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 0.0634863 seconds.
    local lower bound updated to 0.235161
    local upper bound updated to 0.462434

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.062601 seconds.
    local lower bound updated to 0.46228
    local upper bound updated to 0.46228
The Primal step takes 0.128293 (S)
lower bound updated to 0.46228

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.576697
    local lower bound updated to 0.575502

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.575502
    local lower bound updated to 0.575502
The Dual step takes 0.0256753 (S)
upper bound updated to 0.575502
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.191183 seconds.
    local lower bound updated to 0.308988
    local upper bound updated to 0.468525

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.219305 seconds.
    local lower bound updated to 0.462714
    local upper bound updated to 0.462718
The Primal step takes 0.413665 (S)
lower bound updated to 0.462714

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.531369
    local lower bound updated to 0.477422

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.531369
    local lower bound updated to 0.498406

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.531369
    local lower bound updated to 0.517883

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.518296
    local lower bound updated to 0.517906

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.517906
    local lower bound updated to 0.517906
The Dual step takes 0.238537 (S)
upper bound updated to 0.517906
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.635487 seconds.
    local lower bound updated to 0.394029
    local upper bound updated to 0.478048

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.43 seconds.
    local lower bound updated to 0.425861
    local upper bound updated to 0.472808

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.6669 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.472172

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.636284 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.471604

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 0.874769 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.47033

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 0.720553 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.469491

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.927933 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.469482

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.09675 seconds.
    local lower bound updated to 0.469068
    local upper bound updated to 0.469479

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 0.928167 seconds.
    local lower bound updated to 0.469163
    local upper bound updated to 0.469473

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 0.935629 seconds.
    local lower bound updated to 0.469473
    local upper bound updated to 0.469473
The Primal step takes 7.88241 (S)
lower bound updated to 0.469473

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.511364
    local lower bound updated to 0.490924

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.497336
    local lower bound updated to 0.491536

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.494381
    local lower bound updated to 0.491706

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.491706
    local lower bound updated to 0.491706
The Dual step takes 0.778569 (S)
upper bound updated to 0.491706
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.23229 seconds.
    local lower bound updated to 0.418019
    local upper bound updated to 0.477497

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.780461 seconds.
    local lower bound updated to 0.437732
    local upper bound updated to 0.476382

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.814485 seconds.
    local lower bound updated to 0.465042
    local upper bound updated to 0.475071

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.11159 seconds.
    local lower bound updated to 0.465042
    local upper bound updated to 0.474602

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.2069 seconds.
    local lower bound updated to 0.466836
    local upper bound updated to 0.47349

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.09975 seconds.
    local lower bound updated to 0.470242
    local upper bound updated to 0.472876

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 0.800029 seconds.
    local lower bound updated to 0.470242
    local upper bound updated to 0.472167

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.91433 seconds.
    local lower bound updated to 0.470242
    local upper bound updated to 0.471974

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 1.35179 seconds.
    local lower bound updated to 0.470985
    local upper bound updated to 0.471905

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 1.32704 seconds.
    local lower bound updated to 0.471189
    local upper bound updated to 0.471769

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 2.27272 seconds.
    local lower bound updated to 0.471189
    local upper bound updated to 0.471609

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 1.38403 seconds.
    local lower bound updated to 0.471189
    local upper bound updated to 0.471497

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 1.54748 seconds.
    local lower bound updated to 0.471189
    local upper bound updated to 0.471436

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 1.41345 seconds.
    local lower bound updated to 0.471189
    local upper bound updated to 0.471409

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 1.85119 seconds.
    local lower bound updated to 0.47132
    local upper bound updated to 0.471401

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 1.18502 seconds.
    local lower bound updated to 0.471401
    local upper bound updated to 0.471401
The Primal step takes 21.3597 (S)
lower bound updated to 0.471401

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.493128
    local lower bound updated to 0.475799

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.493128
    local lower bound updated to 0.484388

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.491149
    local lower bound updated to 0.48523

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.487811
    local lower bound updated to 0.485516

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.485516
    local lower bound updated to 0.485516
The Dual step takes 5.78755 (S)
upper bound updated to 0.485516
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.88261 seconds.
    local lower bound updated to 0.440302
    local upper bound updated to 0.485516

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.45768 seconds.
    local lower bound updated to 0.463964
    local upper bound updated to 0.481682

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.37114 seconds.
    local lower bound updated to 0.4722
    local upper bound updated to 0.4814

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 7.31326 seconds.
    local lower bound updated to 0.476526
    local upper bound updated to 0.48102

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.3929 seconds.
    local lower bound updated to 0.476526
    local upper bound updated to 0.48013

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.93694 seconds.
    local lower bound updated to 0.476526
    local upper bound updated to 0.479839

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 8.75516 seconds.
    local lower bound updated to 0.476526
    local upper bound updated to 0.47971

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 12.65 seconds.
    local lower bound updated to 0.477334
    local upper bound updated to 0.479381

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 7.85711 seconds.
    local lower bound updated to 0.477334
    local upper bound updated to 0.479083

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 5.49034 seconds.
    local lower bound updated to 0.478433
    local upper bound updated to 0.478946

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 7.48659 seconds.
    local lower bound updated to 0.478433
    local upper bound updated to 0.478899

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 7.69227 seconds.
    local lower bound updated to 0.478791
    local upper bound updated to 0.478898

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 5.75182 seconds.
    local lower bound updated to 0.478791
    local upper bound updated to 0.478895

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 6.22897 seconds.
    local lower bound updated to 0.478807
    local upper bound updated to 0.478893

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 7.64306 seconds.
    local lower bound updated to 0.478807
    local upper bound updated to 0.478881

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 9.3732 seconds.
    local lower bound updated to 0.478881
    local upper bound updated to 0.478881
The Primal step takes 100.376 (S)
lower bound updated to 0.478881

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.488861
    local lower bound updated to 0.478881

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.486084
    local lower bound updated to 0.479097

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.485746
    local lower bound updated to 0.479568

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.481427
    local lower bound updated to 0.479728

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.48007
    local lower bound updated to 0.479761

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.48007
    local lower bound updated to 0.479761

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.479761
    local lower bound updated to 0.479761
The Dual step takes 15.1913 (S)
upper bound updated to 0.479761
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.29904 seconds.
    local lower bound updated to 0.446289
    local upper bound updated to 0.479761

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.358 seconds.
    local lower bound updated to 0.473687
    local upper bound updated to 0.479574

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.8965 seconds.
    local lower bound updated to 0.478327
    local upper bound updated to 0.479509

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.9614 seconds.
    local lower bound updated to 0.478714
    local upper bound updated to 0.479501

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 11.3176 seconds.
    local lower bound updated to 0.478714
    local upper bound updated to 0.479446

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 10.6716 seconds.
    local lower bound updated to 0.478957
    local upper bound updated to 0.479443

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 12.9203 seconds.
    local lower bound updated to 0.478979
    local upper bound updated to 0.479426

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 19.8554 seconds.
    local lower bound updated to 0.479195
    local upper bound updated to 0.479421

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 12.2663 seconds.
    local lower bound updated to 0.479195
    local upper bound updated to 0.479415

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 11.6625 seconds.
    local lower bound updated to 0.479195
    local upper bound updated to 0.47941

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 12.8273 seconds.
    local lower bound updated to 0.479217
    local upper bound updated to 0.479407

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 10.5426 seconds.
    local lower bound updated to 0.479314
    local upper bound updated to 0.479405

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 10.4304 seconds.
    local lower bound updated to 0.479314
    local upper bound updated to 0.479402

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 14.2655 seconds.
    local lower bound updated to 0.479314
    local upper bound updated to 0.479401

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 9.93135 seconds.
    local lower bound updated to 0.479401
    local upper bound updated to 0.479401
The Primal step takes 181.327 (S)
lower bound updated to 0.479401

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.488761
    local lower bound updated to 0.479401

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.47943
    local lower bound updated to 0.479402

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.479402
    local lower bound updated to 0.479402
The Dual step takes 13.373 (S)
upper bound updated to 0.479402
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.03645 seconds.
    local lower bound updated to 0.446959
    local upper bound updated to 0.479402

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 10.3218 seconds.
    local lower bound updated to 0.479395
    local upper bound updated to 0.479402
The time obtain the optimal randomized assortment is 362.256 (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_60.000000_63016.log"
The computation time limit for a lower bound is 85636
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 3280 rows, 2658 columns and 10441 nonzeros
Model fingerprint: 0x827c5101
Variable types: 2601 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [8e-04, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 987 rows and 1671 columns
Presolve time: 0.03s
Presolved: 2293 rows, 987 columns, 8797 nonzeros
Variable types: 934 continuous, 53 integer (53 binary)
Found heuristic solution: objective 0.5701949
Found heuristic solution: objective 0.5495942

Root relaxation: objective 3.372881e-01, 232 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    0.33729    0   18    0.54959    0.33729  38.6%     -    0s
H    0     0                       0.5077710    0.33729  33.6%     -    0s
     0     0    0.36537    0   23    0.50777    0.36537  28.0%     -    0s
H    0     0                       0.4869680    0.36537  25.0%     -    0s
     0     0    0.40873    0   25    0.48697    0.40873  16.1%     -    0s
     0     0    0.40898    0   25    0.48697    0.40898  16.0%     -    0s
     0     0    0.42260    0   25    0.48697    0.42260  13.2%     -    0s
H    0     0                       0.4795604    0.42260  11.9%     -    0s
     0     0    0.42366    0   24    0.47956    0.42366  11.7%     -    0s
     0     0    0.42746    0   24    0.47956    0.42746  10.9%     -    0s
     0     0    0.42809    0   22    0.47956    0.42809  10.7%     -    0s
     0     0    0.42852    0   20    0.47956    0.42852  10.6%     -    0s
H    0     0                       0.4794019    0.42852  10.6%     -    1s
     0     2    0.42852    0   20    0.47940    0.42852  10.6%     -    1s
H  205    97                       0.4794019    0.44203  7.80%  35.1    3s
H  248   115                       0.4794019    0.44373  7.44%  33.2    3s
H  294   128                       0.4794019    0.44643  6.88%  31.6    3s
H  303   128                       0.4794019    0.44643  6.88%  31.9    3s
H  398   145                       0.4794019    0.44731  6.69%  30.5    3s
  1092   304    0.45862   13    9    0.47940    0.45533  5.02%  28.3    5s
  3357   453     cutoff   11         0.47940    0.46498  3.01%  24.6   10s

Cutting planes:
  Gomory: 1
  Implied bound: 353
  MIR: 104
  Flow cover: 340
  RLT: 24
  Relax-and-lift: 156

Explored 5445 nodes (122009 simplex iterations) in 13.93 seconds (11.45 work units)
Thread count was 4 (of 48 available processors)

Solution count 6: 0.479402 0.47956 0.486968 ... 0.570195

Optimal solution found (tolerance 1.00e-04)
Best objective 4.794019290391e-01, best bound 4.794019290391e-01, gap 0.0000%
The objective bound is 0.479402 while the objective upper bound is 0.479402

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   2.67 (ave)

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