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 0.366925 seconds.
    local lower bound updated to 0.230623
    local upper bound updated to 0.441854

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.447217 seconds.
    local lower bound updated to 0.440956
    local upper bound updated to 0.440956
The Primal step takes 0.816453 (S)
lower bound updated to 0.440956

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.578006
    local lower bound updated to 0.578006
The Dual step takes 0.0155226 (S)
upper bound updated to 0.578006
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.04016 seconds.
    local lower bound updated to 0.314491
    local upper bound updated to 0.474973

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.69394 seconds.
    local lower bound updated to 0.473508
    local upper bound updated to 0.47385

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.83961 seconds.
    local lower bound updated to 0.473508
    local upper bound updated to 0.47357

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.19134 seconds.
    local lower bound updated to 0.47357
    local upper bound updated to 0.47357
The Primal step takes 6.77321 (S)
lower bound updated to 0.47357

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.532093
    local lower bound updated to 0.514349

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.531497
    local lower bound updated to 0.514827

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.516913
    local lower bound updated to 0.5149

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.5149
    local lower bound updated to 0.5149
The Dual step takes 0.980305 (S)
upper bound updated to 0.5149
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 16.9074 seconds.
    local lower bound updated to 0.393981
    local upper bound updated to 0.494142

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.46065 seconds.
    local lower bound updated to 0.478007
    local upper bound updated to 0.490462

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.45774 seconds.
    local lower bound updated to 0.478007
    local upper bound updated to 0.489664

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.07329 seconds.
    local lower bound updated to 0.47952
    local upper bound updated to 0.487164

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.90634 seconds.
    local lower bound updated to 0.483064
    local upper bound updated to 0.486075

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 4.51486 seconds.
    local lower bound updated to 0.486075
    local upper bound updated to 0.486075
The Primal step takes 42.3386 (S)
lower bound updated to 0.486075

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.538044
    local lower bound updated to 0.499861

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.503431
    local lower bound updated to 0.499962

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.501858
    local lower bound updated to 0.50071

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.501858
    local lower bound updated to 0.501198

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.501198
    local lower bound updated to 0.501198
The Dual step takes 3.15477 (S)
upper bound updated to 0.501198
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 13.4595 seconds.
    local lower bound updated to 0.427352
    local upper bound updated to 0.50119

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 10.2163 seconds.
    local lower bound updated to 0.460366
    local upper bound updated to 0.500941

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.1121 seconds.
    local lower bound updated to 0.465181
    local upper bound updated to 0.495983

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 17.298 seconds.
    local lower bound updated to 0.490138
    local upper bound updated to 0.495114

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.1408 seconds.
    local lower bound updated to 0.492301
    local upper bound updated to 0.494086

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 18.8402 seconds.
    local lower bound updated to 0.492301
    local upper bound updated to 0.49399

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 14.5373 seconds.
    local lower bound updated to 0.493025
    local upper bound updated to 0.493909

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 23.4113 seconds.
    local lower bound updated to 0.493092
    local upper bound updated to 0.493774

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 15.8573 seconds.
    local lower bound updated to 0.493774
    local upper bound updated to 0.493774
The Primal step takes 143.923 (S)
lower bound updated to 0.493774

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.517579
    local lower bound updated to 0.496974

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.496974
    local lower bound updated to 0.496974
The Dual step takes 2.8094 (S)
upper bound updated to 0.496974
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.5778 seconds.
    local lower bound updated to 0.434277
    local upper bound updated to 0.496974

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 30.9608 seconds.
    local lower bound updated to 0.494815
    local upper bound updated to 0.496969

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 20.2022 seconds.
    local lower bound updated to 0.495798
    local upper bound updated to 0.496459

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 27.5338 seconds.
    local lower bound updated to 0.495798
    local upper bound updated to 0.496403

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 28.5989 seconds.
    local lower bound updated to 0.495798
    local upper bound updated to 0.496291

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 25.0322 seconds.
    local lower bound updated to 0.496094
    local upper bound updated to 0.496231

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 22.796 seconds.
    local lower bound updated to 0.496128
    local upper bound updated to 0.496197

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 28.9508 seconds.
    local lower bound updated to 0.496197
    local upper bound updated to 0.496197
The Primal step takes 201.696 (S)
lower bound updated to 0.496197

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.51314
    local lower bound updated to 0.496197

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.499279
    local lower bound updated to 0.496274

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.496274
    local lower bound updated to 0.496274
The Dual step takes 5.48043 (S)
upper bound updated to 0.496274
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 23.8896 seconds.
    local lower bound updated to 0.438761
    local upper bound updated to 0.496274

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 18.5137 seconds.
    local lower bound updated to 0.496274
    local upper bound updated to 0.496274
The Primal step takes 42.4176 (S)
lower bound updated to 0.496274

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.510821
    local lower bound updated to 0.496274

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.496274
    local lower bound updated to 0.496274
The Dual step takes 4.45034 (S)
upper bound updated to 0.496274
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 24.3936 seconds.
    local lower bound updated to 0.438761
    local upper bound updated to 0.496274

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 18.0818 seconds.
    local lower bound updated to 0.496274
    local upper bound updated to 0.496274
The time obtain the optimal randomized assortment is 497.342 (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_15_4_200.000000_203016.log"
The computation time limit for a lower bound is 85497
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 2000 rows, 1618 columns and 6368 nonzeros
Model fingerprint: 0x4e4b7c70
Variable types: 1561 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [1e-05, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 550 rows and 974 columns
Presolve time: 0.02s
Presolved: 1450 rows, 644 columns, 5482 nonzeros
Variable types: 589 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6998317
Found heuristic solution: objective 0.6764644
Found heuristic solution: objective 0.6127001

Root relaxation: objective 2.503480e-01, 177 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    0.25035    0   21    0.61270    0.25035  59.1%     -    0s
H    0     0                       0.5823265    0.25035  57.0%     -    0s
H    0     0                       0.5459659    0.25035  54.1%     -    0s
     0     0    0.27822    0   21    0.54597    0.27822  49.0%     -    0s
     0     0    0.27822    0   21    0.54597    0.27822  49.0%     -    0s
H    0     0                       0.5451086    0.32130  41.1%     -    0s
H    0     0                       0.5303497    0.32130  39.4%     -    0s
     0     0    0.32529    0   25    0.53035    0.32529  38.7%     -    0s
H    0     0                       0.5169819    0.32770  36.6%     -    0s
     0     0    0.32770    0   25    0.51698    0.32770  36.6%     -    0s
H    0     0                       0.5091718    0.35402  30.5%     -    0s
     0     0    0.35402    0   25    0.50917    0.35402  30.5%     -    0s
H    0     0                       0.5059888    0.35402  30.0%     -    0s
     0     0    0.35452    0   25    0.50599    0.35452  29.9%     -    0s
     0     0    0.36600    0   25    0.50599    0.36600  27.7%     -    0s
     0     0    0.36668    0   26    0.50599    0.36668  27.5%     -    0s
     0     0    0.36933    0   25    0.50599    0.36933  27.0%     -    0s
H    0     0                       0.4965181    0.36933  25.6%     -    1s
     0     2    0.36933    0   25    0.49652    0.36933  25.6%     -    1s
*  162   100              18       0.4962736    0.38295  22.8%  28.7    2s
H  378   160                       0.4962735    0.39696  20.0%  25.2    2s
  1485   408    0.43344    8   18    0.49627    0.42387  14.6%  21.8    5s
H 3781   584                       0.4962735    0.44353  10.6%  19.6    7s
  4686   596     cutoff   12         0.49627    0.44981  9.36%  19.2   10s
  7352   494    0.48156   13    8    0.49627    0.46397  6.51%  18.2   15s

Cutting planes:
  Gomory: 3
  Implied bound: 238
  MIR: 79
  Flow cover: 221
  RLT: 20
  Relax-and-lift: 107

Explored 10371 nodes (173895 simplex iterations) in 17.96 seconds (11.57 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.496274 0.496518 0.505989 ... 0.6127

Optimal solution found (tolerance 1.00e-04)
Best objective 4.962735464537e-01, best bound 4.962735464537e-01, gap 0.0000%
The objective bound is 0.496274 while the objective upper bound is 0.496274

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.19 (ave)

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