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 0.291918 seconds.
    local lower bound updated to 0.299356
    local upper bound updated to 0.509205

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.191987 seconds.
    local lower bound updated to 0.509205
    local upper bound updated to 0.509205
The Primal step takes 0.487352 (S)
lower bound updated to 0.509205

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.625423
    local lower bound updated to 0.625423
The Dual step takes 0.0160359 (S)
upper bound updated to 0.625423
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.285804 seconds.
    local lower bound updated to 0.346107
    local upper bound updated to 0.50978

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.335975 seconds.
    local lower bound updated to 0.509362
    local upper bound updated to 0.509377

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.268188 seconds.
    local lower bound updated to 0.509377
    local upper bound updated to 0.509377
The Primal step takes 0.896361 (S)
lower bound updated to 0.509377

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.558724
    local lower bound updated to 0.509929

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.556707
    local lower bound updated to 0.54645

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.54645
    local lower bound updated to 0.54645
The Dual step takes 0.281418 (S)
upper bound updated to 0.54645
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.451549 seconds.
    local lower bound updated to 0.406144
    local upper bound updated to 0.510142

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.542434 seconds.
    local lower bound updated to 0.509548
    local upper bound updated to 0.509994

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.398015 seconds.
    local lower bound updated to 0.509748
    local upper bound updated to 0.509941

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.493204 seconds.
    local lower bound updated to 0.509748
    local upper bound updated to 0.509913

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.671953 seconds.
    local lower bound updated to 0.509851
    local upper bound updated to 0.509912

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.640657 seconds.
    local lower bound updated to 0.509912
    local upper bound updated to 0.509912
The Primal step takes 3.21347 (S)
lower bound updated to 0.509912

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.552553
    local lower bound updated to 0.510095

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.523873
    local lower bound updated to 0.520548

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.523873
    local lower bound updated to 0.52164

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.52164
    local lower bound updated to 0.52164
The Dual step takes 1.402 (S)
upper bound updated to 0.52164
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.34017 seconds.
    local lower bound updated to 0.445264
    local upper bound updated to 0.517904

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.32555 seconds.
    local lower bound updated to 0.459465
    local upper bound updated to 0.515605

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.32342 seconds.
    local lower bound updated to 0.486546
    local upper bound updated to 0.513477

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.40105 seconds.
    local lower bound updated to 0.498185
    local upper bound updated to 0.513097

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 7.09089 seconds.
    local lower bound updated to 0.500717
    local upper bound updated to 0.512262

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 5.71383 seconds.
    local lower bound updated to 0.507007
    local upper bound updated to 0.512174

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 8.228 seconds.
    local lower bound updated to 0.510096
    local upper bound updated to 0.512115

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 8.83229 seconds.
    local lower bound updated to 0.510304
    local upper bound updated to 0.511943

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 7.01123 seconds.
    local lower bound updated to 0.510304
    local upper bound updated to 0.511923

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 6.79322 seconds.
    local lower bound updated to 0.511275
    local upper bound updated to 0.511882

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 7.46485 seconds.
    local lower bound updated to 0.511796
    local upper bound updated to 0.511877

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 8.55816 seconds.
    local lower bound updated to 0.511808
    local upper bound updated to 0.511872

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 8.0171 seconds.
    local lower bound updated to 0.511872
    local upper bound updated to 0.511872
The Primal step takes 78.1613 (S)
lower bound updated to 0.511872

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.567572
    local lower bound updated to 0.511872

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518702
    local lower bound updated to 0.516609

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.518702
    local lower bound updated to 0.517031

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.518702
    local lower bound updated to 0.51706

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.517305
    local lower bound updated to 0.51706

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.51706
    local lower bound updated to 0.51706
The Dual step takes 7.69312 (S)
upper bound updated to 0.51706
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.2872 seconds.
    local lower bound updated to 0.467314
    local upper bound updated to 0.515203

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.7313 seconds.
    local lower bound updated to 0.497739
    local upper bound updated to 0.513941

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.24285 seconds.
    local lower bound updated to 0.511596
    local upper bound updated to 0.513863

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.92144 seconds.
    local lower bound updated to 0.511596
    local upper bound updated to 0.513544

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.12497 seconds.
    local lower bound updated to 0.512336
    local upper bound updated to 0.513447

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.04668 seconds.
    local lower bound updated to 0.512336
    local upper bound updated to 0.51342

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 9.30052 seconds.
    local lower bound updated to 0.512336
    local upper bound updated to 0.513408

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 5.58754 seconds.
    local lower bound updated to 0.513191
    local upper bound updated to 0.51338

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 6.24713 seconds.
    local lower bound updated to 0.51338
    local upper bound updated to 0.51338
The Primal step takes 56.544 (S)
lower bound updated to 0.51338

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.560462
    local lower bound updated to 0.51338

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.516407
    local lower bound updated to 0.513383

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.513383
    local lower bound updated to 0.513383
The Dual step takes 6.79591 (S)
upper bound updated to 0.513383
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.70311 seconds.
    local lower bound updated to 0.471284
    local upper bound updated to 0.513383

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.42016 seconds.
    local lower bound updated to 0.511235
    local upper bound updated to 0.513382

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.1861 seconds.
    local lower bound updated to 0.513382
    local upper bound updated to 0.513382
The time obtain the optimal randomized assortment is 175.821 (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_13_4_200.000000_202714.log"
The computation time limit for a lower bound is 85823
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 20 physical cores, 40 logical processors, using up to 4 threads
Optimize a model with 1716 rows, 1506 columns and 5391 nonzeros
Model fingerprint: 0x62b4addb
Variable types: 1457 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [3e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 525 rows and 989 columns
Presolve time: 0.02s
Presolved: 1191 rows, 517 columns, 4519 nonzeros
Variable types: 470 continuous, 47 integer (47 binary)
Found heuristic solution: objective 0.6265170
Found heuristic solution: objective 0.5584784

Root relaxation: objective 3.837572e-01, 162 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    0.38376    0   18    0.55848    0.38376  31.3%     -    0s
H    0     0                       0.5536830    0.38376  30.7%     -    0s
     0     0    0.40844    0   22    0.55368    0.40844  26.2%     -    0s
H    0     0                       0.5212847    0.40844  21.6%     -    0s
     0     0    0.40844    0   22    0.52128    0.40844  21.6%     -    0s
     0     0    0.43635    0   23    0.52128    0.43635  16.3%     -    0s
     0     0    0.43638    0   23    0.52128    0.43638  16.3%     -    0s
     0     0    0.45405    0   22    0.52128    0.45405  12.9%     -    0s
     0     0    0.45467    0   22    0.52128    0.45467  12.8%     -    0s
     0     0    0.45819    0   22    0.52128    0.45819  12.1%     -    0s
H    0     0                       0.5189116    0.45922  11.5%     -    0s
     0     0    0.45922    0   23    0.51891    0.45922  11.5%     -    0s
     0     0    0.45951    0   23    0.51891    0.45951  11.4%     -    0s
H    0     0                       0.5133819    0.45951  10.5%     -    1s
     0     2    0.45951    0   23    0.51338    0.45951  10.5%     -    1s
  1390   206     cutoff   10         0.51338    0.48788  4.97%  19.9    5s
H 1431   206                       0.5133819    0.48814  4.92%  19.8    5s
H 1466   198                       0.5133819    0.48829  4.89%  19.6    5s
H 1923   184                       0.5133818    0.49146  4.27%  19.2    6s
H 1990   186                       0.5133818    0.49191  4.18%  19.2    6s

Cutting planes:
  Implied bound: 180
  MIR: 80
  Flow cover: 169
  RLT: 14
  Relax-and-lift: 71

Explored 3219 nodes (59740 simplex iterations) in 8.39 seconds (4.14 work units)
Thread count was 4 (of 40 available processors)

Solution count 8: 0.513382 0.513382 0.513382 ... 0.626517

Optimal solution found (tolerance 1.00e-04)
Best objective 5.133818351549e-01, best bound 5.133818351549e-01, gap 0.0000%
The objective bound is 0.513382 while the objective upper bound is 0.513382

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.14 (ave)

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