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 0.0431359 seconds.
    local lower bound updated to 0.356814
    local upper bound updated to 0.536936

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0552624 seconds.
    local lower bound updated to 0.536936
    local upper bound updated to 0.536936
The Primal step takes 0.100739 (S)
lower bound updated to 0.536936

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.576053
    local lower bound updated to 0.576053
The Dual step takes 0.0127818 (S)
upper bound updated to 0.576053
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.186315 seconds.
    local lower bound updated to 0.404226
    local upper bound updated to 0.547029

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0732075 seconds.
    local lower bound updated to 0.524109
    local upper bound updated to 0.537916

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.117961 seconds.
    local lower bound updated to 0.536604
    local upper bound updated to 0.537091

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.0772718 seconds.
    local lower bound updated to 0.536975
    local upper bound updated to 0.537009

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.120398 seconds.
    local lower bound updated to 0.537009
    local upper bound updated to 0.537009
The Primal step takes 0.582305 (S)
lower bound updated to 0.537009

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.556721
    local lower bound updated to 0.538871

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.555904
    local lower bound updated to 0.541683

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.54232
    local lower bound updated to 0.542169

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.542169
    local lower bound updated to 0.542169
The Dual step takes 0.251413 (S)
upper bound updated to 0.542169
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.32491 seconds.
    local lower bound updated to 0.454134
    local upper bound updated to 0.538871

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.213641 seconds.
    local lower bound updated to 0.53834
    local upper bound updated to 0.538696

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.284117 seconds.
    local lower bound updated to 0.53834
    local upper bound updated to 0.538454

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.183352 seconds.
    local lower bound updated to 0.538454
    local upper bound updated to 0.538454
The Primal step takes 1.01558 (S)
lower bound updated to 0.538454

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.564103
    local lower bound updated to 0.538724

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.546111
    local lower bound updated to 0.538847

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.541414
    local lower bound updated to 0.539465

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.539465
    local lower bound updated to 0.539465
The Dual step takes 0.341932 (S)
upper bound updated to 0.539465
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.492437 seconds.
    local lower bound updated to 0.471218
    local upper bound updated to 0.538639

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.413346 seconds.
    local lower bound updated to 0.538148
    local upper bound updated to 0.538493

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.386854 seconds.
    local lower bound updated to 0.538372
    local upper bound updated to 0.538482

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.474021 seconds.
    local lower bound updated to 0.538432
    local upper bound updated to 0.538482

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.327689 seconds.
    local lower bound updated to 0.538432
    local upper bound updated to 0.538476

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.313226 seconds.
    local lower bound updated to 0.538435
    local upper bound updated to 0.538465

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.368489 seconds.
    local lower bound updated to 0.538464
    local upper bound updated to 0.538465
The Primal step takes 2.79694 (S)
lower bound updated to 0.538464

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.54801
    local lower bound updated to 0.538465

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.54801
    local lower bound updated to 0.538635

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.538635
    local lower bound updated to 0.538635
The Dual step takes 0.518945 (S)
upper bound updated to 0.538635
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.451237 seconds.
    local lower bound updated to 0.476336
    local upper bound updated to 0.538635

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.321598 seconds.
    local lower bound updated to 0.538635
    local upper bound updated to 0.538635
The Primal step takes 0.779009 (S)
lower bound updated to 0.538635

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.547848
    local lower bound updated to 0.538635

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.539238
    local lower bound updated to 0.538635

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.539238
    local lower bound updated to 0.538635

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.538635
    local lower bound updated to 0.538635
The Dual step takes 0.906206 (S)
upper bound updated to 0.538635
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.68946 seconds.
    local lower bound updated to 0.480318
    local upper bound updated to 0.538635

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.542684 seconds.
    local lower bound updated to 0.538635
    local upper bound updated to 0.538635
The time obtain the optimal randomized assortment is 8.54608 (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_11_4_60.000000_68312.log"
The computation time limit for a lower bound is 85990
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 1180 rows, 1170 columns and 3551 nonzeros
Model fingerprint: 0xcfb800ed
Variable types: 1129 continuous, 41 integer (41 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 442 rows and 847 columns
Presolve time: 0.01s
Presolved: 738 rows, 323 columns, 2666 nonzeros
Variable types: 287 continuous, 36 integer (36 binary)
Found heuristic solution: objective 0.6405304
Found heuristic solution: objective 0.5933337

Root relaxation: objective 4.677368e-01, 165 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    0.46774    0   13    0.59333    0.46774  21.2%     -    0s
H    0     0                       0.5752764    0.46774  18.7%     -    0s
H    0     0                       0.5703372    0.48582  14.8%     -    0s
     0     0    0.48914    0   17    0.57034    0.48914  14.2%     -    0s
     0     0    0.48914    0   17    0.57034    0.48914  14.2%     -    0s
H    0     0                       0.5689446    0.48914  14.0%     -    0s
     0     0    0.50769    0   15    0.56894    0.50769  10.8%     -    0s
H    0     0                       0.5588992    0.50769  9.16%     -    0s
H    0     0                       0.5583658    0.50769  9.08%     -    0s
     0     0    0.51143    0   15    0.55837    0.51143  8.41%     -    0s
     0     0    0.52128    0   16    0.55837    0.52128  6.64%     -    0s
H    0     0                       0.5514388    0.52128  5.47%     -    0s
     0     0    0.52132    0   16    0.55144    0.52132  5.46%     -    0s
     0     0    0.52350    0   15    0.55144    0.52350  5.07%     -    0s
H    0     0                       0.5512375    0.52493  4.77%     -    0s
     0     0    0.52493    0   15    0.55124    0.52493  4.77%     -    0s
H    0     0                       0.5474008    0.52493  4.10%     -    0s
H    0     0                       0.5430549    0.52493  3.34%     -    0s
     0     0    0.52627    0   14    0.54305    0.52627  3.09%     -    0s
H    0     0                       0.5424896    0.52627  2.99%     -    0s
H    0     0                       0.5386355    0.52627  2.30%     -    0s
     0     0    0.52627    0   13    0.53864    0.52627  2.30%     -    0s
     0     0    0.52627    0   12    0.53864    0.52627  2.30%     -    0s
     0     0    0.52627    0    9    0.53864    0.52627  2.30%     -    0s
H    0     0                       0.5386355    0.52627  2.30%     -    0s
     0     0    0.53393    0    9    0.53864    0.53393  0.87%     -    0s
     0     0    0.53395    0    9    0.53864    0.53395  0.87%     -    0s
H    0     0                       0.5386355    0.53395  0.87%     -    0s
     0     0    0.53518    0    9    0.53864    0.53518  0.64%     -    0s
H    0     0                       0.5386355    0.53518  0.64%     -    0s
     0     0    0.53522    0    9    0.53864    0.53522  0.63%     -    0s
     0     0    0.53837    0    9    0.53864    0.53837  0.05%     -    0s
     0     0    0.53864    0    9    0.53864    0.53864  0.00%     -    0s

Cutting planes:
  Gomory: 5
  Implied bound: 63
  MIR: 13
  Flow cover: 54
  RLT: 6
  Relax-and-lift: 26

Explored 1 nodes (1715 simplex iterations) in 0.50 seconds (0.16 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.538635 0.538635 0.538635 ... 0.558899

Optimal solution found (tolerance 1.00e-04)
Best objective 5.386354507777e-01, best bound 5.386354507777e-01, gap 0.0000%
The objective bound is 0.538635 while the objective upper bound is 0.538635

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.70 (ave)

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