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 0.38364 seconds.
    local lower bound updated to 0.280766
    local upper bound updated to 0.510538

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.761299 seconds.
    local lower bound updated to 0.507967
    local upper bound updated to 0.507967
The Primal step takes 1.14856 (S)
lower bound updated to 0.507967

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.550171
    local lower bound updated to 0.546514

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.546514
    local lower bound updated to 0.546514
The Dual step takes 0.156594 (S)
upper bound updated to 0.546514
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.01794 seconds.
    local lower bound updated to 0.337935
    local upper bound updated to 0.517076

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.89801 seconds.
    local lower bound updated to 0.505545
    local upper bound updated to 0.513002

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.8914 seconds.
    local lower bound updated to 0.509761
    local upper bound updated to 0.511225

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.18289 seconds.
    local lower bound updated to 0.510773
    local upper bound updated to 0.510884

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.55716 seconds.
    local lower bound updated to 0.510884
    local upper bound updated to 0.510884
The Primal step takes 8.55929 (S)
lower bound updated to 0.510884

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.555652
    local lower bound updated to 0.515347

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.537857
    local lower bound updated to 0.528835

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.537857
    local lower bound updated to 0.532625

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.532625
    local lower bound updated to 0.532625
The Dual step takes 1.09665 (S)
upper bound updated to 0.532625
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.97228 seconds.
    local lower bound updated to 0.404833
    local upper bound updated to 0.514438

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.95632 seconds.
    local lower bound updated to 0.51049
    local upper bound updated to 0.51208

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.20437 seconds.
    local lower bound updated to 0.510702
    local upper bound updated to 0.51201

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.50449 seconds.
    local lower bound updated to 0.51191
    local upper bound updated to 0.512005

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.57089 seconds.
    local lower bound updated to 0.51191
    local upper bound updated to 0.511987

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.49802 seconds.
    local lower bound updated to 0.511987
    local upper bound updated to 0.511987
The Primal step takes 21.7286 (S)
lower bound updated to 0.511987

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.527995
    local lower bound updated to 0.511987

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.524485
    local lower bound updated to 0.513632

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.520608
    local lower bound updated to 0.51377

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.519527
    local lower bound updated to 0.515401

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.5191
    local lower bound updated to 0.515926

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.519097
    local lower bound updated to 0.516801

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.516801
    local lower bound updated to 0.516801
The Dual step takes 4.27806 (S)
upper bound updated to 0.516801
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.53248 seconds.
    local lower bound updated to 0.452005
    local upper bound updated to 0.515739

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 8.54313 seconds.
    local lower bound updated to 0.511561
    local upper bound updated to 0.51509

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.09215 seconds.
    local lower bound updated to 0.511561
    local upper bound updated to 0.515006

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 15.7989 seconds.
    local lower bound updated to 0.511693
    local upper bound updated to 0.514829

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.3865 seconds.
    local lower bound updated to 0.51299
    local upper bound updated to 0.514323

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 11.7263 seconds.
    local lower bound updated to 0.513377
    local upper bound updated to 0.514266

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 13.4879 seconds.
    local lower bound updated to 0.513574
    local upper bound updated to 0.513996

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 10.5366 seconds.
    local lower bound updated to 0.513574
    local upper bound updated to 0.513911

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 17.2132 seconds.
    local lower bound updated to 0.513754
    local upper bound updated to 0.513876

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 14.3938 seconds.
    local lower bound updated to 0.513754
    local upper bound updated to 0.513866

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 15.1257 seconds.
    local lower bound updated to 0.513754
    local upper bound updated to 0.513857

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 13.6194 seconds.
    local lower bound updated to 0.513824
    local upper bound updated to 0.513855

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 13.7227 seconds.
    local lower bound updated to 0.513855
    local upper bound updated to 0.513855
The Primal step takes 160.255 (S)
lower bound updated to 0.513855

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.525354
    local lower bound updated to 0.513855

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.516464
    local lower bound updated to 0.513888

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513888
    local lower bound updated to 0.513888
The Dual step takes 7.3529 (S)
upper bound updated to 0.513888
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.33582 seconds.
    local lower bound updated to 0.455903
    local upper bound updated to 0.513888

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 22.1878 seconds.
    local lower bound updated to 0.513793
    local upper bound updated to 0.513882

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 17.9385 seconds.
    local lower bound updated to 0.513825
    local upper bound updated to 0.513876

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 15.0356 seconds.
    local lower bound updated to 0.513827
    local upper bound updated to 0.513866

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.7185 seconds.
    local lower bound updated to 0.513866
    local upper bound updated to 0.513866
The Primal step takes 81.2443 (S)
lower bound updated to 0.513866

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.524943
    local lower bound updated to 0.513866

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.515363
    local lower bound updated to 0.513876

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513876
    local lower bound updated to 0.513876
The Dual step takes 9.60579 (S)
upper bound updated to 0.513876
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 8.63147 seconds.
    local lower bound updated to 0.459903
    local upper bound updated to 0.513876

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.6688 seconds.
    local lower bound updated to 0.513876
    local upper bound updated to 0.513876
The Primal step takes 29.3159 (S)
lower bound updated to 0.513876

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.524488
    local lower bound updated to 0.513876

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.513876
    local lower bound updated to 0.513876
The Dual step takes 6.96435 (S)
upper bound updated to 0.513876
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.21752 seconds.
    local lower bound updated to 0.459903
    local upper bound updated to 0.513876

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.0607 seconds.
    local lower bound updated to 0.513876
    local upper bound updated to 0.513876
The time obtain the optimal randomized assortment is 360.996 (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_17_4_200.000000_202618.log"
The computation time limit for a lower bound is 85635
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 2604 rows, 1990 columns and 8570 nonzeros
Model fingerprint: 0xcbbf14d4
Variable types: 1925 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [5e-01, 1e+00]
Presolve removed 601 rows and 1099 columns
Presolve time: 0.03s
Presolved: 2003 rows, 891 columns, 7915 nonzeros
Variable types: 828 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.7469829
Found heuristic solution: objective 0.6976808
Found heuristic solution: objective 0.6798595

Root relaxation: objective 3.595108e-01, 203 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    0.35951    0   26    0.67986    0.35951  47.1%     -    0s
H    0     0                       0.6164364    0.35951  41.7%     -    0s
H    0     0                       0.6077314    0.35951  40.8%     -    0s
     0     0    0.36763    0   31    0.60773    0.36763  39.5%     -    0s
H    0     0                       0.5892651    0.36763  37.6%     -    0s
     0     0    0.41806    0   29    0.58927    0.41806  29.1%     -    0s
H    0     0                       0.5246090    0.41806  20.3%     -    0s
     0     0    0.41807    0   28    0.52461    0.41807  20.3%     -    0s
     0     0    0.44212    0   31    0.52461    0.44212  15.7%     -    0s
H    0     0                       0.5233114    0.44212  15.5%     -    0s
H    0     0                       0.5183423    0.44277  14.6%     -    0s
     0     0    0.44277    0   29    0.51834    0.44277  14.6%     -    0s
H    0     0                       0.5161616    0.44277  14.2%     -    0s
H    0     0                       0.5138763    0.44277  13.8%     -    0s
     0     0    0.44837    0   31    0.51388    0.44837  12.7%     -    0s
     0     0    0.44995    0   35    0.51388    0.44995  12.4%     -    0s
     0     0    0.45195    0   32    0.51388    0.45195  12.1%     -    0s
     0     2    0.45195    0   32    0.51388    0.45195  12.1%     -    2s
   594   212    0.50788   13   12    0.51388    0.48392  5.83%  26.9    5s
  1899   384    0.51035   13   12    0.51388    0.49261  4.14%  23.2   10s
  3843   423     cutoff   17         0.51388    0.49884  2.93%  21.2   15s
  6002   121    0.51382   19    4    0.51388    0.50632  1.47%  19.8   20s

Cutting planes:
  Gomory: 2
  Implied bound: 288
  MIR: 114
  Flow cover: 324
  RLT: 14
  Relax-and-lift: 85

Explored 6694 nodes (130733 simplex iterations) in 20.19 seconds (16.52 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.513876 0.516162 0.518342 ... 0.697681

Optimal solution found (tolerance 1.00e-04)
Best objective 5.138763450228e-01, best bound 5.138763450228e-01, gap 0.0000%
The objective bound is 0.513876 while the objective upper bound is 0.513876

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.32 (ave)

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