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 0.870852 seconds.
    local lower bound updated to 0.239009
    local upper bound updated to 0.453266

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 3.39125 seconds.
    local lower bound updated to 0.451924
    local upper bound updated to 0.451924
The Primal step takes 4.26465 (S)
lower bound updated to 0.451924

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.62347
    local lower bound updated to 0.58518

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.62347
    local lower bound updated to 0.614682

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.616435
    local lower bound updated to 0.615751

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.615751
    local lower bound updated to 0.615751
The Dual step takes 0.240587 (S)
upper bound updated to 0.615751
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.809482 seconds.
    local lower bound updated to 0.327173
    local upper bound updated to 0.461864

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 6.8043 seconds.
    local lower bound updated to 0.456571
    local upper bound updated to 0.458018

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 4.24314 seconds.
    local lower bound updated to 0.456571
    local upper bound updated to 0.457423

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 4.24579 seconds.
    local lower bound updated to 0.457423
    local upper bound updated to 0.457423
The Primal step takes 16.1182 (S)
lower bound updated to 0.457423

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.539212
    local lower bound updated to 0.516372

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.539212
    local lower bound updated to 0.51762

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.527296
    local lower bound updated to 0.523108

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.524072
    local lower bound updated to 0.52313

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.52313
    local lower bound updated to 0.52313
The Dual step takes 0.793719 (S)
upper bound updated to 0.52313
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.28781 seconds.
    local lower bound updated to 0.400649
    local upper bound updated to 0.521737

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.32464 seconds.
    local lower bound updated to 0.400649
    local upper bound updated to 0.508082

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.91814 seconds.
    local lower bound updated to 0.429953
    local upper bound updated to 0.489384

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 8.91348 seconds.
    local lower bound updated to 0.461779
    local upper bound updated to 0.473205

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 6.74197 seconds.
    local lower bound updated to 0.461779
    local upper bound updated to 0.472206

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 18.0004 seconds.
    local lower bound updated to 0.46317
    local upper bound updated to 0.472068

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 18.98 seconds.
    local lower bound updated to 0.468203
    local upper bound updated to 0.471779

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 21.624 seconds.
    local lower bound updated to 0.469624
    local upper bound updated to 0.471302

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 18.6701 seconds.
    local lower bound updated to 0.469624
    local upper bound updated to 0.470985

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 19.8818 seconds.
    local lower bound updated to 0.469624
    local upper bound updated to 0.470229

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 17.5463 seconds.
    local lower bound updated to 0.469624
    local upper bound updated to 0.470014

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 17.9724 seconds.
    local lower bound updated to 0.469836
    local upper bound updated to 0.470009

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 21.9113 seconds.
    local lower bound updated to 0.470009
    local upper bound updated to 0.470009
The Primal step takes 176.854 (S)
lower bound updated to 0.470009

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.520629
    local lower bound updated to 0.470276

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.515003
    local lower bound updated to 0.476562

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.496564
    local lower bound updated to 0.485735

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.496564
    local lower bound updated to 0.487389

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.488478
    local lower bound updated to 0.487543

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.487543
    local lower bound updated to 0.487543
The Dual step takes 11.037 (S)
upper bound updated to 0.487543
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 7.18536 seconds.
    local lower bound updated to 0.41426
    local upper bound updated to 0.487543

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 23.3214 seconds.
    local lower bound updated to 0.452446
    local upper bound updated to 0.48601

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 76.5902 seconds.
    local lower bound updated to 0.468256
    local upper bound updated to 0.483281

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 82.5785 seconds.
    local lower bound updated to 0.472824
    local upper bound updated to 0.479853

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 112.05 seconds.
    local lower bound updated to 0.472824
    local upper bound updated to 0.479391

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 111.986 seconds.
    local lower bound updated to 0.475038
    local upper bound updated to 0.479089

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 107.448 seconds.
    local lower bound updated to 0.475038
    local upper bound updated to 0.478771

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 135.996 seconds.
    local lower bound updated to 0.476538
    local upper bound updated to 0.478689

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.477892
    local upper bound updated to 0.478641

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 123.213 seconds.
    local lower bound updated to 0.477892
    local upper bound updated to 0.478558

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.026 seconds.
    local lower bound updated to 0.477892
    local upper bound updated to 0.478391

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 128.185 seconds.
    local lower bound updated to 0.477892
    local upper bound updated to 0.478023

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 200.036 seconds.
    local lower bound updated to 0.477892
    local upper bound updated to 0.478021

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 147.834 seconds.
    local lower bound updated to 0.478021
    local upper bound updated to 0.478021
The Primal step takes 1656.62 (S)
lower bound updated to 0.478021

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.510756
    local lower bound updated to 0.478789

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.494022
    local lower bound updated to 0.480716

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.489557
    local lower bound updated to 0.482062

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.488399
    local lower bound updated to 0.483514

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.485167
    local lower bound updated to 0.483709

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.485167
    local lower bound updated to 0.483709

    ++ RESTRICTED DUAL ITERATION 7 ++
    local upper bound updated to 0.483709
    local lower bound updated to 0.483709
The Dual step takes 31.9515 (S)
upper bound updated to 0.483709
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 10.1879 seconds.
    local lower bound updated to 0.425522
    local upper bound updated to 0.483709

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.043 seconds.
    local lower bound updated to 0.476995
    local upper bound updated to 0.483089

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.037 seconds.
    local lower bound updated to 0.478861
    local upper bound updated to 0.48277

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 200.059 seconds.
    local lower bound updated to 0.481195
    local upper bound updated to 0.482721

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 150.174 seconds.
    local lower bound updated to 0.481195
    local upper bound updated to 0.48232

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 200.041 seconds.
    local lower bound updated to 0.481195
    local upper bound updated to 0.482237

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 200.055 seconds.
    local lower bound updated to 0.481276
    local upper bound updated to 0.482164

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 200.049 seconds.
    local lower bound updated to 0.481276
    local upper bound updated to 0.481977

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 200.052 seconds.
    local lower bound updated to 0.481276
    local upper bound updated to 0.481969

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 200.053 seconds.
    local lower bound updated to 0.481276
    local upper bound updated to 0.481959

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 200.033 seconds.
    local lower bound updated to 0.481306
    local upper bound updated to 0.481952

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 200.035 seconds.
    local lower bound updated to 0.481653
    local upper bound updated to 0.481929

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 200.049 seconds.
    local lower bound updated to 0.481836
    local upper bound updated to 0.481925

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 200.057 seconds.
    local lower bound updated to 0.481925
    local upper bound updated to 0.481925
The Primal step takes 2561.11 (S)
lower bound updated to 0.481925

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.500703
    local lower bound updated to 0.481925

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.489162
    local lower bound updated to 0.481958

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.482742
    local lower bound updated to 0.481969

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.481969
    local lower bound updated to 0.481969
The Dual step takes 23.5873 (S)
upper bound updated to 0.481969
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 19.4837 seconds.
    local lower bound updated to 0.427175
    local upper bound updated to 0.481969

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.069 seconds.
    local lower bound updated to 0.481583
    local upper bound updated to 0.481937

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.481937
    local upper bound updated to 0.481937
The Primal step takes 419.637 (S)
lower bound updated to 0.481937

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.499551
    local lower bound updated to 0.481937

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.482152
    local lower bound updated to 0.48194

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.48194
    local lower bound updated to 0.48194
The Dual step takes 20.997 (S)
upper bound updated to 0.48194
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 16.8618 seconds.
    local lower bound updated to 0.428602
    local upper bound updated to 0.48194

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 200.033 seconds.
    local lower bound updated to 0.481913
    local upper bound updated to 0.48194

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 200.04 seconds.
    local lower bound updated to 0.48194
    local upper bound updated to 0.48194
The time obtain the optimal randomized assortment is 5340.2 (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_208918.log"
The computation time limit for a lower bound is 80652
The model output flag is 1
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (linux64)
Thread count: 20 physical cores, 40 logical processors, using up to 4 threads
Optimize a model with 4738 rows, 3618 columns and 15653 nonzeros
Model fingerprint: 0xa5eb1959
Variable types: 3553 continuous, 65 integer (65 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 1063 rows and 1995 columns
Presolve time: 0.08s
Presolved: 3675 rows, 1623 columns, 14177 nonzeros
Variable types: 1559 continuous, 64 integer (64 binary)
Found heuristic solution: objective 0.6634556
Found heuristic solution: objective 0.6595200
Found heuristic solution: objective 0.5952756

Root relaxation: objective 3.468207e-01, 448 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    0.34682    0   28    0.59528    0.34682  41.7%     -    0s
H    0     0                       0.5479432    0.34682  36.7%     -    0s
     0     0    0.35817    0   30    0.54794    0.35817  34.6%     -    0s
H    0     0                       0.5400245    0.35817  33.7%     -    0s
H    0     0                       0.5176154    0.35817  30.8%     -    0s
H    0     0                       0.5127426    0.35817  30.1%     -    0s
     0     0    0.38463    0   28    0.51274    0.38463  25.0%     -    0s
H    0     0                       0.4827493    0.38463  20.3%     -    1s
     0     0    0.38463    0   28    0.48275    0.38463  20.3%     -    1s
     0     0    0.39811    0   30    0.48275    0.39811  17.5%     -    1s
     0     0    0.39858    0   31    0.48275    0.39858  17.4%     -    1s
     0     0    0.40240    0   29    0.48275    0.40240  16.6%     -    1s
     0     0    0.40286    0   29    0.48275    0.40286  16.5%     -    1s
     0     0    0.40355    0   29    0.48275    0.40355  16.4%     -    2s
H    0     0                       0.4822280    0.40355  16.3%     -    6s
     0     2    0.40355    0   29    0.48223    0.40355  16.3%     -    6s
H   56    60                       0.4820456    0.41110  14.7%  84.0    7s
*  349   211              25       0.4819397    0.42184  12.5%  49.8    8s
   399   219    0.44796    8   18    0.48194    0.42464  11.9%  49.7   13s
   498   254     cutoff   19         0.48194    0.42704  11.4%  48.7   16s
H  557   279                       0.4819397    0.42704  11.4%  49.1   17s
   699   324    0.46374   17   10    0.48194    0.42924  10.9%  47.3   22s
  1010   477    0.47107   14   12    0.48194    0.43470  9.80%  46.0   25s
  1427   544     cutoff   13         0.48194    0.43694  9.34%  45.9   31s
  2077   707    0.45079   11   17    0.48194    0.44035  8.63%  44.8   37s
  2199   713     cutoff   15         0.48194    0.44057  8.58%  44.6   41s
  3116   935    0.45477   12   29    0.48194    0.44385  7.90%  43.2   48s
  3126   942    0.47428   16   33    0.48194    0.44385  7.90%  43.0   50s
  3135   951    0.44385   12   33    0.48194    0.44385  7.90%  44.3   55s
  4000  1068    0.47991   28   10    0.48194    0.44385  7.90%  46.7   63s
  4157  1084    0.45232   20   16    0.48194    0.44385  7.90%  47.1   65s
  4493  1074     cutoff   25         0.48194    0.44385  7.90%  47.4   71s
  5179   986    0.46585   22   10    0.48194    0.44506  7.65%  47.1   76s
  5384   942 infeasible   24         0.48194    0.44557  7.55%  46.9   82s
  5799   877    0.47338   23   14    0.48194    0.44650  7.35%  47.0   85s
  6355   945    0.47380   23   14    0.48194    0.44843  6.95%  46.7   91s
  6548   970    0.46516   26    8    0.48194    0.44879  6.88%  46.7   98s
  6758  1025    0.46010   24   14    0.48194    0.44933  6.77%  46.8  101s
  7194  1096     cutoff   23         0.48194    0.44993  6.64%  46.7  106s
  7846  1221     cutoff   28         0.48194    0.45154  6.31%  46.6  113s
  8066  1252     cutoff   27         0.48194    0.45206  6.20%  46.5  116s
  8319  1298     cutoff   30         0.48194    0.45225  6.16%  46.5  121s
  8647  1344    0.47240   24   12    0.48194    0.45265  6.08%  46.3  126s
  8934  1398    0.47625   28    6    0.48194    0.45331  5.94%  46.2  130s
  9177  1437    0.47557   27   10    0.48194    0.45357  5.89%  46.1  135s
  9588  1443     cutoff   29         0.48194    0.45384  5.83%  46.0  140s
  9740  1502    0.47625   23    8    0.48194    0.45408  5.78%  46.0  146s
 10380  1551    0.48142   28   12    0.48194    0.45530  5.53%  45.8  151s
 11008  1589    0.47661   26   12    0.48194    0.45574  5.44%  45.6  156s
 11547  1651    0.45952   24   14    0.48194    0.45648  5.28%  45.6  162s
 12048  1674    0.46802   25   17    0.48194    0.45697  5.18%  45.3  165s
 12731  1695     cutoff   24         0.48194    0.45755  5.06%  45.1  174s
 13145  1746    0.47104   21   18    0.48194    0.45795  4.98%  45.0  179s
 13756  1755    0.46999   23   16    0.48194    0.45826  4.91%  44.9  184s
 14545  1794     cutoff   29         0.48194    0.45893  4.77%  44.7  187s
 15408  1795 infeasible   24         0.48194    0.45961  4.63%  44.6  192s
 16026  1800    0.47414   23   15    0.48194    0.46028  4.49%  44.6  197s
 16566  1816     cutoff   25         0.48194    0.46075  4.40%  44.4  204s
 17006  1836    0.47547   23   17    0.48194    0.46104  4.34%  44.3  209s
 17788  1810    0.47817   28    8    0.48194    0.46143  4.25%  44.1  215s
 18371  1800     cutoff   21         0.48194    0.46208  4.12%  44.2  220s
 19618  1778     cutoff   23         0.48194    0.46334  3.86%  44.0  227s
 20246  1774    0.46865   25   12    0.48194    0.46366  3.79%  44.0  230s
 21574  1692 infeasible   31         0.48194    0.46468  3.58%  43.8  236s
 22023  1652    0.47562   26   10    0.48194    0.46491  3.53%  43.8  240s
 23059  1595    0.48091   27   12    0.48194    0.46571  3.37%  43.7  250s
 24020  1491    0.48055   26   12    0.48194    0.46627  3.25%  43.5  258s
 24735  1395    0.47243   29   10    0.48194    0.46704  3.09%  43.4  261s
 25632  1351 infeasible   28         0.48194    0.46782  2.93%  43.3  267s
 26664  1196    0.47234   23   12    0.48194    0.46859  2.77%  43.2  272s
 27286  1171     cutoff   24         0.48194    0.46939  2.60%  43.1  275s
 28272  1031    0.47547   31   10    0.48194    0.46997  2.48%  43.0  284s
 28532   858     cutoff   26         0.48194    0.47061  2.35%  42.9  288s
 29388   755    0.47661   33    4    0.48194    0.47211  2.04%  42.7  291s
 29853   653     cutoff   34         0.48194    0.47231  2.00%  42.6  297s
 30293   542    0.48194   27    8    0.48194    0.47329  1.79%  42.6  300s
H30301   542                       0.4819396    0.47329  1.79%  42.6  300s
 31257   119     cutoff   28         0.48194    0.47502  1.44%  42.3  306s

Cutting planes:
  Gomory: 1
  Implied bound: 498
  MIR: 248
  Flow cover: 623
  RLT: 124
  Relax-and-lift: 180

Explored 31841 nodes (1339545 simplex iterations) in 307.38 seconds (205.36 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.48194 0.48194 0.482046 ... 0.595276

Optimal solution found (tolerance 1.00e-04)
Best objective 4.819396546217e-01, best bound 4.819396441365e-01, gap 0.0000%
The objective bound is 0.48194 while the objective upper bound is 0.48194

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.68 (ave)

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