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 1.00106 seconds.
    local lower bound updated to 0.288767
    local upper bound updated to 0.523066

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.205493 seconds.
    local lower bound updated to 0.506574
    local upper bound updated to 0.506574
The Primal step takes 1.2091 (S)
lower bound updated to 0.506574

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.593506
    local lower bound updated to 0.583921

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.583921
    local lower bound updated to 0.583921
The Dual step takes 0.0563698 (S)
upper bound updated to 0.583921
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.784117 seconds.
    local lower bound updated to 0.36076
    local upper bound updated to 0.52496

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.796441 seconds.
    local lower bound updated to 0.520649
    local upper bound updated to 0.522979

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.24245 seconds.
    local lower bound updated to 0.522979
    local upper bound updated to 0.522979
The Primal step takes 2.82811 (S)
lower bound updated to 0.522979

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.564503
    local lower bound updated to 0.535887

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.562753
    local lower bound updated to 0.549264

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.554298
    local lower bound updated to 0.550545

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.551502
    local lower bound updated to 0.550827

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.550827
    local lower bound updated to 0.550827
The Dual step takes 0.691419 (S)
upper bound updated to 0.550827
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.5321 seconds.
    local lower bound updated to 0.450961
    local upper bound updated to 0.536596

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.03603 seconds.
    local lower bound updated to 0.522347
    local upper bound updated to 0.534468

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.68369 seconds.
    local lower bound updated to 0.522347
    local upper bound updated to 0.534427

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.55699 seconds.
    local lower bound updated to 0.524498
    local upper bound updated to 0.527485

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 5.51388 seconds.
    local lower bound updated to 0.524498
    local upper bound updated to 0.52747

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 5.64237 seconds.
    local lower bound updated to 0.524856
    local upper bound updated to 0.526975

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 6.44111 seconds.
    local lower bound updated to 0.525025
    local upper bound updated to 0.52694

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.26528 seconds.
    local lower bound updated to 0.526536
    local upper bound updated to 0.526924

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 11.2604 seconds.
    local lower bound updated to 0.526642
    local upper bound updated to 0.52692

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 9.40564 seconds.
    local lower bound updated to 0.526677
    local upper bound updated to 0.526737

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 10.502 seconds.
    local lower bound updated to 0.526737
    local upper bound updated to 0.526737
The Primal step takes 69.879 (S)
lower bound updated to 0.526737

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.554916
    local lower bound updated to 0.528246

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.539059
    local lower bound updated to 0.529701

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.535829
    local lower bound updated to 0.531558

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.531558
    local lower bound updated to 0.531558
The Dual step takes 1.93508 (S)
upper bound updated to 0.531558
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.71237 seconds.
    local lower bound updated to 0.467223
    local upper bound updated to 0.531151

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 9.11388 seconds.
    local lower bound updated to 0.522668
    local upper bound updated to 0.530496

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 14.9939 seconds.
    local lower bound updated to 0.527368
    local upper bound updated to 0.529767

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 17.0735 seconds.
    local lower bound updated to 0.528513
    local upper bound updated to 0.529631

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 16.7561 seconds.
    local lower bound updated to 0.529194
    local upper bound updated to 0.529568

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 9.93177 seconds.
    local lower bound updated to 0.529247
    local upper bound updated to 0.529556

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 17.5425 seconds.
    local lower bound updated to 0.529445
    local upper bound updated to 0.52954

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 16.0588 seconds.
    local lower bound updated to 0.529452
    local upper bound updated to 0.529534

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 16.2033 seconds.
    local lower bound updated to 0.529459
    local upper bound updated to 0.529525

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 14.7703 seconds.
    local lower bound updated to 0.529525
    local upper bound updated to 0.529525
The Primal step takes 136.207 (S)
lower bound updated to 0.529525

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.542632
    local lower bound updated to 0.529561

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529561
    local lower bound updated to 0.529561
The Dual step takes 4.38854 (S)
upper bound updated to 0.529561
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.45081 seconds.
    local lower bound updated to 0.47232
    local upper bound updated to 0.529555

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 20.9364 seconds.
    local lower bound updated to 0.529504
    local upper bound updated to 0.529548

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 22.5165 seconds.
    local lower bound updated to 0.529548
    local upper bound updated to 0.529548
The Primal step takes 46.9217 (S)
lower bound updated to 0.529548

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.540784
    local lower bound updated to 0.529548

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529548
    local lower bound updated to 0.529548
The Dual step takes 6.00387 (S)
upper bound updated to 0.529548
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.39187 seconds.
    local lower bound updated to 0.47232
    local upper bound updated to 0.529548

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 23.6809 seconds.
    local lower bound updated to 0.529548
    local upper bound updated to 0.529548
The time obtain the optimal randomized assortment is 297.207 (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_209016.log"
The computation time limit for a lower bound is 85700
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 1840 rows, 1488 columns and 5971 nonzeros
Model fingerprint: 0x5b934917
Variable types: 1431 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [3e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 474 rows and 874 columns
Presolve time: 0.02s
Presolved: 1366 rows, 614 columns, 5335 nonzeros
Variable types: 560 continuous, 54 integer (54 binary)
Found heuristic solution: objective 0.7310044
Found heuristic solution: objective 0.7041160
Found heuristic solution: objective 0.6633162

Root relaxation: objective 3.842462e-01, 189 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    0.38425    0   18    0.66332    0.38425  42.1%     -    0s
H    0     0                       0.5822260    0.38425  34.0%     -    0s
H    0     0                       0.5768942    0.38425  33.4%     -    0s
     0     0    0.38820    0   24    0.57689    0.38820  32.7%     -    0s
H    0     0                       0.5683218    0.38820  31.7%     -    0s
     0     0    0.38820    0   24    0.56832    0.38820  31.7%     -    0s
H    0     0                       0.5569164    0.38820  30.3%     -    0s
H    0     0                       0.5355334    0.43015  19.7%     -    0s
     0     0    0.43015    0   26    0.53553    0.43015  19.7%     -    0s
     0     0    0.43072    0   25    0.53553    0.43072  19.6%     -    0s
     0     0    0.44584    0   25    0.53553    0.44584  16.7%     -    0s
H    0     0                       0.5335743    0.44710  16.2%     -    0s
     0     0    0.44710    0   27    0.53357    0.44710  16.2%     -    0s
     0     0    0.45105    0   26    0.53357    0.45105  15.5%     -    0s
     0     0    0.45172    0   26    0.53357    0.45172  15.3%     -    0s
     0     0    0.45310    0   26    0.53357    0.45310  15.1%     -    0s
H    0     0                       0.5295480    0.45310  14.4%     -    1s
     0     2    0.45310    0   26    0.52955    0.45310  14.4%     -    1s
   699   265    0.49045    9   12    0.52955    0.48143  9.09%  18.0    5s
  2455   516     cutoff   14         0.52955    0.49378  6.76%  15.8   10s
  4643   627    0.51936   16    8    0.52955    0.50242  5.12%  15.3   15s
H 5500   614                       0.5295480    0.50506  4.62%  15.1   17s
  6566   566     cutoff   12         0.52955    0.50904  3.87%  14.8   20s

Cutting planes:
  Gomory: 1
  Implied bound: 227
  MIR: 89
  Flow cover: 180
  RLT: 29
  Relax-and-lift: 101

Explored 9006 nodes (129213 simplex iterations) in 24.43 seconds (16.31 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.529548 0.529548 0.533574 ... 0.704116

Optimal solution found (tolerance 1.00e-04)
Best objective 5.295479896720e-01, best bound 5.295479896720e-01, gap 0.0000%
The objective bound is 0.529548 while the objective upper bound is 0.529548

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.35 (ave)

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