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 0.524976 seconds.
    local lower bound updated to 0.235367
    local upper bound updated to 0.465962

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.561824 seconds.
    local lower bound updated to 0.457942
    local upper bound updated to 0.457942
The Primal step takes 1.08876 (S)
lower bound updated to 0.457942

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.57631
    local lower bound updated to 0.555033

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.555033
    local lower bound updated to 0.555033
The Dual step takes 0.139389 (S)
upper bound updated to 0.555033
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.463496 seconds.
    local lower bound updated to 0.289537
    local upper bound updated to 0.473477

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.703184 seconds.
    local lower bound updated to 0.459332
    local upper bound updated to 0.45985

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.643678 seconds.
    local lower bound updated to 0.459332
    local upper bound updated to 0.459659

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 0.687758 seconds.
    local lower bound updated to 0.459659
    local upper bound updated to 0.459659
The Primal step takes 2.50342 (S)
lower bound updated to 0.459659

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.509068
    local lower bound updated to 0.488799

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.509068
    local lower bound updated to 0.490146

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.494189
    local lower bound updated to 0.49062

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.49062
    local lower bound updated to 0.49062
The Dual step takes 0.657135 (S)
upper bound updated to 0.49062
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.02564 seconds.
    local lower bound updated to 0.387441
    local upper bound updated to 0.481383

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.01157 seconds.
    local lower bound updated to 0.417686
    local upper bound updated to 0.47956

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.46702 seconds.
    local lower bound updated to 0.456282
    local upper bound updated to 0.477287

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.87097 seconds.
    local lower bound updated to 0.46982
    local upper bound updated to 0.473577

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.94692 seconds.
    local lower bound updated to 0.46982
    local upper bound updated to 0.472981

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.63095 seconds.
    local lower bound updated to 0.46982
    local upper bound updated to 0.472564

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 7.7153 seconds.
    local lower bound updated to 0.470328
    local upper bound updated to 0.472196

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 6.22315 seconds.
    local lower bound updated to 0.470328
    local upper bound updated to 0.471609

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 4.90461 seconds.
    local lower bound updated to 0.471582
    local upper bound updated to 0.4716

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 5.63774 seconds.
    local lower bound updated to 0.471582
    local upper bound updated to 0.471596

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 5.08784 seconds.
    local lower bound updated to 0.471596
    local upper bound updated to 0.471596
The Primal step takes 48.543 (S)
lower bound updated to 0.471596

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.513779
    local lower bound updated to 0.473303

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.481092
    local lower bound updated to 0.477456

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.477456
    local lower bound updated to 0.477456
The Dual step takes 1.19556 (S)
upper bound updated to 0.477456
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.9888 seconds.
    local lower bound updated to 0.412008
    local upper bound updated to 0.477456

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.57318 seconds.
    local lower bound updated to 0.473762
    local upper bound updated to 0.476941

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 2.6059 seconds.
    local lower bound updated to 0.475025
    local upper bound updated to 0.476474

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 2.46295 seconds.
    local lower bound updated to 0.475749
    local upper bound updated to 0.476444

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 2.13362 seconds.
    local lower bound updated to 0.47643
    local upper bound updated to 0.476444

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 2.25822 seconds.
    local lower bound updated to 0.47643
    local upper bound updated to 0.476441

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.58706 seconds.
    local lower bound updated to 0.476431
    local upper bound updated to 0.47644
The Primal step takes 15.6252 (S)
lower bound updated to 0.476431

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.505319
    local lower bound updated to 0.47644

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.478401
    local lower bound updated to 0.476442

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.476442
    local lower bound updated to 0.476442
The Dual step takes 2.22937 (S)
upper bound updated to 0.476442
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.12929 seconds.
    local lower bound updated to 0.418697
    local upper bound updated to 0.476442

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.14224 seconds.
    local lower bound updated to 0.476434
    local upper bound updated to 0.476441
The Primal step takes 5.27649 (S)
lower bound updated to 0.476434

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.503435
    local lower bound updated to 0.476441

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.476441
    local lower bound updated to 0.476441
The Dual step takes 2.01077 (S)
upper bound updated to 0.476441
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.2179 seconds.
    local lower bound updated to 0.418697
    local upper bound updated to 0.476441

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.79431 seconds.
    local lower bound updated to 0.476441
    local upper bound updated to 0.476441
The time obtain the optimal randomized assortment is 84.2866 (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_60.000000_65216.log"
The computation time limit for a lower bound is 85912
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 128 physical cores, 128 logical processors, using up to 4 threads
Optimize a model with 1520 rows, 1228 columns and 4893 nonzeros
Model fingerprint: 0xe139d61d
Variable types: 1171 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-08, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 384 rows and 710 columns
Presolve time: 0.01s
Presolved: 1136 rows, 518 columns, 4332 nonzeros
Variable types: 463 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.6769213
Found heuristic solution: objective 0.6133817
Found heuristic solution: objective 0.5831759

Root relaxation: objective 3.300041e-01, 163 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    0.33000    0   12    0.58318    0.33000  43.4%     -    0s
H    0     0                       0.5730374    0.33000  42.4%     -    0s
H    0     0                       0.4956718    0.33787  31.8%     -    0s
H    0     0                       0.4915130    0.33787  31.3%     -    0s
     0     0    0.33787    0   18    0.49151    0.33787  31.3%     -    0s
     0     0    0.36722    0   24    0.49151    0.36722  25.3%     -    0s
     0     0    0.38641    0   25    0.49151    0.38641  21.4%     -    0s
     0     0    0.38641    0   26    0.49151    0.38641  21.4%     -    0s
     0     0    0.38915    0   27    0.49151    0.38915  20.8%     -    0s
H    0     0                       0.4859558    0.38915  19.9%     -    0s
H    0     0                       0.4831911    0.39767  17.7%     -    0s
     0     0    0.39767    0   27    0.48319    0.39767  17.7%     -    0s
     0     0    0.39769    0   28    0.48319    0.39769  17.7%     -    0s
     0     0    0.39862    0   24    0.48319    0.39862  17.5%     -    0s
H    0     0                       0.4778372    0.39862  16.6%     -    0s
     0     2    0.39862    0   24    0.47784    0.39862  16.6%     -    0s
H   98    61                       0.4773070    0.42843  10.2%  24.0    1s
H  210    84                       0.4764409    0.43736  8.20%  19.9    1s
H  623    89                       0.4764409    0.46002  3.45%  18.2    1s

Cutting planes:
  Implied bound: 175
  MIR: 34
  Flow cover: 98
  RLT: 15
  Relax-and-lift: 97
  PSD: 2

Explored 1113 nodes (20418 simplex iterations) in 2.74 seconds (1.54 work units)
Thread count was 4 (of 128 available processors)

Solution count 10: 0.476441 0.476441 0.477307 ... 0.583176
No other solutions better than 0.476441

Optimal solution found (tolerance 1.00e-04)
Best objective 4.764409251915e-01, best bound 4.764409251915e-01, gap 0.0000%
The objective bound is 0.476441 while the objective upper bound is 0.476441

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   1.72 (ave)

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