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 0.562074 seconds.
    local lower bound updated to 0.269819
    local upper bound updated to 0.52482

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.799036 seconds.
    local lower bound updated to 0.523544
    local upper bound updated to 0.523544
The Primal step takes 1.3647 (S)
lower bound updated to 0.523544

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.639823
    local lower bound updated to 0.63772

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.639823
    local lower bound updated to 0.639766

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.639766
    local lower bound updated to 0.639766
The Dual step takes 0.0755697 (S)
upper bound updated to 0.639766
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.37453 seconds.
    local lower bound updated to 0.363511
    local upper bound updated to 0.542309

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.66553 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.529171

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.56485 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.528821

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.07097 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.527934

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.28414 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.527644

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.20581 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.52754

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 3.53561 seconds.
    local lower bound updated to 0.52738
    local upper bound updated to 0.527523

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 5.26903 seconds.
    local lower bound updated to 0.527523
    local upper bound updated to 0.527523
The Primal step takes 27.9938 (S)
lower bound updated to 0.527523

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.577262
    local lower bound updated to 0.551624

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.571621
    local lower bound updated to 0.56225

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.564493
    local lower bound updated to 0.562789

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.562789
    local lower bound updated to 0.562789
The Dual step takes 0.835384 (S)
upper bound updated to 0.562789
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.4197 seconds.
    local lower bound updated to 0.442796
    local upper bound updated to 0.557486

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.62001 seconds.
    local lower bound updated to 0.528015
    local upper bound updated to 0.553667

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.17732 seconds.
    local lower bound updated to 0.546003
    local upper bound updated to 0.549593

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.52409 seconds.
    local lower bound updated to 0.546003
    local upper bound updated to 0.549306

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 4.60057 seconds.
    local lower bound updated to 0.546171
    local upper bound updated to 0.548547

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.89417 seconds.
    local lower bound updated to 0.546171
    local upper bound updated to 0.548349

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.93836 seconds.
    local lower bound updated to 0.546171
    local upper bound updated to 0.548273

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 2.94331 seconds.
    local lower bound updated to 0.547555
    local upper bound updated to 0.548259

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 4.26111 seconds.
    local lower bound updated to 0.547634
    local upper bound updated to 0.547964

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 8.51857 seconds.
    local lower bound updated to 0.547851
    local upper bound updated to 0.547963

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 3.81818 seconds.
    local lower bound updated to 0.547911
    local upper bound updated to 0.547962

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 5.09113 seconds.
    local lower bound updated to 0.54794
    local upper bound updated to 0.547958

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 3.26434 seconds.
    local lower bound updated to 0.547946
    local upper bound updated to 0.547951
The Primal step takes 55.1313 (S)
lower bound updated to 0.547946

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.565238
    local lower bound updated to 0.547951

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.564352
    local lower bound updated to 0.552084

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.553632
    local lower bound updated to 0.552205

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.553632
    local lower bound updated to 0.552299

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.552299
    local lower bound updated to 0.552299
The Dual step takes 9.05103 (S)
upper bound updated to 0.552299
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 17.0104 seconds.
    local lower bound updated to 0.470095
    local upper bound updated to 0.552231

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 8.46102 seconds.
    local lower bound updated to 0.544635
    local upper bound updated to 0.551918

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 19.2064 seconds.
    local lower bound updated to 0.549327
    local upper bound updated to 0.551774

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 20.9667 seconds.
    local lower bound updated to 0.550441
    local upper bound updated to 0.551579

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 15.8172 seconds.
    local lower bound updated to 0.550924
    local upper bound updated to 0.551263

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 14.4614 seconds.
    local lower bound updated to 0.551032
    local upper bound updated to 0.551252

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 20.6324 seconds.
    local lower bound updated to 0.551032
    local upper bound updated to 0.551251

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 21.9423 seconds.
    local lower bound updated to 0.551032
    local upper bound updated to 0.551149

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 19.5095 seconds.
    local lower bound updated to 0.551032
    local upper bound updated to 0.551147

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 16.3933 seconds.
    local lower bound updated to 0.551147
    local upper bound updated to 0.551147
The Primal step takes 174.466 (S)
lower bound updated to 0.551147

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.565468
    local lower bound updated to 0.551147

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.553038
    local lower bound updated to 0.551181

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.552125
    local lower bound updated to 0.551239

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.551239
    local lower bound updated to 0.551239
The Dual step takes 13.2599 (S)
upper bound updated to 0.551239
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 19.2132 seconds.
    local lower bound updated to 0.478221
    local upper bound updated to 0.551239

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 34.836 seconds.
    local lower bound updated to 0.551129
    local upper bound updated to 0.551221

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 26.7184 seconds.
    local lower bound updated to 0.551184
    local upper bound updated to 0.551216

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 24.1097 seconds.
    local lower bound updated to 0.551207
    local upper bound updated to 0.551213
The Primal step takes 104.908 (S)
lower bound updated to 0.551207

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.562548
    local lower bound updated to 0.551213

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.551213
    local lower bound updated to 0.551213
The Dual step takes 8.74667 (S)
upper bound updated to 0.551213
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 19.1091 seconds.
    local lower bound updated to 0.478221
    local upper bound updated to 0.551213

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 38.8759 seconds.
    local lower bound updated to 0.551213
    local upper bound updated to 0.551213
The time obtain the optimal randomized assortment is 453.834 (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_100.000000_109216.log"
The computation time limit for a lower bound is 85542
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 2000 rows, 1618 columns and 6444 nonzeros
Model fingerprint: 0xf9765155
Variable types: 1561 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [4e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e-01, 1e+00]
Presolve removed 516 rows and 956 columns
Presolve time: 0.03s
Presolved: 1484 rows, 662 columns, 5618 nonzeros
Variable types: 607 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6317515
Found heuristic solution: objective 0.6281075
Found heuristic solution: objective 0.6052420

Root relaxation: objective 4.390895e-01, 207 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    0.43909    0   14    0.60524    0.43909  27.5%     -    0s
H    0     0                       0.6030380    0.43909  27.2%     -    0s
H    0     0                       0.5992367    0.44009  26.6%     -    0s
     0     0    0.44009    0   20    0.59924    0.44009  26.6%     -    0s
H    0     0                       0.5916148    0.44009  25.6%     -    0s
H    0     0                       0.5821505    0.44009  24.4%     -    0s
H    0     0                       0.5783235    0.44009  23.9%     -    0s
     0     0    0.46640    0   24    0.57832    0.46640  19.4%     -    0s
H    0     0                       0.5721607    0.46640  18.5%     -    0s
     0     0    0.46642    0   24    0.57216    0.46642  18.5%     -    0s
H    0     0                       0.5720590    0.47584  16.8%     -    0s
     0     0    0.47584    0   23    0.57206    0.47584  16.8%     -    0s
H    0     0                       0.5551793    0.47584  14.3%     -    0s
     0     0    0.47619    0   23    0.55518    0.47619  14.2%     -    0s
     0     0    0.48210    0   24    0.55518    0.48210  13.2%     -    0s
     0     0    0.48339    0   24    0.55518    0.48339  12.9%     -    0s
H    0     0                       0.5549486    0.48339  12.9%     -    0s
     0     0    0.48533    0   22    0.55495    0.48533  12.5%     -    0s
H    0     0                       0.5532955    0.48533  12.3%     -    0s
H    0     0                       0.5512134    0.48533  12.0%     -    1s
     0     2    0.48533    0   22    0.55121    0.48533  12.0%     -    1s
  1891   462     cutoff   15         0.55121    0.51859  5.92%  19.7    5s
H 2074   481                       0.5512134    0.51901  5.84%  19.6    5s
  2584   565    0.54194    9   16    0.55121    0.52230  5.25%  19.4   10s
  4328   714    0.54546   14   11    0.55121    0.52861  4.10%  19.0   15s
  6308   739     cutoff   18         0.55121    0.53624  2.72%  18.7   20s
  8461   474     cutoff   19         0.55121    0.54305  1.48%  17.7   25s

Cutting planes:
  Implied bound: 232
  MIR: 56
  Flow cover: 150
  Inf proof: 1
  RLT: 40
  Relax-and-lift: 131

Explored 9821 nodes (170794 simplex iterations) in 27.02 seconds (14.38 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.551213 0.551213 0.553295 ... 0.591615

Optimal solution found (tolerance 1.00e-04)
Best objective 5.512133742773e-01, best bound 5.512133742773e-01, gap 0.0000%
The objective bound is 0.551213 while the objective upper bound is 0.551213

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.20 (ave)

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