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 2.22366 seconds.
    local lower bound updated to 0.372709
    local upper bound updated to 0.683791

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.300518 seconds.
    local lower bound updated to 0.655348
    local upper bound updated to 0.655348
The Primal step takes 2.52668 (S)
lower bound updated to 0.655348

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.714434
    local lower bound updated to 0.702609

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.714434
    local lower bound updated to 0.707334

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.707334
    local lower bound updated to 0.707334
The Dual step takes 0.134524 (S)
upper bound updated to 0.707334
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.09345 seconds.
    local lower bound updated to 0.511045
    local upper bound updated to 0.672693

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.62872 seconds.
    local lower bound updated to 0.660214
    local upper bound updated to 0.662956

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.88825 seconds.
    local lower bound updated to 0.660214
    local upper bound updated to 0.662041

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.22205 seconds.
    local lower bound updated to 0.662041
    local upper bound updated to 0.662041
The Primal step takes 24.8421 (S)
lower bound updated to 0.662041

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.703857
    local lower bound updated to 0.680717

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.69337
    local lower bound updated to 0.684307

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.693017
    local lower bound updated to 0.688635

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.689735
    local lower bound updated to 0.689063

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.689063
    local lower bound updated to 0.689063
The Dual step takes 0.971012 (S)
upper bound updated to 0.689063
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 43.0321 seconds.
    local lower bound updated to 0.597759
    local upper bound updated to 0.686064

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 31.0727 seconds.
    local lower bound updated to 0.667451
    local upper bound updated to 0.685618

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 24.6814 seconds.
    local lower bound updated to 0.671541
    local upper bound updated to 0.680921

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 22.276 seconds.
    local lower bound updated to 0.673164
    local upper bound updated to 0.679688

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.9462 seconds.
    local lower bound updated to 0.673164
    local upper bound updated to 0.678677

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 38.1746 seconds.
    local lower bound updated to 0.673164
    local upper bound updated to 0.678086

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 35.1655 seconds.
    local lower bound updated to 0.677222
    local upper bound updated to 0.677944

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 40.1271 seconds.
    local lower bound updated to 0.677222
    local upper bound updated to 0.677908

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 44.3843 seconds.
    local lower bound updated to 0.677812
    local upper bound updated to 0.677905

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 38.5388 seconds.
    local lower bound updated to 0.677843
    local upper bound updated to 0.677891

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 40.2598 seconds.
    local lower bound updated to 0.677891
    local upper bound updated to 0.677891
The Primal step takes 374.702 (S)
lower bound updated to 0.677891

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.690271
    local lower bound updated to 0.677891

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.681015
    local lower bound updated to 0.678583

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.678583
    local lower bound updated to 0.678583
The Dual step takes 2.20186 (S)
upper bound updated to 0.678583
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 31.197 seconds.
    local lower bound updated to 0.603631
    local upper bound updated to 0.678287

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 36.763 seconds.
    local lower bound updated to 0.677979
    local upper bound updated to 0.67825

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 46.0211 seconds.
    local lower bound updated to 0.677995
    local upper bound updated to 0.678234

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 38.939 seconds.
    local lower bound updated to 0.678234
    local upper bound updated to 0.678234
The Primal step takes 152.938 (S)
lower bound updated to 0.678234

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.688964
    local lower bound updated to 0.678234

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.678234
    local lower bound updated to 0.678234
The Dual step takes 2.77242 (S)
upper bound updated to 0.678234
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 31.7576 seconds.
    local lower bound updated to 0.603631
    local upper bound updated to 0.678234

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 38.6181 seconds.
    local lower bound updated to 0.678234
    local upper bound updated to 0.678234
The time obtain the optimal randomized assortment is 631.474 (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_209616.log"
The computation time limit for a lower bound is 85363
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 1520 rows, 1228 columns and 4948 nonzeros
Model fingerprint: 0xab907ace
Variable types: 1171 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 375 rows and 709 columns
Presolve time: 0.02s
Presolved: 1145 rows, 519 columns, 4459 nonzeros
Variable types: 465 continuous, 54 integer (54 binary)
Found heuristic solution: objective 0.7991740
Found heuristic solution: objective 0.7793935
Found heuristic solution: objective 0.7399363

Root relaxation: objective 5.041757e-01, 159 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    0.50418    0   21    0.73994    0.50418  31.9%     -    0s
     0     0    0.51128    0   22    0.73994    0.51128  30.9%     -    0s
H    0     0                       0.6995821    0.51128  26.9%     -    0s
     0     0    0.51130    0   22    0.69958    0.51130  26.9%     -    0s
     0     0    0.55214    0   28    0.69958    0.55214  21.1%     -    0s
     0     0    0.56490    0   30    0.69958    0.56490  19.3%     -    0s
H    0     0                       0.6982557    0.56490  19.1%     -    0s
H    0     0                       0.6955379    0.57531  17.3%     -    0s
H    0     0                       0.6927963    0.57531  17.0%     -    0s
     0     0    0.57531    0   29    0.69280    0.57531  17.0%     -    0s
     0     0    0.57686    0   27    0.69280    0.57686  16.7%     -    0s
     0     0    0.58149    0   29    0.69280    0.58149  16.1%     -    0s
     0     0    0.58237    0   28    0.69280    0.58237  15.9%     -    0s
     0     0    0.58402    0   27    0.69280    0.58402  15.7%     -    0s
H    0     0                       0.6867300    0.58402  15.0%     -    0s
H    0     0                       0.6792851    0.58402  14.0%     -    1s
     0     2    0.58402    0   27    0.67929    0.58402  14.0%     -    1s
* 1054   406              22       0.6788737    0.62076  8.56%  23.3    2s
* 1055   404              21       0.6782342    0.62076  8.47%  23.3    2s
  2298   658    0.64404    9   16    0.67823    0.62744  7.49%  21.1    5s
H 3400   810                       0.6782341    0.63234  6.77%  20.0    8s
  4161   935    0.67200   14   27    0.67823    0.63438  6.47%  19.5   10s
H 4624   951                       0.6782341    0.63438  6.47%  20.5   13s
H 4663   915                       0.6782341    0.63438  6.47%  20.6   13s
  5293   823    0.67565   28   10    0.67823    0.63438  6.47%  21.0   15s
H 5433   753                       0.6782341    0.63438  6.47%  21.1   15s
  7639   650     cutoff   30         0.67823    0.64273  5.24%  21.5   20s
 10424   819    0.65435   21   17    0.67823    0.64965  4.21%  21.3   25s
 12081   821 infeasible   27         0.67823    0.65237  3.81%  21.1   30s
 15861   608     cutoff   35         0.67823    0.65942  2.77%  20.6   35s

Cutting planes:
  Implied bound: 130
  MIR: 88
  Flow cover: 265
  RLT: 31
  Relax-and-lift: 44

Explored 19137 nodes (380823 simplex iterations) in 38.49 seconds (28.92 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.678234 0.678874 0.679285 ... 0.779394

Optimal solution found (tolerance 1.00e-04)
Best objective 6.782341394358e-01, best bound 6.782341394358e-01, gap 0.0000%
The objective bound is 0.678234 while the objective upper bound is 0.678234

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.62 (ave)

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