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 0.466038 seconds.
    local lower bound updated to 0.277465
    local upper bound updated to 0.531696

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.714977 seconds.
    local lower bound updated to 0.519546
    local upper bound updated to 0.519546
The Primal step takes 1.18337 (S)
lower bound updated to 0.519546

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.658558
    local lower bound updated to 0.656667

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.656667
    local lower bound updated to 0.656667
The Dual step takes 0.0616897 (S)
upper bound updated to 0.656667
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.365446 seconds.
    local lower bound updated to 0.321699
    local upper bound updated to 0.534071

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.10364 seconds.
    local lower bound updated to 0.527988
    local upper bound updated to 0.530165

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.51108 seconds.
    local lower bound updated to 0.529712
    local upper bound updated to 0.529998

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.38683 seconds.
    local lower bound updated to 0.529998
    local upper bound updated to 0.529998
The Primal step takes 5.37346 (S)
lower bound updated to 0.529998

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.637298
    local lower bound updated to 0.582542

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.626571
    local lower bound updated to 0.605062

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.609184
    local lower bound updated to 0.607833

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.607833
    local lower bound updated to 0.607833
The Dual step takes 0.148619 (S)
upper bound updated to 0.607833
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.50532 seconds.
    local lower bound updated to 0.422767
    local upper bound updated to 0.570241

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.39072 seconds.
    local lower bound updated to 0.504357
    local upper bound updated to 0.557257

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.4052 seconds.
    local lower bound updated to 0.545862
    local upper bound updated to 0.549417

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 11.8512 seconds.
    local lower bound updated to 0.545862
    local upper bound updated to 0.548774

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.7034 seconds.
    local lower bound updated to 0.547991
    local upper bound updated to 0.548161

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 12.2737 seconds.
    local lower bound updated to 0.547991
    local upper bound updated to 0.548122

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 11.6825 seconds.
    local lower bound updated to 0.548122
    local upper bound updated to 0.548122
The Primal step takes 57.8294 (S)
lower bound updated to 0.548122

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.592376
    local lower bound updated to 0.550744

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.590727
    local lower bound updated to 0.552072

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.572256
    local lower bound updated to 0.552656

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.572256
    local lower bound updated to 0.554761

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.563246
    local lower bound updated to 0.555557

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.555557
    local lower bound updated to 0.555557
The Dual step takes 0.738861 (S)
upper bound updated to 0.555557
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.21538 seconds.
    local lower bound updated to 0.451402
    local upper bound updated to 0.554967

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 7.89628 seconds.
    local lower bound updated to 0.531799
    local upper bound updated to 0.551674

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 26.5722 seconds.
    local lower bound updated to 0.546179
    local upper bound updated to 0.550303

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 20.3242 seconds.
    local lower bound updated to 0.546179
    local upper bound updated to 0.549947

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 20.2033 seconds.
    local lower bound updated to 0.548124
    local upper bound updated to 0.549713

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 23.0952 seconds.
    local lower bound updated to 0.549713
    local upper bound updated to 0.549713
The Primal step takes 102.332 (S)
lower bound updated to 0.549713

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.583502
    local lower bound updated to 0.549713

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.55637
    local lower bound updated to 0.549998

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.549998
    local lower bound updated to 0.549998
The Dual step takes 0.661631 (S)
upper bound updated to 0.549998
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.55492 seconds.
    local lower bound updated to 0.45459
    local upper bound updated to 0.549998

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 25.7734 seconds.
    local lower bound updated to 0.549342
    local upper bound updated to 0.549925

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 44.7947 seconds.
    local lower bound updated to 0.549925
    local upper bound updated to 0.549925
The Primal step takes 74.1388 (S)
lower bound updated to 0.549925

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.585393
    local lower bound updated to 0.549925

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.550429
    local lower bound updated to 0.54993

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.54993
    local lower bound updated to 0.54993
The Dual step takes 0.733635 (S)
upper bound updated to 0.54993
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.33165 seconds.
    local lower bound updated to 0.459687
    local upper bound updated to 0.54993

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 36.3798 seconds.
    local lower bound updated to 0.549741
    local upper bound updated to 0.549925

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 41.4763 seconds.
    local lower bound updated to 0.549925
    local upper bound updated to 0.549925
The time obtain the optimal randomized assortment is 324.404 (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_200.000000_209916.log"
The computation time limit for a lower bound is 85673
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 2160 rows, 1748 columns and 6891 nonzeros
Model fingerprint: 0x7580377c
Variable types: 1691 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [3e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e-01, 1e+00]
Presolve removed 573 rows and 1065 columns
Presolve time: 0.02s
Presolved: 1587 rows, 683 columns, 6117 nonzeros
Variable types: 628 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6715605
Found heuristic solution: objective 0.5620308

Root relaxation: objective 3.930297e-01, 262 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    0.39303    0   20    0.56203    0.39303  30.1%     -    0s
     0     0    0.39887    0   26    0.56203    0.39887  29.0%     -    0s
     0     0    0.44166    0   25    0.56203    0.44166  21.4%     -    0s
     0     0    0.44200    0   25    0.56203    0.44200  21.4%     -    0s
     0     0    0.45750    0   22    0.56203    0.45750  18.6%     -    0s
H    0     0                       0.5599918    0.45750  18.3%     -    0s
     0     0    0.45817    0   23    0.55999    0.45817  18.2%     -    0s
     0     0    0.46263    0   24    0.55999    0.46263  17.4%     -    0s
     0     0    0.46392    0   23    0.55999    0.46392  17.2%     -    0s
     0     0    0.46734    0   23    0.55999    0.46734  16.5%     -    0s
H    0     0                       0.5591848    0.46734  16.4%     -    0s
H    0     0                       0.5569933    0.46734  16.1%     -    0s
H    0     0                       0.5499251    0.46734  15.0%     -    1s
     0     2    0.46734    0   23    0.54993    0.46734  15.0%     -    1s
   886   302     cutoff   12         0.54993    0.48854  11.2%  30.2    5s
H 2226   428                       0.5499251    0.50464  8.23%  27.8    7s
H 3000   483                       0.5499251    0.50875  7.49%  26.5    9s
H 3159   489                       0.5499251    0.50899  7.44%  26.3    9s
  3160   493    0.53524   12   12    0.54993    0.50899  7.44%  26.3   10s
H 3457   500                       0.5499251    0.51043  7.18%  25.8   11s
H 3700   528                       0.5499251    0.51211  6.88%  25.5   13s
  4120   563     cutoff   17         0.54993    0.51377  6.57%  25.3   15s
H 4444   570                       0.5499251    0.51486  6.38%  25.0   16s
  5381   651    0.52812   10   27    0.54993    0.51866  5.69%  24.0   21s
H 5675   685                       0.5499251    0.51866  5.69%  25.3   22s
H 5762   645                       0.5499251    0.51866  5.69%  25.4   23s
  6491   510     cutoff   23         0.54993    0.51866  5.69%  26.2   25s
  8104   380    0.53500   24   15    0.54993    0.51866  5.69%  27.2   30s
 10371   338     cutoff   28         0.54993    0.52934  3.74%  27.1   35s
H10400   338                       0.5499251    0.52934  3.74%  27.1   35s
 12075   183     cutoff   26         0.54993    0.53698  2.35%  26.6   40s

Cutting planes:
  Implied bound: 192
  MIR: 160
  Flow cover: 313
  RLT: 45
  Relax-and-lift: 75

Explored 13000 nodes (340471 simplex iterations) in 41.38 seconds (34.97 work units)
Thread count was 4 (of 48 available processors)

Solution count 8: 0.549925 0.549925 0.549925 ... 0.67156

Optimal solution found (tolerance 1.00e-04)
Best objective 5.499250852447e-01, best bound 5.499250852447e-01, gap 0.0000%
The objective bound is 0.549925 while the objective upper bound is 0.549925

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.59 (ave)

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