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 0.712532 seconds.
    local lower bound updated to 0.178746
    local upper bound updated to 0.354248

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.16574 seconds.
    local lower bound updated to 0.350683
    local upper bound updated to 0.350683
The Primal step takes 1.88087 (S)
lower bound updated to 0.350683

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.473226
    local lower bound updated to 0.448187

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.448187
    local lower bound updated to 0.448187
The Dual step takes 0.073242 (S)
upper bound updated to 0.448187
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.08825 seconds.
    local lower bound updated to 0.239819
    local upper bound updated to 0.371934

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.37725 seconds.
    local lower bound updated to 0.363207
    local upper bound updated to 0.36471

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.69892 seconds.
    local lower bound updated to 0.363207
    local upper bound updated to 0.363859

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.29937 seconds.
    local lower bound updated to 0.363838
    local upper bound updated to 0.36385

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.84099 seconds.
    local lower bound updated to 0.36385
    local upper bound updated to 0.36385
The Primal step takes 18.3158 (S)
lower bound updated to 0.36385

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.420351
    local lower bound updated to 0.400276

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.407033
    local lower bound updated to 0.401418

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.403449
    local lower bound updated to 0.403116

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.403449
    local lower bound updated to 0.40321

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.40321
    local lower bound updated to 0.40321
The Dual step takes 1.86774 (S)
upper bound updated to 0.40321
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 18.4847 seconds.
    local lower bound updated to 0.315635
    local upper bound updated to 0.395975

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.86154 seconds.
    local lower bound updated to 0.330528
    local upper bound updated to 0.3883

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.09734 seconds.
    local lower bound updated to 0.371844
    local upper bound updated to 0.38515

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.22473 seconds.
    local lower bound updated to 0.371844
    local upper bound updated to 0.380682

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 12.9315 seconds.
    local lower bound updated to 0.375804
    local upper bound updated to 0.378416

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 26.5646 seconds.
    local lower bound updated to 0.375804
    local upper bound updated to 0.378218

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 21.2651 seconds.
    local lower bound updated to 0.376438
    local upper bound updated to 0.378053

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 17.7686 seconds.
    local lower bound updated to 0.376975
    local upper bound updated to 0.377949

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 24.0736 seconds.
    local lower bound updated to 0.376975
    local upper bound updated to 0.377925

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 21.373 seconds.
    local lower bound updated to 0.377333
    local upper bound updated to 0.377875

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 28.2961 seconds.
    local lower bound updated to 0.377333
    local upper bound updated to 0.377694

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 29.2983 seconds.
    local lower bound updated to 0.377542
    local upper bound updated to 0.377684

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 24.1748 seconds.
    local lower bound updated to 0.377684
    local upper bound updated to 0.377684
The Primal step takes 241.463 (S)
lower bound updated to 0.377684

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.411232
    local lower bound updated to 0.378347

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.402652
    local lower bound updated to 0.381611

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.387989
    local lower bound updated to 0.381786

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.387253
    local lower bound updated to 0.382392

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.387108
    local lower bound updated to 0.382816

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.382816
    local lower bound updated to 0.382816
The Dual step takes 13.6805 (S)
upper bound updated to 0.382816
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 33.7921 seconds.
    local lower bound updated to 0.340222
    local upper bound updated to 0.382816

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.018 seconds.
    local lower bound updated to 0.378894
    local upper bound updated to 0.381393

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0219 seconds.
    local lower bound updated to 0.379618
    local upper bound updated to 0.381389

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0215 seconds.
    local lower bound updated to 0.3811
    local upper bound updated to 0.381382

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.023 seconds.
    local lower bound updated to 0.381167
    local upper bound updated to 0.381366

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0184 seconds.
    local lower bound updated to 0.381209
    local upper bound updated to 0.381365

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0316 seconds.
    local lower bound updated to 0.381259
    local upper bound updated to 0.38136

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0207 seconds.
    local lower bound updated to 0.381259
    local upper bound updated to 0.381359

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0236 seconds.
    local lower bound updated to 0.38131
    local upper bound updated to 0.381349

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.015 seconds.
    local lower bound updated to 0.381349
    local upper bound updated to 0.381349
The Primal step takes 574.049 (S)
lower bound updated to 0.381349

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.40427
    local lower bound updated to 0.381349

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.38538
    local lower bound updated to 0.381594

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.385377
    local lower bound updated to 0.381602

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.381602
    local lower bound updated to 0.381602
The Dual step takes 21.2949 (S)
upper bound updated to 0.381602
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 28.1931 seconds.
    local lower bound updated to 0.339771
    local upper bound updated to 0.381596

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0226 seconds.
    local lower bound updated to 0.38089
    local upper bound updated to 0.381591

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0253 seconds.
    local lower bound updated to 0.381097
    local upper bound updated to 0.381477

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0184 seconds.
    local lower bound updated to 0.381353
    local upper bound updated to 0.381468

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0167 seconds.
    local lower bound updated to 0.381413
    local upper bound updated to 0.381467

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0219 seconds.
    local lower bound updated to 0.381435
    local upper bound updated to 0.381465

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0222 seconds.
    local lower bound updated to 0.381465
    local upper bound updated to 0.381465
The Primal step takes 388.371 (S)
lower bound updated to 0.381465

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.395859
    local lower bound updated to 0.381465

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.382158
    local lower bound updated to 0.381476

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.381476
    local lower bound updated to 0.381476
The Dual step takes 22.8829 (S)
upper bound updated to 0.381476
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 24.9246 seconds.
    local lower bound updated to 0.34068
    local upper bound updated to 0.381476

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0228 seconds.
    local lower bound updated to 0.381425
    local upper bound updated to 0.38147

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0169 seconds.
    local lower bound updated to 0.38147
    local upper bound updated to 0.38147
The Primal step takes 144.988 (S)
lower bound updated to 0.38147

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.391909
    local lower bound updated to 0.38147

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.38147
    local lower bound updated to 0.38147
The Dual step takes 13.7424 (S)
upper bound updated to 0.38147
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 23.9368 seconds.
    local lower bound updated to 0.34068
    local upper bound updated to 0.38147

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0221 seconds.
    local lower bound updated to 0.38147
    local upper bound updated to 0.38147
The time obtain the optimal randomized assortment is 1526.58 (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_60.000000_62118.log"
The computation time limit for a lower bound is 84468
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 2992 rows, 2286 columns and 9845 nonzeros
Model fingerprint: 0x588d79ae
Variable types: 2221 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [4e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 704 rows and 1248 columns
Presolve time: 0.03s
Presolved: 2288 rows, 1038 columns, 8840 nonzeros
Variable types: 974 continuous, 64 integer (64 binary)
Found heuristic solution: objective 0.6069026
Found heuristic solution: objective 0.5134609

Root relaxation: objective 1.495501e-01, 285 iterations, 0.01 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.14955    0   23    0.51346    0.14955  70.9%     -    0s
H    0     0                       0.4728614    0.14955  68.4%     -    0s
H    0     0                       0.4612555    0.14955  67.6%     -    0s
H    0     0                       0.4584166    0.16541  63.9%     -    0s
     0     0    0.16541    0   31    0.45842    0.16541  63.9%     -    0s
     0     0    0.16541    0   31    0.45842    0.16541  63.9%     -    0s
H    0     0                       0.4481147    0.22505  49.8%     -    0s
     0     0    0.22505    0   34    0.44811    0.22505  49.8%     -    0s
     0     0    0.22507    0   33    0.44811    0.22507  49.8%     -    0s
H    0     0                       0.4471223    0.24167  46.0%     -    0s
     0     0    0.24167    0   32    0.44712    0.24167  46.0%     -    0s
H    0     0                       0.4311268    0.24274  43.7%     -    0s
     0     0    0.24274    0   31    0.43113    0.24274  43.7%     -    0s
H    0     0                       0.4249590    0.24274  42.9%     -    0s
     0     0    0.25299    0   33    0.42496    0.25299  40.5%     -    0s
     0     0    0.25336    0   33    0.42496    0.25336  40.4%     -    0s
     0     0    0.25628    0   32    0.42496    0.25628  39.7%     -    0s
H    0     0                       0.4075383    0.25628  37.1%     -    0s
H    0     0                       0.3814696    0.25628  32.8%     -    3s
     0     2    0.25628    0   32    0.38147    0.25628  32.8%     -    3s
   324   210    0.34354    8   28    0.38147    0.28749  24.6%  38.7    5s
H  328   210                       0.3814696    0.28749  24.6%  38.4    5s
  1899   624     cutoff   12         0.38147    0.32110  15.8%  34.7   10s
  2696   753     cutoff   11         0.38147    0.32600  14.5%  34.3   15s
  4286   944    0.33724   10   32    0.38147    0.33324  12.6%  32.3   20s
H 4677   930                       0.3814696    0.33324  12.6%  34.2   22s
  5090   932    0.37860   30   10    0.38147    0.33324  12.6%  34.2   25s
  5681   855    0.35278   24   22    0.38147    0.33324  12.6%  34.6   30s
  6679   634    0.37103   22   24    0.38147    0.33535  12.1%  35.0   36s
  7660   556    0.35107   27   14    0.38147    0.34085  10.6%  34.8   41s
  8244   555    0.37826   26   12    0.38147    0.34324  10.0%  34.7   45s
  8861   554     cutoff   28         0.38147    0.34503  9.55%  34.6   51s
 10233   530     cutoff   25         0.38147    0.35003  8.24%  34.1   56s
 12051   428     cutoff   30         0.38147    0.35737  6.32%  33.3   60s

Cutting planes:
  Implied bound: 276
  MIR: 181
  Flow cover: 435
  RLT: 81
  Relax-and-lift: 94

Explored 14296 nodes (458141 simplex iterations) in 64.07 seconds (56.19 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.38147 0.407538 0.424959 ... 0.513461

Optimal solution found (tolerance 1.00e-04)
Best objective 3.814696006806e-01, best bound 3.814696006806e-01, gap 0.0000%
The objective bound is 0.38147 while the objective upper bound is 0.38147

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.50 (ave)

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