upper bound updated to 0.486101

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 30.53 seconds.
    local lower bound updated to 0.465957
    local upper bound updated to 0.4826

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 100.028 seconds.
    local lower bound updated to 0.480142
    local upper bound updated to 0.482044

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.480142
    local upper bound updated to 0.48103

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.480142
    local upper bound updated to 0.480903

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 100.023 seconds.
    local lower bound updated to 0.480703
    local upper bound updated to 0.480809

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 100.022 seconds.
    local lower bound updated to 0.480798
    local upper bound updated to 0.480807
The Primal step takes 644.474 (S)
lower bound updated to 0.480798

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.512592
    local lower bound updated to 0.480807

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.487863
    local lower bound updated to 0.481634

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.483708
    local lower bound updated to 0.481695

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.483534
    local lower bound updated to 0.481831

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.481831
    local lower bound updated to 0.481831
The Dual step takes 5.98346 (S)
upper bound updated to 0.481831
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.021 seconds.
    local lower bound updated to 0.426989
    local upper bound updated to 0.481521

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.028 seconds.
    local lower bound updated to 0.480036
    local upper bound updated to 0.4815

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 100.032 seconds.
    local lower bound updated to 0.4815
    local upper bound updated to 0.4815
The Primal step takes 300.094 (S)
lower bound updated to 0.4815

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.50715
    local lower bound updated to 0.4815

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.4815
    local lower bound updated to 0.4815
The Dual step takes 3.76032 (S)
upper bound updated to 0.4815
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 100.025 seconds.
    local lower bound updated to 0.426989
    local upper bound updated to 0.4815

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 100.02 seconds.
    local lower bound updated to 0.4815
    local upper bound updated to 0.4815
The time obtain the optimal randomized assortment is 1246.4 (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_19_4_100.000000_100120.log"
The computation time limit for a lower bound is 84730
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 1908 rows, 1402 columns and 6455 nonzeros
Model fingerprint: 0x9e34bb6e
Variable types: 1329 continuous, 73 integer (73 binary)
Coefficient statistics:
  Matrix range     [4e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 365 rows and 661 columns
Presolve time: 0.02s
Presolved: 1543 rows, 741 columns, 6059 nonzeros
Variable types: 671 continuous, 70 integer (70 binary)
Found heuristic solution: objective 0.6783021
Found heuristic solution: objective 0.6710130

Root relaxation: objective 3.564183e-01, 159 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    0.35642    0   22    0.67101    0.35642  46.9%     -    0s
H    0     0                       0.5569937    0.35642  36.0%     -    0s
H    0     0                       0.5424146    0.35642  34.3%     -    0s
     0     0    0.35731    0   23    0.54241    0.35731  34.1%     -    0s
H    0     0                       0.5300440    0.35731  32.6%     -    0s
     0     0    0.38289    0   33    0.53004    0.38289  27.8%     -    0s
H    0     0                       0.5105923    0.38289  25.0%     -    0s
     0     0    0.38331    0   32    0.51059    0.38331  24.9%     -    0s
     0     0    0.38954    0   34    0.51059    0.38954  23.7%     -    0s
H    0     0                       0.5070788    0.39012  23.1%     -    0s
     0     0    0.39012    0   35    0.50708    0.39012  23.1%     -    0s
     0     0    0.39794    0   32    0.50708    0.39794  21.5%     -    0s
     0     0    0.39892    0   33    0.50708    0.39892  21.3%     -    0s
H    0     0                       0.5056327    0.39892  21.1%     -    0s
     0     0    0.40019    0   31    0.50563    0.40019  20.9%     -    0s
H    0     0                       0.5045600    0.40019  20.7%     -    0s
H    0     0                       0.4816907    0.40019  16.9%     -    1s
     0     2    0.40019    0   31    0.48169    0.40019  16.9%     -    1s
H  106    92                       0.4814999    0.40547  15.8%  26.4    2s
  1080   540    0.44890   13   16    0.48150    0.42258  12.2%  18.1    5s
  2100   865    0.42601   17   26    0.48150    0.42601  11.5%  18.4   10s
  3101   995    0.44784   21   20    0.48150    0.42848  11.0%  19.8   15s
  3998   982    0.44857   18   20    0.48150    0.43179  10.3%  19.9   20s
  5247  1343    0.47553   28    8    0.48150    0.43559  9.53%  20.0   25s
  6292  1670    0.45515   25   16    0.48150    0.43735  9.17%  20.2   30s
  7438  2021    0.46318   24   12    0.48150    0.43862  8.90%  20.3   35s
  8447  2265    0.45481   24   12    0.48150    0.44000  8.62%  20.3   40s
  9765  2562    0.46167   30   12    0.48150    0.44161  8.29%  20.3   46s
 11792  3009     cutoff   26         0.48150    0.44339  7.92%  20.1   50s
 14200  3440    0.45558   23   14    0.48150    0.44522  7.53%  20.1   56s
 15136  3631    0.46508   28   18    0.48150    0.44613  7.35%  20.1   60s
 17430  4008    0.47160   31   13    0.48150    0.44761  7.04%  20.0   66s
H18774  4143                       0.4814999    0.44794  6.97%  19.9   69s
 18847  4191    0.47470   26    8    0.48150    0.44818  6.92%  19.9   70s
H18901  4191                       0.4814999    0.44818  6.92%  19.9   70s
 20964  4504    0.47097   24   18    0.48150    0.44921  6.71%  19.9   76s
 22893  4674    0.47007   27   14    0.48150    0.45024  6.49%  19.9   80s
 24944  4804    0.46842   25   14    0.48150    0.45099  6.34%  19.8   85s
 26135  4945    0.46694   23   16    0.48150    0.45159  6.21%  19.7   90s
 28050  5098    0.46013   27   16    0.48150    0.45213  6.10%  19.7   95s
 30512  5299     cutoff   29         0.48150    0.45316  5.89%  19.7  100s
 32888  5389    0.46755   24   14    0.48150    0.45408  5.70%  19.6  105s
 34278  5457    0.47415   32   14    0.48150    0.45450  5.61%  19.6  110s
 36502  5567    0.45873   32   15    0.48150    0.45512  5.48%  19.5  115s
 39212  5627     cutoff   29         0.48150    0.45587  5.32%  19.4  120s
 40990  5671    0.47018   29   12    0.48150    0.45658  5.18%  19.3  126s
 41847  5687     cutoff   27         0.48150    0.45682  5.12%  19.3  130s
H44300  5681                       0.4814999    0.45755  4.97%  19.2  134s
 44566  5681    0.46854   23   16    0.48150    0.45759  4.97%  19.2  135s
 46202  5676    0.46001   25   19    0.48150    0.45811  4.86%  19.2  140s
 49049  5654    0.46888   29   14    0.48150    0.45882  4.71%  19.1  145s
H49252  5654                       0.4814999    0.45884  4.71%  19.1  145s
H50487  5635                       0.4814999    0.45927  4.62%  19.1  147s
 52129  5567     cutoff   27         0.48150    0.45981  4.51%  19.0  150s
 53716  5516    0.47573   28   12    0.48150    0.46024  4.41%  19.0  155s
H56486  5369                       0.4814999    0.46092  4.27%  18.9  159s
 56723  5340    0.47628   26   14    0.48150    0.46110  4.24%  18.9  161s
H57886  5286                       0.4814999    0.46129  4.20%  18.9  163s
 58420  5226    0.47052   29   16    0.48150    0.46160  4.13%  18.9  165s
H59759  5150                       0.4814999    0.46184  4.08%  18.9  168s
 60572  5090    0.47270   26   15    0.48150    0.46225  4.00%  18.9  170s
H61487  5081                       0.4814999    0.46255  3.94%  18.9  172s
 62442  4960    0.46676   30   13    0.48150    0.46280  3.88%  18.8  175s
H63204  4915                       0.4814999    0.46293  3.86%  18.8  176s
H63400  4845                       0.4814999    0.46309  3.82%  18.8  177s
 64317  4750     cutoff   27         0.48150    0.46340  3.76%  18.8  180s
H66000  4589                       0.4814998    0.46385  3.67%  18.8  182s
 67273  4421    0.47813   26    8    0.48150    0.46427  3.58%  18.8  185s
H68200  4274                       0.4814998    0.46462  3.51%  18.7  188s
H69405  4173                       0.4814998    0.46510  3.41%  18.7  189s
 69406  4044     cutoff   28         0.48150    0.46511  3.40%  18.7  190s
H69865  4044                       0.4814998    0.46512  3.40%  18.7  190s
 71235  3797     cutoff   30         0.48150    0.46578  3.27%  18.7  196s
 72212  3601    0.47777   26   12    0.48150    0.46625  3.17%  18.7  200s
H74300  3322                       0.4814998    0.46701  3.01%  18.6  203s
H75128  3178                       0.4814998    0.46722  2.97%  18.6  204s
 75494  3035    0.48021   29   10    0.48150    0.46741  2.93%  18.6  206s
H76567  2950                       0.4814998    0.46771  2.86%  18.6  207s
 77729  2670     cutoff   26         0.48150    0.46870  2.66%  18.6  210s
 79951  1990     cutoff   25         0.48150    0.46993  2.40%  18.5  216s
 82557  1338     cutoff   25         0.48150    0.47248  1.87%  18.4  221s

Cutting planes:
  Implied bound: 194
  MIR: 112
  Flow cover: 272
  RLT: 39
  Relax-and-lift: 58

Explored 85370 nodes (1564049 simplex iterations) in 223.85 seconds (212.20 work units)
Thread count was 4 (of 256 available processors)

Solution count 10: 0.4815 0.4815 0.4815 ... 0.542415

Optimal solution found (tolerance 1.00e-04)
Best objective 4.814999123977e-01, best bound 4.814998224769e-01, gap 0.0000%
The objective bound is 0.4815 while the objective upper bound is 0.4815

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.89 (ave)

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