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 0.510985 seconds.
    local lower bound updated to 0.275248
    local upper bound updated to 0.518695

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.259394 seconds.
    local lower bound updated to 0.473599
    local upper bound updated to 0.473599
The Primal step takes 0.773707 (S)
lower bound updated to 0.473599

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.6508
    local lower bound updated to 0.640005

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.640005
    local lower bound updated to 0.640005
The Dual step takes 0.0387679 (S)
upper bound updated to 0.640005
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.862852 seconds.
    local lower bound updated to 0.317827
    local upper bound updated to 0.513728

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.53147 seconds.
    local lower bound updated to 0.487621
    local upper bound updated to 0.491594

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.740747 seconds.
    local lower bound updated to 0.487621
    local upper bound updated to 0.489181

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.93988 seconds.
    local lower bound updated to 0.489181
    local upper bound updated to 0.489181
The Primal step takes 6.08175 (S)
lower bound updated to 0.489181

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.579171
    local lower bound updated to 0.532061

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.571772
    local lower bound updated to 0.532147

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.541142
    local lower bound updated to 0.532244

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.541142
    local lower bound updated to 0.53685

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.53685
    local lower bound updated to 0.53685
The Dual step takes 0.590047 (S)
upper bound updated to 0.53685
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.35406 seconds.
    local lower bound updated to 0.379942
    local upper bound updated to 0.51316

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.097 seconds.
    local lower bound updated to 0.497979
    local upper bound updated to 0.505205

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.92249 seconds.
    local lower bound updated to 0.497979
    local upper bound updated to 0.504684

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 15.0138 seconds.
    local lower bound updated to 0.503642
    local upper bound updated to 0.504631

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 8.17602 seconds.
    local lower bound updated to 0.503642
    local upper bound updated to 0.503767

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.25346 seconds.
    local lower bound updated to 0.503642
    local upper bound updated to 0.503741

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 11.0277 seconds.
    local lower bound updated to 0.503741
    local upper bound updated to 0.503741
The Primal step takes 53.8659 (S)
lower bound updated to 0.503741

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.555373
    local lower bound updated to 0.517557

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.52628
    local lower bound updated to 0.520818

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.520818
    local lower bound updated to 0.520818
The Dual step takes 0.904372 (S)
upper bound updated to 0.520818
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.97851 seconds.
    local lower bound updated to 0.415534
    local upper bound updated to 0.520818

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.875195 seconds.
    local lower bound updated to 0.490438
    local upper bound updated to 0.51176

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.74285 seconds.
    local lower bound updated to 0.504699
    local upper bound updated to 0.510181

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.80748 seconds.
    local lower bound updated to 0.506492
    local upper bound updated to 0.509187

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 7.09082 seconds.
    local lower bound updated to 0.506492
    local upper bound updated to 0.508288

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.69477 seconds.
    local lower bound updated to 0.507718
    local upper bound updated to 0.508267

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 6.27395 seconds.
    local lower bound updated to 0.507804
    local upper bound updated to 0.508106

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.33975 seconds.
    local lower bound updated to 0.507908
    local upper bound updated to 0.508103

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 7.17113 seconds.
    local lower bound updated to 0.507946
    local upper bound updated to 0.508089

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 9.21157 seconds.
    local lower bound updated to 0.508089
    local upper bound updated to 0.508089
The Primal step takes 54.2233 (S)
lower bound updated to 0.508089

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.538443
    local lower bound updated to 0.508089

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.532839
    local lower bound updated to 0.512613

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.512613
    local lower bound updated to 0.512613
The Dual step takes 2.08488 (S)
upper bound updated to 0.512613
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.44315 seconds.
    local lower bound updated to 0.424592
    local upper bound updated to 0.512613

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.43448 seconds.
    local lower bound updated to 0.508286
    local upper bound updated to 0.511667

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.28412 seconds.
    local lower bound updated to 0.508286
    local upper bound updated to 0.511116

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.98127 seconds.
    local lower bound updated to 0.508298
    local upper bound updated to 0.510872

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.81726 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.510751

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 6.6219 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.510556

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 5.13425 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.510477

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 5.18853 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.510371

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 4.3613 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.51033

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 9.59036 seconds.
    local lower bound updated to 0.50983
    local upper bound updated to 0.510251

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 7.22258 seconds.
    local lower bound updated to 0.510233
    local upper bound updated to 0.510249

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 8.5001 seconds.
    local lower bound updated to 0.510249
    local upper bound updated to 0.510249
The Primal step takes 69.6348 (S)
lower bound updated to 0.510249

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.532122
    local lower bound updated to 0.510249

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.519531
    local lower bound updated to 0.510472

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.510472
    local lower bound updated to 0.510472
The Dual step takes 14.3913 (S)
upper bound updated to 0.510472
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.43345 seconds.
    local lower bound updated to 0.42718
    local upper bound updated to 0.510472

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 13.7683 seconds.
    local lower bound updated to 0.509749
    local upper bound updated to 0.510255

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.609 seconds.
    local lower bound updated to 0.509749
    local upper bound updated to 0.510251

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.2652 seconds.
    local lower bound updated to 0.510238
    local upper bound updated to 0.51025

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.0537 seconds.
    local lower bound updated to 0.510238
    local upper bound updated to 0.510249

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 7.82633 seconds.
    local lower bound updated to 0.510249
    local upper bound updated to 0.510249
The Primal step takes 57.0002 (S)
lower bound updated to 0.510249

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.528828
    local lower bound updated to 0.510249

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.517158
    local lower bound updated to 0.510451

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.510451
    local lower bound updated to 0.510451
The Dual step takes 20.3039 (S)
upper bound updated to 0.510451
*** OUTER ITERATION 6 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.87739 seconds.
    local lower bound updated to 0.430899
    local upper bound updated to 0.510451

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 12.7985 seconds.
    local lower bound updated to 0.510308
    local upper bound updated to 0.510432

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.6363 seconds.
    local lower bound updated to 0.510359
    local upper bound updated to 0.510421

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 11.7144 seconds.
    local lower bound updated to 0.510421
    local upper bound updated to 0.510421
The Primal step takes 44.059 (S)
lower bound updated to 0.510421

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.527174
    local lower bound updated to 0.510421

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.510421
    local lower bound updated to 0.510421
The Dual step takes 13.9613 (S)
upper bound updated to 0.510421
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.52857 seconds.
    local lower bound updated to 0.430899
    local upper bound updated to 0.510421

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 12.3389 seconds.
    local lower bound updated to 0.510421
    local upper bound updated to 0.510421
The time obtain the optimal randomized assortment is 354.796 (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_105916.log"
The computation time limit for a lower bound is 85643
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 2000 rows, 1618 columns and 6439 nonzeros
Model fingerprint: 0x243af5c0
Variable types: 1561 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 522 rows and 958 columns
Presolve time: 0.03s
Presolved: 1478 rows, 660 columns, 5629 nonzeros
Variable types: 604 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.6363340
Found heuristic solution: objective 0.6147533
Found heuristic solution: objective 0.6146038

Root relaxation: objective 3.508134e-01, 168 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    0.35081    0   20    0.61460    0.35081  42.9%     -    0s
H    0     0                       0.5617800    0.35081  37.6%     -    0s
     0     0    0.37752    0   26    0.56178    0.37752  32.8%     -    0s
H    0     0                       0.5563775    0.37752  32.1%     -    0s
     0     0    0.39285    0   26    0.55638    0.39285  29.4%     -    0s
     0     0    0.41822    0   26    0.55638    0.41822  24.8%     -    0s
H    0     0                       0.5157531    0.41822  18.9%     -    0s
H    0     0                       0.5128537    0.42035  18.0%     -    0s
     0     0    0.42035    0   25    0.51285    0.42035  18.0%     -    0s
     0     0    0.43294    0   28    0.51285    0.43294  15.6%     -    0s
H    0     0                       0.5119707    0.43387  15.3%     -    0s
     0     0    0.43387    0   27    0.51197    0.43387  15.3%     -    0s
     0     0    0.43651    0   31    0.51197    0.43651  14.7%     -    0s
     0     0    0.43805    0   31    0.51197    0.43805  14.4%     -    0s
     0     0    0.44039    0   25    0.51197    0.44039  14.0%     -    0s
H    0     0                       0.5104214    0.44039  13.7%     -    1s
     0     2    0.44039    0   25    0.51042    0.44039  13.7%     -    1s
   398   166    0.48340    8   14    0.51042    0.47458  7.02%  25.6    5s
  1967   261     cutoff   14         0.51042    0.49326  3.36%  19.7   10s

Cutting planes:
  Gomory: 2
  Implied bound: 230
  MIR: 76
  Flow cover: 203
  RLT: 24
  Relax-and-lift: 86

Explored 3260 nodes (59797 simplex iterations) in 13.20 seconds (6.39 work units)
Thread count was 4 (of 48 available processors)

Solution count 9: 0.510421 0.511971 0.512854 ... 0.636334

Optimal solution found (tolerance 1.00e-04)
Best objective 5.104213520384e-01, best bound 5.104213520384e-01, gap 0.0000%
The objective bound is 0.510421 while the objective upper bound is 0.510421

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.30 (ave)

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