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 0.215896 seconds.
    local lower bound updated to 0.20967
    local upper bound updated to 0.413716

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.292863 seconds.
    local lower bound updated to 0.390409
    local upper bound updated to 0.390409
The Primal step takes 0.511844 (S)
lower bound updated to 0.390409

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.424761
    local lower bound updated to 0.413161

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.424761
    local lower bound updated to 0.420929

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.420929
    local lower bound updated to 0.420929
The Dual step takes 0.0798321 (S)
upper bound updated to 0.420929
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.265939 seconds.
    local lower bound updated to 0.252313
    local upper bound updated to 0.397164

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.500122 seconds.
    local lower bound updated to 0.38715
    local upper bound updated to 0.390409

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.263598 seconds.
    local lower bound updated to 0.390409
    local upper bound updated to 0.390409
The Primal step takes 1.03662 (S)
lower bound updated to 0.390409

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.416271
    local lower bound updated to 0.40304

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.408147
    local lower bound updated to 0.406862

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.408147
    local lower bound updated to 0.406862

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.408147
    local lower bound updated to 0.407664

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.407664
    local lower bound updated to 0.407664
The Dual step takes 0.529062 (S)
upper bound updated to 0.407664
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.20629 seconds.
    local lower bound updated to 0.31835
    local upper bound updated to 0.407664

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.742001 seconds.
    local lower bound updated to 0.360758
    local upper bound updated to 0.40648

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.51893 seconds.
    local lower bound updated to 0.39001
    local upper bound updated to 0.405551

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.23181 seconds.
    local lower bound updated to 0.394592
    local upper bound updated to 0.401187

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.35887 seconds.
    local lower bound updated to 0.395474
    local upper bound updated to 0.40077

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.74598 seconds.
    local lower bound updated to 0.395474
    local upper bound updated to 0.399663

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.947365 seconds.
    local lower bound updated to 0.397052
    local upper bound updated to 0.399111

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.01265 seconds.
    local lower bound updated to 0.399111
    local upper bound updated to 0.399111
The Primal step takes 9.79291 (S)
lower bound updated to 0.399111

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.420102
    local lower bound updated to 0.399111

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.415599
    local lower bound updated to 0.400491

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.406204
    local lower bound updated to 0.400715

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.401875
    local lower bound updated to 0.401168

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.401875
    local lower bound updated to 0.401197

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.401561
    local lower bound updated to 0.401241

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.401241
    local lower bound updated to 0.401241
The Dual step takes 1.87355 (S)
upper bound updated to 0.401241
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.4236 seconds.
    local lower bound updated to 0.343625
    local upper bound updated to 0.401241

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.47241 seconds.
    local lower bound updated to 0.384846
    local upper bound updated to 0.401084

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.31972 seconds.
    local lower bound updated to 0.391302
    local upper bound updated to 0.400669

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.46166 seconds.
    local lower bound updated to 0.391302
    local upper bound updated to 0.400501

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.66344 seconds.
    local lower bound updated to 0.398861
    local upper bound updated to 0.400409

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.15346 seconds.
    local lower bound updated to 0.398861
    local upper bound updated to 0.400222

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 1.82718 seconds.
    local lower bound updated to 0.400222
    local upper bound updated to 0.400222
The Primal step takes 14.3595 (S)
lower bound updated to 0.400222

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.412687
    local lower bound updated to 0.400222

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.401105
    local lower bound updated to 0.400333

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.401005
    local lower bound updated to 0.400335

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.400335
    local lower bound updated to 0.400335
The Dual step takes 0.961696 (S)
upper bound updated to 0.400335
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.59139 seconds.
    local lower bound updated to 0.344241
    local upper bound updated to 0.400335

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.45165 seconds.
    local lower bound updated to 0.39933
    local upper bound updated to 0.400291

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.92098 seconds.
    local lower bound updated to 0.400048
    local upper bound updated to 0.40025

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 3.65627 seconds.
    local lower bound updated to 0.400197
    local upper bound updated to 0.40025

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.46816 seconds.
    local lower bound updated to 0.40025
    local upper bound updated to 0.40025
The Primal step takes 17.1184 (S)
lower bound updated to 0.40025

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.41196
    local lower bound updated to 0.40025

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.406158
    local lower bound updated to 0.40025

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.40025
    local lower bound updated to 0.40025
The Dual step takes 0.874474 (S)
upper bound updated to 0.40025
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.82681 seconds.
    local lower bound updated to 0.343758
    local upper bound updated to 0.40025

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.87865 seconds.
    local lower bound updated to 0.40025
    local upper bound updated to 0.40025
The time obtain the optimal randomized assortment is 53.8569 (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_100.000000_103214.log"
The computation time limit for a lower bound is 85945
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 2094 rows, 1842 columns and 6541 nonzeros
Model fingerprint: 0xf337bda1
Variable types: 1793 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [7e-09, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 659 rows and 1227 columns
Presolve time: 0.03s
Presolved: 1435 rows, 615 columns, 5435 nonzeros
Variable types: 567 continuous, 48 integer (48 binary)
Found heuristic solution: objective 0.5043303
Found heuristic solution: objective 0.4968633
Found heuristic solution: objective 0.4946252
Found heuristic solution: objective 0.4867695

Root relaxation: objective 2.640855e-01, 223 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    0.26409    0   19    0.48677    0.26409  45.7%     -    0s
H    0     0                       0.4680710    0.26409  43.6%     -    0s
H    0     0                       0.4349110    0.26995  37.9%     -    0s
     0     0    0.27018    0   19    0.43491    0.27018  37.9%     -    0s
H    0     0                       0.4274797    0.27018  36.8%     -    0s
H    0     0                       0.4194760    0.27018  35.6%     -    0s
     0     0    0.27129    0   19    0.41948    0.27129  35.3%     -    0s
     0     0    0.31233    0   21    0.41948    0.31233  25.5%     -    0s
H    0     0                       0.4092433    0.31233  23.7%     -    0s
     0     0    0.31244    0   21    0.40924    0.31244  23.7%     -    0s
H    0     0                       0.4041892    0.32062  20.7%     -    0s
     0     0    0.32062    0   20    0.40419    0.32062  20.7%     -    0s
H    0     0                       0.4037519    0.32291  20.0%     -    0s
     0     0    0.32291    0   21    0.40375    0.32291  20.0%     -    0s
H    0     0                       0.4014088    0.32291  19.6%     -    0s
     0     0    0.33348    0   23    0.40141    0.33348  16.9%     -    0s
     0     0    0.33542    0   24    0.40141    0.33542  16.4%     -    0s
     0     0    0.34532    0   21    0.40141    0.34532  14.0%     -    0s
H    0     0                       0.4012367    0.34532  13.9%     -    1s
     0     2    0.34532    0   21    0.40124    0.34532  13.9%     -    1s
H  127    52                       0.4010733    0.35807  10.7%  26.0    1s
H  167    50                       0.4010649    0.35807  10.7%  25.7    1s
H  223    65                       0.4002500    0.35807  10.5%  25.3    1s
* 1238    75              17       0.4002500    0.39385  1.60%  20.6    2s
* 1281    47              16       0.4002500    0.39411  1.53%  20.3    2s

Cutting planes:
  Implied bound: 186
  MIR: 74
  Flow cover: 205
  RLT: 21
  Relax-and-lift: 82

Explored 1485 nodes (30297 simplex iterations) in 3.02 seconds (1.61 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.40025 0.40025 0.40025 ... 0.419476
No other solutions better than 0.40025

Optimal solution found (tolerance 1.00e-04)
Best objective 4.002499480737e-01, best bound 4.002499480737e-01, gap 0.0000%
The objective bound is 0.40025 while the objective upper bound is 0.40025

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.20 (ave)

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