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 5.98551 seconds.
    local lower bound updated to 0.27883
    local upper bound updated to 0.54

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.49327 seconds.
    local lower bound updated to 0.496981
    local upper bound updated to 0.496981
The Primal step takes 7.4815 (S)
lower bound updated to 0.496981

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.566933
    local lower bound updated to 0.552487

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.553467
    local lower bound updated to 0.553467
The Dual step takes 0.194956 (S)
upper bound updated to 0.553467
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.407859
    local upper bound updated to 0.537741

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 25.3672 seconds.
    local lower bound updated to 0.493068
    local upper bound updated to 0.524144

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 10.7522 seconds.
    local lower bound updated to 0.503381
    local upper bound updated to 0.51357

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 30.3185 seconds.
    local lower bound updated to 0.508691
    local upper bound updated to 0.511713

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 15.638 seconds.
    local lower bound updated to 0.508691
    local upper bound updated to 0.509966

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 23.6124 seconds.
    local lower bound updated to 0.509966
    local upper bound updated to 0.509966
The Primal step takes 305.751 (S)
lower bound updated to 0.509966

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.55469
    local lower bound updated to 0.536489

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.547665
    local lower bound updated to 0.536896

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.543201
    local lower bound updated to 0.53896

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.539071
    local lower bound updated to 0.538985

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.538985
    local lower bound updated to 0.538985
The Dual step takes 5.45336 (S)
upper bound updated to 0.538985
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.048 seconds.
    local lower bound updated to 0.462191
    local upper bound updated to 0.530107

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 54.6163 seconds.
    local lower bound updated to 0.517199
    local upper bound updated to 0.526482

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 59.8519 seconds.
    local lower bound updated to 0.522496
    local upper bound updated to 0.524518

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 76.2108 seconds.
    local lower bound updated to 0.522496
    local upper bound updated to 0.523866

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 80.6784 seconds.
    local lower bound updated to 0.522496
    local upper bound updated to 0.523419

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 86.9746 seconds.
    local lower bound updated to 0.522496
    local upper bound updated to 0.523044

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 70.0218 seconds.
    local lower bound updated to 0.523037
    local upper bound updated to 0.523043
The Primal step takes 628.446 (S)
lower bound updated to 0.523037

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.543886
    local lower bound updated to 0.529315

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.532221
    local lower bound updated to 0.529639

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.5305
    local lower bound updated to 0.529758

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.530401
    local lower bound updated to 0.529758

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.529758
    local lower bound updated to 0.529758
The Dual step takes 13.3254 (S)
upper bound updated to 0.529758
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.051 seconds.
    local lower bound updated to 0.470503
    local upper bound updated to 0.529642

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.045 seconds.
    local lower bound updated to 0.528398
    local upper bound updated to 0.529406

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.038 seconds.
    local lower bound updated to 0.528974
    local upper bound updated to 0.529225

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.529225
    local upper bound updated to 0.529225
The Primal step takes 800.202 (S)
lower bound updated to 0.529225

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.539996
    local lower bound updated to 0.529377

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.529377
    local lower bound updated to 0.529377
The Dual step takes 7.15214 (S)
upper bound updated to 0.529377
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.057 seconds.
    local lower bound updated to 0.476609
    local upper bound updated to 0.529377

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.529058
    local upper bound updated to 0.529314

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.042 seconds.
    local lower bound updated to 0.529058
    local upper bound updated to 0.529312

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.046 seconds.
    local lower bound updated to 0.529141
    local upper bound updated to 0.529312

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.529247
    local upper bound updated to 0.529312

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.529312
    local upper bound updated to 0.529312
The Primal step takes 1200.32 (S)
lower bound updated to 0.529312

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.541034
    local lower bound updated to 0.529312

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.531036
    local lower bound updated to 0.529312

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.529312
    local lower bound updated to 0.529312
The Dual step takes 13.8801 (S)
upper bound updated to 0.529312
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.045 seconds.
    local lower bound updated to 0.471618
    local upper bound updated to 0.529312

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.529312
    local upper bound updated to 0.529312
The time obtain the optimal randomized assortment is 3382.31 (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_17_4_200.000000_202918.log"
The computation time limit for a lower bound is 82607
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 2798 rows, 2138 columns and 9185 nonzeros
Model fingerprint: 0x2b3fc6c0
Variable types: 2073 continuous, 65 integer (65 binary)
Coefficient statistics:
  Matrix range     [5e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 643 rows and 1183 columns
Presolve time: 0.04s
Presolved: 2155 rows, 955 columns, 8459 nonzeros
Variable types: 892 continuous, 63 integer (63 binary)
Found heuristic solution: objective 0.6465359
Found heuristic solution: objective 0.5929491

Root relaxation: objective 3.847606e-01, 270 iterations, 0.01 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0    0.38476    0   20    0.59295    0.38476  35.1%     -    0s
H    0     0                       0.5783579    0.38476  33.5%     -    0s
     0     0    0.38493    0   23    0.57836    0.38493  33.4%     -    0s
H    0     0                       0.5707809    0.38493  32.6%     -    0s
H    0     0                       0.5631104    0.42661  24.2%     -    0s
     0     0    0.42661    0   26    0.56311    0.42661  24.2%     -    0s
H    0     0                       0.5627252    0.42661  24.2%     -    0s
     0     0    0.42661    0   26    0.56273    0.42661  24.2%     -    0s
     0     0    0.43039    0   28    0.56273    0.43039  23.5%     -    0s
     0     0    0.43111    0   29    0.56273    0.43111  23.4%     -    0s
H    0     0                       0.5423407    0.43111  20.5%     -    0s
H    0     0                       0.5375155    0.43111  19.8%     -    0s
     0     0    0.44257    0   31    0.53752    0.44257  17.7%     -    0s
H    0     0                       0.5369917    0.44299  17.5%     -    0s
H    0     0                       0.5367175    0.44299  17.5%     -    0s
     0     0    0.44299    0   31    0.53672    0.44299  17.5%     -    0s
     0     0    0.44515    0   31    0.53672    0.44515  17.1%     -    1s
H    0     0                       0.5293121    0.44515  15.9%     -    3s
     0     2    0.44515    0   31    0.52931    0.44515  15.9%     -    3s
   314   192    0.51959   13   10    0.52931    0.45564  13.9%  29.3    5s
   886   453    0.48512   12   17    0.52931    0.46896  11.4%  29.2   11s
  1299   610    0.49218   11   19    0.52931    0.47137  10.9%  28.4   15s
  2169   866    0.51032   16   31    0.52931    0.47527  10.2%  26.2   20s
  2200   892    0.47527   17   30    0.52931    0.47527  10.2%  27.9   27s
  2617   982     cutoff   29         0.52931    0.47527  10.2%  29.0   30s
  3192  1000    0.52638   28   10    0.52931    0.47527  10.2%  30.0   36s
  3680   935     cutoff   32         0.52931    0.47759  9.77%  30.3   41s
  4554   907    0.48940   26   18    0.52931    0.48238  8.87%  30.7   46s
  5482   988    0.49751   21   19    0.52931    0.48505  8.36%  30.7   51s
  5776  1067    0.50768   31   22    0.52931    0.48621  8.14%  30.8   55s
  6887  1254    0.49701   25   19    0.52931    0.48826  7.76%  31.1   60s
  7119  1327     cutoff   28         0.52931    0.48858  7.70%  31.0   65s
  7776  1453    0.52565   24   14    0.52931    0.48992  7.44%  31.0   71s
  8417  1602    0.50762   26   16    0.52931    0.49074  7.29%  31.0   75s
  9837  1789    0.52756   36    4    0.52931    0.49293  6.87%  30.8   81s
 10960  1934    0.51286   29   18    0.52931    0.49447  6.58%  30.7   86s
 11757  2002    0.51768   25   15    0.52931    0.49514  6.46%  30.7   91s
 12244  2100    0.51695   31   16    0.52931    0.49576  6.34%  30.6   95s
 13190  2188    0.52425   30   12    0.52931    0.49668  6.17%  30.6  101s
 14301  2302    0.52353   31   10    0.52931    0.49734  6.04%  30.7  106s
 15375  2359    0.51875   30   10    0.52931    0.49836  5.85%  30.5  111s
 16602  2445    0.51995   28   12    0.52931    0.49931  5.67%  30.4  116s
 17986  2512     cutoff   28         0.52931    0.50044  5.45%  30.3  121s
 19083  2570    0.52831   32    8    0.52931    0.50110  5.33%  30.2  125s
 20532  2639    0.51903   31   16    0.52931    0.50188  5.18%  30.1  131s
 21993  2651     cutoff   32         0.52931    0.50314  4.94%  30.0  137s
 22382  2668    0.51301   29   17    0.52931    0.50330  4.91%  30.0  140s
 23705  2701 infeasible   29         0.52931    0.50407  4.77%  29.9  147s
 24256  2684    0.52642   31   16    0.52931    0.50437  4.71%  29.9  150s
 25542  2679    0.51708   29   15    0.52931    0.50509  4.58%  29.8  155s
 26432  2678     cutoff   28         0.52931    0.50562  4.48%  29.7  160s
H27001  2677                       0.5293121    0.50595  4.41%  29.7  163s
 27247  2672    0.52651   27   12    0.52931    0.50599  4.41%  29.6  165s
 27681  2670     cutoff   34         0.52931    0.50633  4.34%  29.6  171s
 28482  2655 infeasible   29         0.52931    0.50655  4.30%  29.6  176s
 29701  2579    0.51329   29   14    0.52931    0.50724  4.17%  29.6  182s
 30351  2550    0.52695   28   14    0.52931    0.50766  4.09%  29.5  185s
 31747  2494    0.52164   26   19    0.52931    0.50841  3.95%  29.4  192s
 32187  2463    0.52386   29   12    0.52931    0.50865  3.90%  29.4  195s
 33533  2353     cutoff   29         0.52931    0.50937  3.77%  29.3  204s
 34245  2310    0.52079   30   16    0.52931    0.50967  3.71%  29.3  206s
 35859  2166     cutoff   31         0.52931    0.51042  3.57%  29.2  213s
 36246  2081    0.51672   31   15    0.52931    0.51086  3.49%  29.2  216s
 37440  1936     cutoff   29         0.52931    0.51148  3.37%  29.2  222s
 38288  1906    0.52156   29   18    0.52931    0.51219  3.24%  29.1  225s
 39051  1801 infeasible   33         0.52931    0.51268  3.14%  29.0  230s
 40366  1534    0.52072   32   18    0.52931    0.51353  2.98%  28.9  237s
 41196  1463    0.52393   34   11    0.52931    0.51397  2.90%  28.9  240s
 42246  1236    0.52467   31   10    0.52931    0.51466  2.77%  28.8  246s
 43769   803     cutoff   28         0.52931    0.51823  2.09%  28.7  251s
 45024   439 infeasible   30         0.52931    0.52061  1.64%  28.5  255s
H45600   175                       0.5293121    0.52264  1.26%  28.5  258s
 46080    39     cutoff   31         0.52931    0.52444  0.92%  28.4  260s

Cutting planes:
  Implied bound: 251
  MIR: 119
  Flow cover: 469
  RLT: 91
  Relax-and-lift: 79
  BQP: 1

Explored 46311 nodes (1312391 simplex iterations) in 260.67 seconds (161.15 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.529312 0.529312 0.536718 ... 0.578358

Optimal solution found (tolerance 1.00e-04)
Best objective 5.293121485118e-01, best bound 5.293121485118e-01, gap 0.0000%
The objective bound is 0.529312 while the objective upper bound is 0.529312

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.71 (ave)

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