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 0.0136583 seconds.
    local lower bound updated to 0.312811
    local upper bound updated to 0.461714

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0117275 seconds.
    local lower bound updated to 0.461714
    local upper bound updated to 0.461714
The Primal step takes 0.0273929 (S)
lower bound updated to 0.461714

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.662919
    local lower bound updated to 0.662919
The Dual step takes 0.0101703 (S)
upper bound updated to 0.662919
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.0358543 seconds.
    local lower bound updated to 0.346126
    local upper bound updated to 0.461714

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0172101 seconds.
    local lower bound updated to 0.461714
    local upper bound updated to 0.461714
The Primal step takes 0.0559332 (S)
lower bound updated to 0.461714

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.590393
    local lower bound updated to 0.461714

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.488172
    local lower bound updated to 0.483344

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.488172
    local lower bound updated to 0.485028

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.485028
    local lower bound updated to 0.485028
The Dual step takes 0.0883733 (S)
upper bound updated to 0.485028
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.0982798 seconds.
    local lower bound updated to 0.40264
    local upper bound updated to 0.473032

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.0633106 seconds.
    local lower bound updated to 0.447639
    local upper bound updated to 0.46976

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.235375 seconds.
    local lower bound updated to 0.46152
    local upper bound updated to 0.468687

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.111231 seconds.
    local lower bound updated to 0.464422
    local upper bound updated to 0.467948

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.112959 seconds.
    local lower bound updated to 0.464422
    local upper bound updated to 0.46585

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.0869589 seconds.
    local lower bound updated to 0.464675
    local upper bound updated to 0.465628

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.100166 seconds.
    local lower bound updated to 0.464982
    local upper bound updated to 0.465587

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 0.092946 seconds.
    local lower bound updated to 0.465022
    local upper bound updated to 0.465544

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 0.106877 seconds.
    local lower bound updated to 0.465151
    local upper bound updated to 0.465489

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 0.0823127 seconds.
    local lower bound updated to 0.465151
    local upper bound updated to 0.465388

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 0.18018 seconds.
    local lower bound updated to 0.465388
    local upper bound updated to 0.465388
The Primal step takes 1.29742 (S)
lower bound updated to 0.465388

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.541545
    local lower bound updated to 0.465388

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.484127
    local lower bound updated to 0.470088

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.480222
    local lower bound updated to 0.471133

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.480222
    local lower bound updated to 0.47166

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.479988
    local lower bound updated to 0.474695

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.478717
    local lower bound updated to 0.474778

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.474915
    local lower bound updated to 0.474793

    ++ RESTRICTED DUAL ITERATION 8 ++
    local upper bound updated to 0.474793
    local lower bound updated to 0.474793
The Dual step takes 0.881928 (S)
upper bound updated to 0.474793
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.500985 seconds.
    local lower bound updated to 0.426319
    local upper bound updated to 0.467871

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.50173 seconds.
    local lower bound updated to 0.457728
    local upper bound updated to 0.46722

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.436881 seconds.
    local lower bound updated to 0.458298
    local upper bound updated to 0.466749

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.431953 seconds.
    local lower bound updated to 0.463854
    local upper bound updated to 0.466621

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.532698 seconds.
    local lower bound updated to 0.463854
    local upper bound updated to 0.466607

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.536485 seconds.
    local lower bound updated to 0.463855
    local upper bound updated to 0.465533

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.184429 seconds.
    local lower bound updated to 0.464961
    local upper bound updated to 0.465388

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 0.198943 seconds.
    local lower bound updated to 0.465388
    local upper bound updated to 0.465388
The Primal step takes 3.35994 (S)
lower bound updated to 0.465388

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.527593
    local lower bound updated to 0.465388

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.481687
    local lower bound updated to 0.470033

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.474204
    local lower bound updated to 0.471121

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.47202
    local lower bound updated to 0.471134

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.471134
    local lower bound updated to 0.471134
The Dual step takes 0.957344 (S)
upper bound updated to 0.471134
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.634933 seconds.
    local lower bound updated to 0.433187
    local upper bound updated to 0.47044

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.248251 seconds.
    local lower bound updated to 0.465679
    local upper bound updated to 0.470281

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.493948 seconds.
    local lower bound updated to 0.467576
    local upper bound updated to 0.469836

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.520599 seconds.
    local lower bound updated to 0.468694
    local upper bound updated to 0.469561

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.657432 seconds.
    local lower bound updated to 0.469343
    local upper bound updated to 0.469553

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.636201 seconds.
    local lower bound updated to 0.469553
    local upper bound updated to 0.469553
The Primal step takes 3.22325 (S)
lower bound updated to 0.469553

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.519308
    local lower bound updated to 0.469553

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.473083
    local lower bound updated to 0.469724

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.469724
    local lower bound updated to 0.469724
The Dual step takes 0.784319 (S)
upper bound updated to 0.469724
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.651468 seconds.
    local lower bound updated to 0.434936
    local upper bound updated to 0.469724

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.550855 seconds.
    local lower bound updated to 0.469634
    local upper bound updated to 0.469721

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.62592 seconds.
    local lower bound updated to 0.469721
    local upper bound updated to 0.469721
The Primal step takes 1.84583 (S)
lower bound updated to 0.469721

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.522465
    local lower bound updated to 0.469721

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.469721
    local lower bound updated to 0.469721
The Dual step takes 0.511531 (S)
upper bound updated to 0.469721
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.637249 seconds.
    local lower bound updated to 0.434936
    local upper bound updated to 0.469721

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.534363 seconds.
    local lower bound updated to 0.469721
    local upper bound updated to 0.469721
The time obtain the optimal randomized assortment is 14.2247 (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_60612.log"
The computation time limit for a lower bound is 85984
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 1640 rows, 1640 columns and 4901 nonzeros
Model fingerprint: 0x12589ba9
Variable types: 1599 continuous, 41 integer (41 binary)
Coefficient statistics:
  Matrix range     [1e-02, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 715 rows and 1236 columns
Presolve time: 0.01s
Presolved: 925 rows, 404 columns, 3395 nonzeros
Variable types: 368 continuous, 36 integer (36 binary)
Found heuristic solution: objective 0.5695261
Found heuristic solution: objective 0.5031109

Root relaxation: objective 4.107364e-01, 145 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    0.41074    0   14    0.50311    0.41074  18.4%     -    0s
H    0     0                       0.4822405    0.41074  14.8%     -    0s
H    0     0                       0.4814993    0.42795  11.1%     -    0s
     0     0    0.42795    0   13    0.48150    0.42795  11.1%     -    0s
H    0     0                       0.4743868    0.42795  9.79%     -    0s
     0     0    0.42795    0   13    0.47439    0.42795  9.79%     -    0s
H    0     0                       0.4733569    0.44302  6.41%     -    0s
     0     0    0.44302    0   16    0.47336    0.44302  6.41%     -    0s
     0     0    0.44334    0   15    0.47336    0.44334  6.34%     -    0s
H    0     0                       0.4728686    0.44597  5.69%     -    0s
     0     0    0.44597    0   16    0.47287    0.44597  5.69%     -    0s
H    0     0                       0.4716883    0.44597  5.45%     -    0s
H    0     0                       0.4698375    0.44659  4.95%     -    0s
     0     0    0.44659    0   16    0.46984    0.44659  4.95%     -    0s
H    0     0                       0.4697210    0.45506  3.12%     -    0s
     0     0    0.45506    0   11    0.46972    0.45506  3.12%     -    0s
     0     0    0.45785    0   14    0.46972    0.45785  2.53%     -    0s
H    0     0                       0.4697210    0.45785  2.53%     -    0s
     0     0    0.46058    0   12    0.46972    0.46058  1.95%     -    0s
     0     2    0.46058    0   12    0.46972    0.46058  1.95%     -    0s

Cutting planes:
  Gomory: 1
  Implied bound: 105
  MIR: 23
  Flow cover: 61
  RLT: 3
  Relax-and-lift: 50

Explored 84 nodes (2407 simplex iterations) in 0.54 seconds (0.24 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.469721 0.469721 0.469837 ... 0.503111

Optimal solution found (tolerance 1.00e-04)
Best objective 4.697210070283e-01, best bound 4.697210070283e-01, gap 0.0000%
The objective bound is 0.469721 while the objective upper bound is 0.469721

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.63 (ave)

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