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 1.73338 seconds.
    local lower bound updated to 0.239707
    local upper bound updated to 0.476979

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.15752 seconds.
    local lower bound updated to 0.465897
    local upper bound updated to 0.465897
The Primal step takes 2.89435 (S)
lower bound updated to 0.465897

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.523873
    local lower bound updated to 0.512753

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.518456
    local lower bound updated to 0.518377

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.518377
    local lower bound updated to 0.518377
The Dual step takes 0.155006 (S)
upper bound updated to 0.518377
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.3012 seconds.
    local lower bound updated to 0.332611
    local upper bound updated to 0.485001

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 13.0271 seconds.
    local lower bound updated to 0.452089
    local upper bound updated to 0.474432

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 12.1052 seconds.
    local lower bound updated to 0.463542
    local upper bound updated to 0.473899

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 14.9116 seconds.
    local lower bound updated to 0.466375
    local upper bound updated to 0.469256

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.62965 seconds.
    local lower bound updated to 0.466773
    local upper bound updated to 0.46768

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 11.6105 seconds.
    local lower bound updated to 0.467031
    local upper bound updated to 0.467117

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 16.884 seconds.
    local lower bound updated to 0.467117
    local upper bound updated to 0.467117
The Primal step takes 82.491 (S)
lower bound updated to 0.467117

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.500242
    local lower bound updated to 0.478912

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.491807
    local lower bound updated to 0.481641

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.489151
    local lower bound updated to 0.48342

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.48342
    local lower bound updated to 0.48342
The Dual step takes 1.62863 (S)
upper bound updated to 0.48342
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 29.1492 seconds.
    local lower bound updated to 0.38248
    local upper bound updated to 0.474496

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 19.8869 seconds.
    local lower bound updated to 0.468357
    local upper bound updated to 0.473361

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 39.3297 seconds.
    local lower bound updated to 0.470412
    local upper bound updated to 0.472073

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 26.5927 seconds.
    local lower bound updated to 0.471024
    local upper bound updated to 0.471883

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 29.0244 seconds.
    local lower bound updated to 0.471024
    local upper bound updated to 0.471646

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 34.4097 seconds.
    local lower bound updated to 0.471024
    local upper bound updated to 0.471509

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 36.622 seconds.
    local lower bound updated to 0.471249
    local upper bound updated to 0.471471

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 29.7754 seconds.
    local lower bound updated to 0.471249
    local upper bound updated to 0.471399

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 34.3628 seconds.
    local lower bound updated to 0.471399
    local upper bound updated to 0.471399
The Primal step takes 279.193 (S)
lower bound updated to 0.471399

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.489038
    local lower bound updated to 0.473176

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.488082
    local lower bound updated to 0.473176

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.479158
    local lower bound updated to 0.474435

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.479158
    local lower bound updated to 0.474526

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.476727
    local lower bound updated to 0.474745

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.474745
    local lower bound updated to 0.474745
The Dual step takes 8.91374 (S)
upper bound updated to 0.474745
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 90.8935 seconds.
    local lower bound updated to 0.406948
    local upper bound updated to 0.474658

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 14.5301 seconds.
    local lower bound updated to 0.445674
    local upper bound updated to 0.473545

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 96.4379 seconds.
    local lower bound updated to 0.465266
    local upper bound updated to 0.473008

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 68.0831 seconds.
    local lower bound updated to 0.469735
    local upper bound updated to 0.472793

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 73.6177 seconds.
    local lower bound updated to 0.471337
    local upper bound updated to 0.472596

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 97.8796 seconds.
    local lower bound updated to 0.471337
    local upper bound updated to 0.472483

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 92.7167 seconds.
    local lower bound updated to 0.472176
    local upper bound updated to 0.472443

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 93.9132 seconds.
    local lower bound updated to 0.472176
    local upper bound updated to 0.472386

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 86.4265 seconds.
    local lower bound updated to 0.472279
    local upper bound updated to 0.472384

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 98.1951 seconds.
    local lower bound updated to 0.472302
    local upper bound updated to 0.472381

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 107.019 seconds.
    local lower bound updated to 0.472302
    local upper bound updated to 0.472364

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 108.871 seconds.
    local lower bound updated to 0.472302
    local upper bound updated to 0.472352

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 97.0543 seconds.
    local lower bound updated to 0.472352
    local upper bound updated to 0.472352
The Primal step takes 1125.74 (S)
lower bound updated to 0.472352

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.482426
    local lower bound updated to 0.47237

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.47326
    local lower bound updated to 0.472377

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.47326
    local lower bound updated to 0.47239

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.47239
    local lower bound updated to 0.47239
The Dual step takes 16.7021 (S)
upper bound updated to 0.47239
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.031 seconds.
    local lower bound updated to 0.416756
    local upper bound updated to 0.47239

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.033 seconds.
    local lower bound updated to 0.472262
    local upper bound updated to 0.472389

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.472389
    local upper bound updated to 0.472389
The Primal step takes 600.128 (S)
lower bound updated to 0.472389

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.481903
    local lower bound updated to 0.472389

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.472389
    local lower bound updated to 0.472389
The Dual step takes 9.95171 (S)
upper bound updated to 0.472389
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 200.039 seconds.
    local lower bound updated to 0.416756
    local upper bound updated to 0.472389

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.03 seconds.
    local lower bound updated to 0.472389
    local upper bound updated to 0.472389
The time obtain the optimal randomized assortment is 2527.88 (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_203616.log"
The computation time limit for a lower bound is 83468
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 2480 rows, 2008 columns and 8003 nonzeros
Model fingerprint: 0x5bd602af
Variable types: 1951 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 641 rows and 1211 columns
Presolve time: 0.03s
Presolved: 1839 rows, 797 columns, 7108 nonzeros
Variable types: 741 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.5419852
Found heuristic solution: objective 0.5057063

Root relaxation: objective 3.390204e-01, 217 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    0.33902    0   24    0.50571    0.33902  33.0%     -    0s
H    0     0                       0.4906923    0.33902  30.9%     -    0s
     0     0    0.34289    0   28    0.49069    0.34289  30.1%     -    0s
H    0     0                       0.4903538    0.34289  30.1%     -    0s
     0     0    0.38559    0   26    0.49035    0.38559  21.4%     -    0s
H    0     0                       0.4820532    0.38559  20.0%     -    0s
     0     0    0.38614    0   24    0.48205    0.38614  19.9%     -    0s
     0     0    0.39839    0   25    0.48205    0.39839  17.4%     -    0s
     0     0    0.40211    0   26    0.48205    0.40211  16.6%     -    0s
H    0     0                       0.4805835    0.40211  16.3%     -    0s
     0     0    0.41196    0   24    0.48058    0.41196  14.3%     -    0s
H    0     0                       0.4805812    0.41302  14.1%     -    0s
H    0     0                       0.4803675    0.41302  14.0%     -    0s
     0     0    0.41302    0   26    0.48037    0.41302  14.0%     -    0s
     0     0    0.41555    0   26    0.48037    0.41555  13.5%     -    0s
H    0     0                       0.4726536    0.41555  12.1%     -    2s
     0     2    0.41555    0   26    0.47265    0.41555  12.1%     -    2s
H  100    75                       0.4723886    0.42545  9.94%  37.1    4s
   199   130    0.46772   18    6    0.47239    0.42663  9.69%  31.8    6s
   591   282    0.46597   14    8    0.47239    0.43195  8.56%  29.8   10s
  1686   600    0.45038   11   18    0.47239    0.43785  7.31%  25.9   15s
  2081   689    0.45217   16   10    0.47239    0.43913  7.04%  25.5   20s
  3116   902    0.45145   13   26    0.47239    0.44194  6.45%  24.8   25s
  3438   978    0.46528   20    6    0.47239    0.44194  6.45%  26.8   30s
H 3702   913                       0.4723886    0.44384  6.04%  27.4   30s
  4490   878    0.46960   25    8    0.47239    0.44741  5.29%  28.2   35s
  4981   808    0.45138   20   17    0.47239    0.44892  4.97%  28.5   41s
  5398   736    0.46632   25    8    0.47239    0.44989  4.76%  28.9   45s
  6751   755    0.46039   23   13    0.47239    0.45190  4.34%  29.0   50s
H 7512   803                       0.4723886    0.45242  4.23%  28.8   54s
  7596   825    0.46240   21   17    0.47239    0.45249  4.21%  28.9   55s
  8451   907    0.45704   20   16    0.47239    0.45344  4.01%  28.8   60s
H 8773   911                       0.4723886    0.45359  3.98%  28.9   61s
  9221   959     cutoff   22         0.47239    0.45398  3.90%  28.8   65s
H10258   986                       0.4723886    0.45453  3.78%  29.0   69s
 10334  1037    0.47127   25    6    0.47239    0.45468  3.75%  29.0   71s
H10567  1037                       0.4723886    0.45469  3.75%  29.0   71s
 10782  1071    0.46876   20   10    0.47239    0.45487  3.71%  29.0   75s
H10801  1071                       0.4723886    0.45487  3.71%  29.0   75s
 11959  1158     cutoff   25         0.47239    0.45558  3.56%  29.0   81s
 12810  1247    0.47145   23   12    0.47239    0.45618  3.43%  28.8   86s
 14067  1296     cutoff   29         0.47239    0.45677  3.31%  28.8   91s
 14873  1326    0.47127   25   13    0.47239    0.45711  3.24%  28.8   97s
 15953  1377    0.47139   24    8    0.47239    0.45792  3.06%  28.8  101s
 16734  1397    0.46121   23   17    0.47239    0.45813  3.02%  28.7  105s
 17951  1423    0.46823   26   10    0.47239    0.45881  2.87%  28.5  110s
 18931  1458     cutoff   30         0.47239    0.45920  2.79%  28.4  116s
 20015  1462    0.47233   24   11    0.47239    0.45990  2.64%  28.4  122s
 20659  1444     cutoff   28         0.47239    0.46015  2.59%  28.4  125s
 22629  1366     cutoff   25         0.47239    0.46081  2.45%  28.2  131s
 24264  1293     cutoff   28         0.47239    0.46174  2.25%  28.0  136s
 25114  1200    0.47098   26    8    0.47239    0.46216  2.16%  27.9  141s
 27450  1019    0.46638   18   22    0.47239    0.46328  1.93%  27.8  146s
 29072   875    0.46805   26   11    0.47239    0.46412  1.75%  27.6  151s
 29544   788    0.47147   26    4    0.47239    0.46446  1.68%  27.6  156s
 31140   481     cutoff   24         0.47239    0.46615  1.32%  27.5  163s
 32077   103     cutoff   21         0.47239    0.46818  0.89%  27.4  165s

Cutting planes:
  Implied bound: 229
  MIR: 177
  Flow cover: 442
  RLT: 71
  Relax-and-lift: 77

Explored 32519 nodes (889192 simplex iterations) in 166.03 seconds (105.56 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.472389 0.472389 0.472654 ... 0.505706

Optimal solution found (tolerance 1.00e-04)
Best objective 4.723886118844e-01, best bound 4.723885965030e-01, gap 0.0000%
The objective bound is 0.472389 while the objective upper bound is 0.472389

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.49 (ave)

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