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 0.485783 seconds.
    local lower bound updated to 0.4852
    local upper bound updated to 0.618255

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.393489 seconds.
    local lower bound updated to 0.610866
    local upper bound updated to 0.610866
The Primal step takes 0.88413 (S)
lower bound updated to 0.610866

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.62654
    local lower bound updated to 0.622879

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.62654
    local lower bound updated to 0.626118

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.626276
    local lower bound updated to 0.626246

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.626246
    local lower bound updated to 0.626246
The Dual step takes 0.361777 (S)
upper bound updated to 0.626246
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.925861 seconds.
    local lower bound updated to 0.539357
    local upper bound updated to 0.619296

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.43558 seconds.
    local lower bound updated to 0.605159
    local upper bound updated to 0.618601

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.21116 seconds.
    local lower bound updated to 0.612371
    local upper bound updated to 0.617683

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.27626 seconds.
    local lower bound updated to 0.614012
    local upper bound updated to 0.615226

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.52402 seconds.
    local lower bound updated to 0.614721
    local upper bound updated to 0.615042

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.06891 seconds.
    local lower bound updated to 0.615042
    local upper bound updated to 0.615042
The Primal step takes 15.4692 (S)
lower bound updated to 0.615042

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.63386
    local lower bound updated to 0.615234

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.629522
    local lower bound updated to 0.619965

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.629522
    local lower bound updated to 0.621355

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.623749
    local lower bound updated to 0.621641

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.621641
    local lower bound updated to 0.621641
The Dual step takes 4.81202 (S)
upper bound updated to 0.621641
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 15.9189 seconds.
    local lower bound updated to 0.580484
    local upper bound updated to 0.621354

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.36492 seconds.
    local lower bound updated to 0.607791
    local upper bound updated to 0.620894

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 15.1349 seconds.
    local lower bound updated to 0.613347
    local upper bound updated to 0.619792

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 17.2485 seconds.
    local lower bound updated to 0.617755
    local upper bound updated to 0.61906

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 23.7024 seconds.
    local lower bound updated to 0.617755
    local upper bound updated to 0.618693

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 23.9694 seconds.
    local lower bound updated to 0.617918
    local upper bound updated to 0.618663

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 7.55707 seconds.
    local lower bound updated to 0.618414
    local upper bound updated to 0.618661

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 11.7282 seconds.
    local lower bound updated to 0.618476
    local upper bound updated to 0.618567

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 11.8541 seconds.
    local lower bound updated to 0.618506
    local upper bound updated to 0.618566

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 13.4469 seconds.
    local lower bound updated to 0.618534
    local upper bound updated to 0.618566

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 13.2264 seconds.
    local lower bound updated to 0.618556
    local upper bound updated to 0.618566
The Primal step takes 159.266 (S)
lower bound updated to 0.618556

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.631132
    local lower bound updated to 0.618566

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.620222
    local lower bound updated to 0.618925

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.620222
    local lower bound updated to 0.618928

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.620222
    local lower bound updated to 0.619146

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.619749
    local lower bound updated to 0.619165

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.619664
    local lower bound updated to 0.619201

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.619201
    local lower bound updated to 0.619201
The Dual step takes 17.3535 (S)
upper bound updated to 0.619201
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 42.9101 seconds.
    local lower bound updated to 0.593581
    local upper bound updated to 0.619201

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0352 seconds.
    local lower bound updated to 0.61756
    local upper bound updated to 0.618947

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 39.9192 seconds.
    local lower bound updated to 0.618183
    local upper bound updated to 0.618888

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 24.3341 seconds.
    local lower bound updated to 0.618473
    local upper bound updated to 0.618857

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 42.4631 seconds.
    local lower bound updated to 0.618473
    local upper bound updated to 0.61883

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 30.582 seconds.
    local lower bound updated to 0.618473
    local upper bound updated to 0.618724

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 35.8449 seconds.
    local lower bound updated to 0.618707
    local upper bound updated to 0.618723

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 29.074 seconds.
    local lower bound updated to 0.618716
    local upper bound updated to 0.618723
The Primal step takes 305.383 (S)
lower bound updated to 0.618716

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.625317
    local lower bound updated to 0.618723

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.620579
    local lower bound updated to 0.618814

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.619698
    local lower bound updated to 0.618918

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.618918
    local lower bound updated to 0.618918
The Dual step takes 18.358 (S)
upper bound updated to 0.618918
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0415 seconds.
    local lower bound updated to 0.596811
    local upper bound updated to 0.618918

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 33.006 seconds.
    local lower bound updated to 0.618323
    local upper bound updated to 0.618866

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 47.1946 seconds.
    local lower bound updated to 0.61881
    local upper bound updated to 0.618862

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 47.6231 seconds.
    local lower bound updated to 0.618822
    local upper bound updated to 0.618859

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0476 seconds.
    local lower bound updated to 0.618852
    local upper bound updated to 0.618859
The Primal step takes 247.984 (S)
lower bound updated to 0.618852

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.624573
    local lower bound updated to 0.618859

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.618859
    local lower bound updated to 0.618859
The Dual step takes 12.9557 (S)
upper bound updated to 0.618859
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0458 seconds.
    local lower bound updated to 0.596811
    local upper bound updated to 0.618859

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 44.4791 seconds.
    local lower bound updated to 0.618847
    local upper bound updated to 0.618858

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 42.2027 seconds.
    local lower bound updated to 0.618851
    local upper bound updated to 0.618857
The time obtain the optimal randomized assortment is 929.6 (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_63616.log"
The computation time limit for a lower bound is 85066
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 24 physical cores, 48 logical processors, using up to 4 threads
Optimize a model with 2640 rows, 2138 columns and 8512 nonzeros
Model fingerprint: 0x533e7514
Variable types: 2081 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [9e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 703 rows and 1292 columns
Presolve time: 0.05s
Presolved: 1937 rows, 846 columns, 7439 nonzeros
Variable types: 795 continuous, 51 integer (51 binary)
Found heuristic solution: objective 0.7439393
Found heuristic solution: objective 0.6991710
Found heuristic solution: objective 0.6988276

Root relaxation: objective 4.926886e-01, 257 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    0.49269    0   25    0.69883    0.49269  29.5%     -    0s
H    0     0                       0.6652205    0.49269  25.9%     -    0s
     0     0    0.49949    0   25    0.66522    0.49949  24.9%     -    0s
H    0     0                       0.6511825    0.49949  23.3%     -    0s
H    0     0                       0.6388470    0.49949  21.8%     -    0s
     0     0    0.49949    0   25    0.63885    0.49949  21.8%     -    0s
H    0     0                       0.6357597    0.55060  13.4%     -    0s
     0     0    0.55062    0   26    0.63576    0.55062  13.4%     -    0s
H    0     0                       0.6237873    0.55062  11.7%     -    0s
     0     0    0.55134    0   26    0.62379    0.55134  11.6%     -    0s
     0     0    0.56343    0   28    0.62379    0.56343  9.68%     -    0s
     0     0    0.56418    0   28    0.62379    0.56418  9.55%     -    0s
H    0     0                       0.6210979    0.56418  9.16%     -    0s
H    0     0                       0.6210738    0.56418  9.16%     -    0s
     0     0    0.56852    0   27    0.62107    0.56852  8.46%     -    0s
     0     0    0.56923    0   28    0.62107    0.56923  8.35%     -    1s
     0     0    0.56963    0   29    0.62107    0.56963  8.28%     -    1s
H    0     0                       0.6188572    0.56963  7.95%     -    4s
     0     2    0.56963    0   29    0.61886    0.56963  7.95%     -    4s
    97    85    0.59888    8   17    0.61886    0.58011  6.26%  32.0    5s
H  440   189                       0.6188572    0.59239  4.28%  25.5    6s
   883   286    0.60705   10   16    0.61886    0.59654  3.61%  25.4   10s
H 1767   443                       0.6188572    0.60024  3.01%  24.6   12s
  2500   512    0.61156   14   14    0.61886    0.60251  2.64%  25.0   16s
  2890   530    0.61520   12    8    0.61886    0.60366  2.46%  25.1   20s
  3567   521    0.61238   12   11    0.61886    0.60553  2.15%  24.7   25s
  4169   494     cutoff   15         0.61886    0.60690  1.93%  24.6   30s
  4938   436    0.61634   17   10    0.61886    0.60870  1.64%  24.4   35s
  5947   302     cutoff   14         0.61886    0.61043  1.36%  24.2   40s
  7856    20    0.61852   19    4    0.61886    0.61499  0.63%  22.6   45s

Cutting planes:
  Implied bound: 308
  MIR: 142
  Flow cover: 276
  RLT: 24
  Relax-and-lift: 106

Explored 8128 nodes (183902 simplex iterations) in 45.85 seconds (19.03 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.618857 0.621074 0.621098 ... 0.699171

Optimal solution found (tolerance 1.00e-04)
Best objective 6.188572179323e-01, best bound 6.188572179323e-01, gap 0.0000%
The objective bound is 0.618857 while the objective upper bound is 0.618857

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.05 (ave)

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