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 0.474591 seconds.
    local lower bound updated to 0.228931
    local upper bound updated to 0.436825

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.865858 seconds.
    local lower bound updated to 0.426948
    local upper bound updated to 0.426948
The Primal step takes 1.34283 (S)
lower bound updated to 0.426948

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.588459
    local lower bound updated to 0.574401

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.574401
    local lower bound updated to 0.574401
The Dual step takes 0.0597334 (S)
upper bound updated to 0.574401
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.735675 seconds.
    local lower bound updated to 0.284783
    local upper bound updated to 0.445029

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.51771 seconds.
    local lower bound updated to 0.426213
    local upper bound updated to 0.431985

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.47373 seconds.
    local lower bound updated to 0.427537
    local upper bound updated to 0.428419

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.03419 seconds.
    local lower bound updated to 0.428419
    local upper bound updated to 0.428419
The Primal step takes 7.76786 (S)
lower bound updated to 0.428419

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.489815
    local lower bound updated to 0.452131

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.467639
    local lower bound updated to 0.466494

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.467639
    local lower bound updated to 0.467081

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.467081
    local lower bound updated to 0.467081
The Dual step takes 0.293577 (S)
upper bound updated to 0.467081
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.58476 seconds.
    local lower bound updated to 0.3542
    local upper bound updated to 0.447392

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.7245 seconds.
    local lower bound updated to 0.437339
    local upper bound updated to 0.445768

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.81114 seconds.
    local lower bound updated to 0.437339
    local upper bound updated to 0.440809

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.71877 seconds.
    local lower bound updated to 0.437339
    local upper bound updated to 0.438649

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 10.3141 seconds.
    local lower bound updated to 0.437748
    local upper bound updated to 0.438237

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 10.1075 seconds.
    local lower bound updated to 0.437748
    local upper bound updated to 0.438075

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 8.61172 seconds.
    local lower bound updated to 0.437748
    local upper bound updated to 0.438023

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 8.9243 seconds.
    local lower bound updated to 0.437748
    local upper bound updated to 0.438012

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 11.0344 seconds.
    local lower bound updated to 0.438012
    local upper bound updated to 0.438012
The Primal step takes 75.8566 (S)
lower bound updated to 0.438012

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.462042
    local lower bound updated to 0.457272

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.457272
    local lower bound updated to 0.457272
The Dual step takes 1.00019 (S)
upper bound updated to 0.457272
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.62348 seconds.
    local lower bound updated to 0.368848
    local upper bound updated to 0.448244

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.55749 seconds.
    local lower bound updated to 0.438122
    local upper bound updated to 0.445324

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.49861 seconds.
    local lower bound updated to 0.439675
    local upper bound updated to 0.442148

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 10.5089 seconds.
    local lower bound updated to 0.440813
    local upper bound updated to 0.441956

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 7.52007 seconds.
    local lower bound updated to 0.441439
    local upper bound updated to 0.44191

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.22654 seconds.
    local lower bound updated to 0.441696
    local upper bound updated to 0.441876

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 8.99378 seconds.
    local lower bound updated to 0.441876
    local upper bound updated to 0.441876
The Primal step takes 52.9508 (S)
lower bound updated to 0.441876

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.463137
    local lower bound updated to 0.444689

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.463137
    local lower bound updated to 0.444964

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.463137
    local lower bound updated to 0.445462

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.456981
    local lower bound updated to 0.449304

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.450262
    local lower bound updated to 0.449378

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.449378
    local lower bound updated to 0.449378
The Dual step takes 3.18485 (S)
upper bound updated to 0.449378
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 11.3402 seconds.
    local lower bound updated to 0.391739
    local upper bound updated to 0.447287

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 26.0423 seconds.
    local lower bound updated to 0.446002
    local upper bound updated to 0.447073

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 20.4851 seconds.
    local lower bound updated to 0.446002
    local upper bound updated to 0.447007

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 31.4929 seconds.
    local lower bound updated to 0.446106
    local upper bound updated to 0.44651

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 36.1658 seconds.
    local lower bound updated to 0.446106
    local upper bound updated to 0.446487

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 30.1762 seconds.
    local lower bound updated to 0.446106
    local upper bound updated to 0.446376

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 41.3724 seconds.
    local lower bound updated to 0.446106
    local upper bound updated to 0.446353

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 28.8031 seconds.
    local lower bound updated to 0.446106
    local upper bound updated to 0.446307

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 40.7919 seconds.
    local lower bound updated to 0.446274
    local upper bound updated to 0.446284

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 26.069 seconds.
    local lower bound updated to 0.446274
    local upper bound updated to 0.446283
The Primal step takes 292.792 (S)
lower bound updated to 0.446274

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.463238
    local lower bound updated to 0.446283

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.463238
    local lower bound updated to 0.446294

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.448087
    local lower bound updated to 0.446295

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.446295
    local lower bound updated to 0.446295
The Dual step takes 4.86643 (S)
upper bound updated to 0.446295
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.64021 seconds.
    local lower bound updated to 0.394278
    local upper bound updated to 0.446295

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 34.5395 seconds.
    local lower bound updated to 0.446223
    local upper bound updated to 0.446292

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 42.1989 seconds.
    local lower bound updated to 0.446227
    local upper bound updated to 0.44629

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 35.8051 seconds.
    local lower bound updated to 0.44626
    local upper bound updated to 0.446283

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 40.0249 seconds.
    local lower bound updated to 0.446283
    local upper bound updated to 0.446283
The Primal step takes 162.24 (S)
lower bound updated to 0.446283

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.460153
    local lower bound updated to 0.446283

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.446283
    local lower bound updated to 0.446283
The Dual step takes 7.08978 (S)
upper bound updated to 0.446283
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 9.40336 seconds.
    local lower bound updated to 0.394278
    local upper bound updated to 0.446283

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 34.1116 seconds.
    local lower bound updated to 0.446283
    local upper bound updated to 0.446283
The time obtain the optimal randomized assortment is 652.972 (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_201718.log"
The computation time limit for a lower bound is 85342
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 2798 rows, 2138 columns and 9201 nonzeros
Model fingerprint: 0x0ca30711
Variable types: 2073 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [2e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 663 rows and 1181 columns
Presolve time: 0.03s
Presolved: 2135 rows, 957 columns, 8267 nonzeros
Variable types: 894 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.5846466
Found heuristic solution: objective 0.4477100

Root relaxation: objective 3.735104e-01, 306 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    0.37351    0   24    0.44771    0.37351  16.6%     -    0s
     0     0    0.37600    0   25    0.44771    0.37600  16.0%     -    0s
     0     0    0.37600    0   25    0.44771    0.37600  16.0%     -    0s
     0     0    0.39841    0   27    0.44771    0.39841  11.0%     -    0s
     0     0    0.39845    0   27    0.44771    0.39845  11.0%     -    0s
     0     0    0.40456    0   26    0.44771    0.40456  9.64%     -    0s
     0     0    0.40589    0   28    0.44771    0.40589  9.34%     -    0s
     0     0    0.40822    0   25    0.44771    0.40822  8.82%     -    0s
     0     0    0.40909    0   25    0.44771    0.40909  8.63%     -    0s
     0     0    0.41028    0   27    0.44771    0.41028  8.36%     -    0s
H    0     0                       0.4462834    0.41028  8.07%     -    2s
     0     2    0.41028    0   27    0.44628    0.41028  8.07%     -    2s
   599   193     cutoff   14         0.44628    0.42385  5.03%  30.6    5s
H  800   244                       0.4462834    0.42512  4.74%  29.2    6s
H 1600   391                       0.4462834    0.42821  4.05%  28.8    8s
  1879   446    0.44177   13   10    0.44628    0.42928  3.81%  28.3   10s
  3064   547     cutoff   12         0.44628    0.43199  3.20%  27.3   15s
  4562   598     cutoff   15         0.44628    0.43443  2.66%  26.8   20s
  6540   597    0.44146   15   10    0.44628    0.43661  2.17%  25.4   25s
  7936   521     cutoff   14         0.44628    0.43812  1.83%  24.7   30s
 10759    32    0.44580   18    4    0.44628    0.44240  0.87%  23.3   35s

Cutting planes:
  Gomory: 3
  Implied bound: 312
  MIR: 102
  Flow cover: 316
  RLT: 28
  Relax-and-lift: 146
  PSD: 1

Explored 11167 nodes (261026 simplex iterations) in 35.55 seconds (29.23 work units)
Thread count was 4 (of 48 available processors)

Solution count 5: 0.446283 0.446283 0.446283 ... 0.584647

Optimal solution found (tolerance 1.00e-04)
Best objective 4.462834207368e-01, best bound 4.462834207368e-01, gap 0.0000%
The objective bound is 0.446283 while the objective upper bound is 0.446283

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.59 (ave)

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