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 1.13457 seconds.
    local lower bound updated to 0.342884
    local upper bound updated to 0.616489

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.10163 seconds.
    local lower bound updated to 0.614154
    local upper bound updated to 0.614154
The Primal step takes 2.23917 (S)
lower bound updated to 0.614154

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.700597
    local lower bound updated to 0.700265

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.700597
    local lower bound updated to 0.700296

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.700296
    local lower bound updated to 0.700296
The Dual step takes 0.104347 (S)
upper bound updated to 0.700296
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.86356 seconds.
    local lower bound updated to 0.419301
    local upper bound updated to 0.636735

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.9474 seconds.
    local lower bound updated to 0.593159
    local upper bound updated to 0.625796

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 6.24464 seconds.
    local lower bound updated to 0.610283
    local upper bound updated to 0.619097

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.30077 seconds.
    local lower bound updated to 0.613328
    local upper bound updated to 0.616549

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 6.3494 seconds.
    local lower bound updated to 0.616538
    local upper bound updated to 0.61654
The Primal step takes 25.7197 (S)
lower bound updated to 0.616538

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.677341
    local lower bound updated to 0.656658

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.674263
    local lower bound updated to 0.658323

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.663304
    local lower bound updated to 0.661492

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.661492
    local lower bound updated to 0.661492
The Dual step takes 0.480224 (S)
upper bound updated to 0.661492
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 1.91169 seconds.
    local lower bound updated to 0.461741
    local upper bound updated to 0.633092

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 5.30339 seconds.
    local lower bound updated to 0.591018
    local upper bound updated to 0.621118

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 8.14252 seconds.
    local lower bound updated to 0.61248
    local upper bound updated to 0.61654

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.1051 seconds.
    local lower bound updated to 0.61654
    local upper bound updated to 0.61654
The Primal step takes 23.4777 (S)
lower bound updated to 0.61654

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.664333
    local lower bound updated to 0.634581

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.65932
    local lower bound updated to 0.639492

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.639492
    local lower bound updated to 0.639492
The Dual step takes 0.402106 (S)
upper bound updated to 0.639492
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.80967 seconds.
    local lower bound updated to 0.491488
    local upper bound updated to 0.639492

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 11.891 seconds.
    local lower bound updated to 0.611434
    local upper bound updated to 0.634938

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 39.498 seconds.
    local lower bound updated to 0.629733
    local upper bound updated to 0.63274

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 23.1746 seconds.
    local lower bound updated to 0.629733
    local upper bound updated to 0.632105

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 29.9327 seconds.
    local lower bound updated to 0.629782
    local upper bound updated to 0.631933

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 29.9989 seconds.
    local lower bound updated to 0.629782
    local upper bound updated to 0.63169

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 25.0841 seconds.
    local lower bound updated to 0.629994
    local upper bound updated to 0.631354

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 39.3147 seconds.
    local lower bound updated to 0.631354
    local upper bound updated to 0.631354
The Primal step takes 201.742 (S)
lower bound updated to 0.631354

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.65702
    local lower bound updated to 0.631354

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.635441
    local lower bound updated to 0.632415

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.632415
    local lower bound updated to 0.632415
The Dual step takes 0.893554 (S)
upper bound updated to 0.632415
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.77171 seconds.
    local lower bound updated to 0.502735
    local upper bound updated to 0.631464

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 65.0589 seconds.
    local lower bound updated to 0.626171
    local upper bound updated to 0.631354

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 38.5288 seconds.
    local lower bound updated to 0.631354
    local upper bound updated to 0.631354
The Primal step takes 109.377 (S)
lower bound updated to 0.631354

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.656477
    local lower bound updated to 0.631354

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.631354
    local lower bound updated to 0.631354
The Dual step takes 0.579389 (S)
upper bound updated to 0.631354
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 5.98504 seconds.
    local lower bound updated to 0.502735
    local upper bound updated to 0.631354

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 35.8201 seconds.
    local lower bound updated to 0.631354
    local upper bound updated to 0.631354
The time obtain the optimal randomized assortment is 406.829 (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_109316.log"
The computation time limit for a lower bound is 85588
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 1680 rows, 1358 columns and 5397 nonzeros
Model fingerprint: 0x4da39e85
Variable types: 1301 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [3e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [3e-01, 1e+00]
Presolve removed 467 rows and 809 columns
Presolve time: 0.01s
Presolved: 1213 rows, 549 columns, 4706 nonzeros
Variable types: 493 continuous, 56 integer (56 binary)
Found heuristic solution: objective 0.7358691
Found heuristic solution: objective 0.7118809

Root relaxation: objective 3.165770e-01, 166 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    0.31658    0   23    0.71188    0.31658  55.5%     -    0s
H    0     0                       0.6750834    0.31658  53.1%     -    0s
     0     0    0.34549    0   27    0.67508    0.34549  48.8%     -    0s
H    0     0                       0.6670364    0.34577  48.2%     -    0s
     0     0    0.34624    0   27    0.66704    0.34624  48.1%     -    0s
H    0     0                       0.6612182    0.41566  37.1%     -    0s
     0     0    0.41566    0   27    0.66122    0.41566  37.1%     -    0s
     0     0    0.41570    0   27    0.66122    0.41570  37.1%     -    0s
     0     0    0.44350    0   27    0.66122    0.44350  32.9%     -    0s
     0     0    0.44693    0   26    0.66122    0.44693  32.4%     -    0s
H    0     0                       0.6587693    0.44693  32.2%     -    0s
     0     0    0.47791    0   26    0.65877    0.47791  27.5%     -    0s
     0     0    0.48176    0   27    0.65877    0.48176  26.9%     -    0s
     0     0    0.48798    0   27    0.65877    0.48798  25.9%     -    0s
H    0     0                       0.6440709    0.48798  24.2%     -    1s
     0     2    0.48798    0   27    0.64407    0.48798  24.2%     -    1s
*  143    83              20       0.6420163    0.52828  17.7%  19.1    1s
H  314   162                       0.6334815    0.54009  14.7%  20.4    1s
H  321   162                       0.6334730    0.54009  14.7%  20.1    1s
H  506   217                       0.6330344    0.54999  13.1%  19.3    3s
H  582   235                       0.6330237    0.55119  12.9%  19.0    3s
H  912   342                       0.6313537    0.55882  11.5%  18.4    3s
  1512   470    0.62162   11   10    0.63135    0.56517  10.5%  17.1    5s
  3304   868    0.59171   22   16    0.63135    0.57643  8.70%  17.3   10s
  5187   570    0.61738   28   13    0.63135    0.59429  5.87%  18.6   15s
H 5538   439                       0.6313537    0.59621  5.57%  18.6   16s
  7680   550     cutoff   27         0.63135    0.60334  4.44%  18.5   20s
 10685   728    0.62438   32   13    0.63135    0.60961  3.44%  17.9   25s
 15360   712     cutoff   29         0.63135    0.61624  2.39%  17.0   30s
 18896   105    0.62789   29   13    0.63135    0.62220  1.45%  16.4   35s

Cutting planes:
  Gomory: 1
  Implied bound: 116
  MIR: 87
  Flow cover: 298
  RLT: 18
  Relax-and-lift: 68

Explored 19517 nodes (319372 simplex iterations) in 35.25 seconds (24.72 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.631354 0.631354 0.633024 ... 0.661218

Optimal solution found (tolerance 1.00e-04)
Best objective 6.313536813307e-01, best bound 6.313536813307e-01, gap 0.0000%
The objective bound is 0.631354 while the objective upper bound is 0.631354

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.61 (ave)

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