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 0.285795 seconds.
    local lower bound updated to 0.419479
    local upper bound updated to 0.656723

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.287936 seconds.
    local lower bound updated to 0.637674
    local upper bound updated to 0.637674
The Primal step takes 0.576878 (S)
lower bound updated to 0.637674

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.707015
    local lower bound updated to 0.699782

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.699782
    local lower bound updated to 0.699782
The Dual step takes 0.0483532 (S)
upper bound updated to 0.699782
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.7673 seconds.
    local lower bound updated to 0.510324
    local upper bound updated to 0.687377

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.329889 seconds.
    local lower bound updated to 0.623409
    local upper bound updated to 0.66051

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.617567 seconds.
    local lower bound updated to 0.652259
    local upper bound updated to 0.655395

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.828914 seconds.
    local lower bound updated to 0.653432
    local upper bound updated to 0.653504

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.05665 seconds.
    local lower bound updated to 0.653504
    local upper bound updated to 0.653504
The Primal step takes 4.61175 (S)
lower bound updated to 0.653504

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.692496
    local lower bound updated to 0.675041

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.689246
    local lower bound updated to 0.678548

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.678548
    local lower bound updated to 0.678548
The Dual step takes 0.186605 (S)
upper bound updated to 0.678548
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.40618 seconds.
    local lower bound updated to 0.569267
    local upper bound updated to 0.671637

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.491414 seconds.
    local lower bound updated to 0.629598
    local upper bound updated to 0.662324

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.30786 seconds.
    local lower bound updated to 0.657652
    local upper bound updated to 0.661063

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.3301 seconds.
    local lower bound updated to 0.657652
    local upper bound updated to 0.660634

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.61433 seconds.
    local lower bound updated to 0.660634
    local upper bound updated to 0.660634
The Primal step takes 8.16809 (S)
lower bound updated to 0.660634

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.685751
    local lower bound updated to 0.669664

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.669664
    local lower bound updated to 0.669664
The Dual step takes 0.248701 (S)
upper bound updated to 0.669664
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.52258 seconds.
    local lower bound updated to 0.592908
    local upper bound updated to 0.669664

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.69259 seconds.
    local lower bound updated to 0.664107
    local upper bound updated to 0.668872

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.87348 seconds.
    local lower bound updated to 0.666065
    local upper bound updated to 0.667956

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.04131 seconds.
    local lower bound updated to 0.667188
    local upper bound updated to 0.667756

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.28121 seconds.
    local lower bound updated to 0.667188
    local upper bound updated to 0.667669

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.07606 seconds.
    local lower bound updated to 0.667295
    local upper bound updated to 0.667615

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.47749 seconds.
    local lower bound updated to 0.667506
    local upper bound updated to 0.667561

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.6566 seconds.
    local lower bound updated to 0.667561
    local upper bound updated to 0.667561
The Primal step takes 16.6526 (S)
lower bound updated to 0.667561

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.680662
    local lower bound updated to 0.667561

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.667942
    local lower bound updated to 0.667574

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.667574
    local lower bound updated to 0.667574
The Dual step takes 0.559197 (S)
upper bound updated to 0.667574
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.69903 seconds.
    local lower bound updated to 0.599137
    local upper bound updated to 0.667574

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.82291 seconds.
    local lower bound updated to 0.66747
    local upper bound updated to 0.667571

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.17507 seconds.
    local lower bound updated to 0.667571
    local upper bound updated to 0.667571
The Primal step takes 9.71226 (S)
lower bound updated to 0.667571

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.682047
    local lower bound updated to 0.667571

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.667571
    local lower bound updated to 0.667571
The Dual step takes 0.45823 (S)
upper bound updated to 0.667571
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.76499 seconds.
    local lower bound updated to 0.599137
    local upper bound updated to 0.667571

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.18103 seconds.
    local lower bound updated to 0.667571
    local upper bound updated to 0.667571
The time obtain the optimal randomized assortment is 48.1786 (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_200.000000_202914.log"
The computation time limit for a lower bound is 85950
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 960 rows, 834 columns and 3035 nonzeros
Model fingerprint: 0xe435e628
Variable types: 785 continuous, 49 integer (49 binary)
Coefficient statistics:
  Matrix range     [5e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [6e-01, 1e+00]
Presolve removed 285 rows and 524 columns
Presolve time: 0.01s
Presolved: 675 rows, 310 columns, 2546 nonzeros
Variable types: 267 continuous, 43 integer (43 binary)
Found heuristic solution: objective 0.7595473
Found heuristic solution: objective 0.7246657

Root relaxation: objective 4.972466e-01, 106 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    0.49725    0   12    0.72467    0.49725  31.4%     -    0s
H    0     0                       0.6813993    0.49725  27.0%     -    0s
     0     0    0.51541    0   17    0.68140    0.51541  24.4%     -    0s
     0     0    0.55968    0   17    0.68140    0.55968  17.9%     -    0s
     0     0    0.56034    0   17    0.68140    0.56034  17.8%     -    0s
H    0     0                       0.6777370    0.56034  17.3%     -    0s
     0     0    0.57952    0   20    0.67774    0.57952  14.5%     -    0s
H    0     0                       0.6769163    0.58010  14.3%     -    0s
     0     0    0.58010    0   20    0.67692    0.58010  14.3%     -    0s
H    0     0                       0.6712214    0.58010  13.6%     -    0s
     0     0    0.58420    0   22    0.67122    0.58420  13.0%     -    0s
     0     0    0.58469    0   21    0.67122    0.58469  12.9%     -    0s
     0     0    0.58772    0   21    0.67122    0.58772  12.4%     -    0s
H    0     0                       0.6703050    0.58772  12.3%     -    0s
     0     2    0.58772    0   21    0.67030    0.58772  12.3%     -    0s
*   73    51              18       0.6695792    0.59403  11.3%  15.0    1s
*   76    51              17       0.6693457    0.59403  11.3%  14.6    1s
*   82    51              17       0.6681977    0.59403  11.1%  13.8    1s
H  109    62                       0.6676986    0.61094  8.50%  14.1    1s
H  220    67                       0.6675714    0.61230  8.28%  12.9    1s

Cutting planes:
  Implied bound: 104
  MIR: 31
  Flow cover: 106
  RLT: 2
  Relax-and-lift: 55

Explored 1513 nodes (16340 simplex iterations) in 3.17 seconds (1.03 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.667571 0.667699 0.668198 ... 0.681399

Optimal solution found (tolerance 1.00e-04)
Best objective 6.675714241950e-01, best bound 6.675714241950e-01, gap 0.0000%
The objective bound is 0.667571 while the objective upper bound is 0.667571

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.40 (ave)

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