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 0.483738 seconds.
    local lower bound updated to 0.237239
    local upper bound updated to 0.397119

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.03755 seconds.
    local lower bound updated to 0.397119
    local upper bound updated to 0.397119
The Primal step takes 1.52402 (S)
lower bound updated to 0.397119

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.477132
    local lower bound updated to 0.430939

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.430939
    local lower bound updated to 0.430939
The Dual step takes 0.115955 (S)
upper bound updated to 0.430939
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.18597 seconds.
    local lower bound updated to 0.270979
    local upper bound updated to 0.402712

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 4.03393 seconds.
    local lower bound updated to 0.392608
    local upper bound updated to 0.398868

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 7.67938 seconds.
    local lower bound updated to 0.398794
    local upper bound updated to 0.398813

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 6.44953 seconds.
    local lower bound updated to 0.398813
    local upper bound updated to 0.398813
The Primal step takes 20.356 (S)
lower bound updated to 0.398813

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.425087
    local lower bound updated to 0.409752

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.422172
    local lower bound updated to 0.410331

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.410331
    local lower bound updated to 0.410331
The Dual step takes 1.40721 (S)
upper bound updated to 0.410331
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.40997 seconds.
    local lower bound updated to 0.308088
    local upper bound updated to 0.400517

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 19.6658 seconds.
    local lower bound updated to 0.398154
    local upper bound updated to 0.400211

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 18.2324 seconds.
    local lower bound updated to 0.39913
    local upper bound updated to 0.3998

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 23.1759 seconds.
    local lower bound updated to 0.39913
    local upper bound updated to 0.399756

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 19.5874 seconds.
    local lower bound updated to 0.39913
    local upper bound updated to 0.399708

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 22.0128 seconds.
    local lower bound updated to 0.399189
    local upper bound updated to 0.399509

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 14.8726 seconds.
    local lower bound updated to 0.399318
    local upper bound updated to 0.399456

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 19.7093 seconds.
    local lower bound updated to 0.399448
    local upper bound updated to 0.399454
The Primal step takes 139.689 (S)
lower bound updated to 0.399448

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.414767
    local lower bound updated to 0.403594

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.409546
    local lower bound updated to 0.404938

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.409546
    local lower bound updated to 0.407215

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.409546
    local lower bound updated to 0.407838

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.407838
    local lower bound updated to 0.407838
The Dual step takes 7.37372 (S)
upper bound updated to 0.407838
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 30.2741 seconds.
    local lower bound updated to 0.35384
    local upper bound updated to 0.407838

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 42.8544 seconds.
    local lower bound updated to 0.402038
    local upper bound updated to 0.406399

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 46.1149 seconds.
    local lower bound updated to 0.402038
    local upper bound updated to 0.406229

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 32.6904 seconds.
    local lower bound updated to 0.402038
    local upper bound updated to 0.405698

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0213 seconds.
    local lower bound updated to 0.402038
    local upper bound updated to 0.404887

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0211 seconds.
    local lower bound updated to 0.403108
    local upper bound updated to 0.404569

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0244 seconds.
    local lower bound updated to 0.403108
    local upper bound updated to 0.404249

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0216 seconds.
    local lower bound updated to 0.403108
    local upper bound updated to 0.404162

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0138 seconds.
    local lower bound updated to 0.403342
    local upper bound updated to 0.404155

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0146 seconds.
    local lower bound updated to 0.403342
    local upper bound updated to 0.40403

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0153 seconds.
    local lower bound updated to 0.403622
    local upper bound updated to 0.40399

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0157 seconds.
    local lower bound updated to 0.403622
    local upper bound updated to 0.403924

    ++ RESTRICTED PRIMAL ITERATION 13 ++
One worst-case parameter optimization takes 60.0148 seconds.
    local lower bound updated to 0.403622
    local upper bound updated to 0.403905

    ++ RESTRICTED PRIMAL ITERATION 14 ++
One worst-case parameter optimization takes 60.017 seconds.
    local lower bound updated to 0.403622
    local upper bound updated to 0.403874

    ++ RESTRICTED PRIMAL ITERATION 15 ++
One worst-case parameter optimization takes 60.0154 seconds.
    local lower bound updated to 0.403791
    local upper bound updated to 0.403861

    ++ RESTRICTED PRIMAL ITERATION 16 ++
One worst-case parameter optimization takes 60.0131 seconds.
    local lower bound updated to 0.403825
    local upper bound updated to 0.403849

    ++ RESTRICTED PRIMAL ITERATION 17 ++
One worst-case parameter optimization takes 60.0156 seconds.
    local lower bound updated to 0.403825
    local upper bound updated to 0.403848

    ++ RESTRICTED PRIMAL ITERATION 18 ++
One worst-case parameter optimization takes 60.0169 seconds.
    local lower bound updated to 0.403848
    local upper bound updated to 0.403848
The Primal step takes 992.256 (S)
lower bound updated to 0.403848

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.413326
    local lower bound updated to 0.404218

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.407084
    local lower bound updated to 0.404418

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.405155
    local lower bound updated to 0.404461

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.404461
    local lower bound updated to 0.404461
The Dual step takes 20.0985 (S)
upper bound updated to 0.404461
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0158 seconds.
    local lower bound updated to 0.356435
    local upper bound updated to 0.40443

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0173 seconds.
    local lower bound updated to 0.400079
    local upper bound updated to 0.404354

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0195 seconds.
    local lower bound updated to 0.403211
    local upper bound updated to 0.404244

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0172 seconds.
    local lower bound updated to 0.403537
    local upper bound updated to 0.404236

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.0311 seconds.
    local lower bound updated to 0.403762
    local upper bound updated to 0.404196

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 60.0169 seconds.
    local lower bound updated to 0.403825
    local upper bound updated to 0.404191

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 60.0162 seconds.
    local lower bound updated to 0.403873
    local upper bound updated to 0.404182

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 60.0178 seconds.
    local lower bound updated to 0.404001
    local upper bound updated to 0.404167

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 60.0248 seconds.
    local lower bound updated to 0.404128
    local upper bound updated to 0.404166

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 60.0162 seconds.
    local lower bound updated to 0.404153
    local upper bound updated to 0.404166

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 60.0161 seconds.
    local lower bound updated to 0.404153
    local upper bound updated to 0.404165

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 60.0186 seconds.
    local lower bound updated to 0.404165
    local upper bound updated to 0.404165
The Primal step takes 720.3 (S)
lower bound updated to 0.404165

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.410631
    local lower bound updated to 0.404165

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.404836
    local lower bound updated to 0.404188

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.404374
    local lower bound updated to 0.404193

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.404243
    local lower bound updated to 0.404193

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.404193
    local lower bound updated to 0.404193
The Dual step takes 40.6839 (S)
upper bound updated to 0.404193
*** OUTER ITERATION 5 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.0181 seconds.
    local lower bound updated to 0.359318
    local upper bound updated to 0.404193

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0216 seconds.
    local lower bound updated to 0.404106
    local upper bound updated to 0.404189

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0293 seconds.
    local lower bound updated to 0.404135
    local upper bound updated to 0.404185

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 60.0337 seconds.
    local lower bound updated to 0.404158
    local upper bound updated to 0.404185

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 60.021 seconds.
    local lower bound updated to 0.404185
    local upper bound updated to 0.404185
The Primal step takes 300.161 (S)
lower bound updated to 0.404185

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.411887
    local lower bound updated to 0.404185

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.404185
    local lower bound updated to 0.404185
The Dual step takes 19.4727 (S)
upper bound updated to 0.404185
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 60.019 seconds.
    local lower bound updated to 0.363757
    local upper bound updated to 0.404185

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 60.0196 seconds.
    local lower bound updated to 0.404168
    local upper bound updated to 0.404185

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 60.0246 seconds.
    local lower bound updated to 0.404185
    local upper bound updated to 0.404185
The time obtain the optimal randomized assortment is 2443.52 (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_19_4_60.000000_67720.log"
The computation time limit for a lower bound is 83547
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 3732 rows, 2730 columns and 12616 nonzeros
Model fingerprint: 0xe7502724
Variable types: 2657 continuous, 73 integer (73 binary)
Coefficient statistics:
  Matrix range     [1e-06, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [2e-01, 1e+00]
Presolve removed 728 rows and 1371 columns
Presolve time: 0.04s
Presolved: 3004 rows, 1359 columns, 11911 nonzeros
Variable types: 1292 continuous, 67 integer (67 binary)
Found heuristic solution: objective 0.5999681
Found heuristic solution: objective 0.5972208
Found heuristic solution: objective 0.4781557

Root relaxation: objective 3.330967e-01, 281 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    0.33310    0   26    0.47816    0.33310  30.3%     -    0s
H    0     0                       0.4433218    0.33310  24.9%     -    0s
     0     0    0.33410    0   32    0.44332    0.33410  24.6%     -    0s
H    0     0                       0.4377948    0.33410  23.7%     -    0s
H    0     0                       0.4348887    0.35028  19.5%     -    0s
     0     0    0.35028    0   32    0.43489    0.35028  19.5%     -    0s
H    0     0                       0.4163033    0.35043  15.8%     -    0s
     0     0    0.35043    0   32    0.41630    0.35043  15.8%     -    0s
     0     0    0.36131    0   34    0.41630    0.36131  13.2%     -    0s
H    0     0                       0.4085178    0.36131  11.6%     -    0s
H    0     0                       0.4043432    0.36164  10.6%     -    0s
     0     0    0.36164    0   34    0.40434    0.36164  10.6%     -    0s
     0     0    0.36779    0   34    0.40434    0.36779  9.04%     -    0s
     0     0    0.36849    0   36    0.40434    0.36849  8.87%     -    0s
     0     0    0.37009    0   35    0.40434    0.37009  8.47%     -    1s
H    0     0                       0.4041851    0.37009  8.43%     -    4s
     0     2    0.37009    0   35    0.40419    0.37009  8.43%     -    4s
    78    66     cutoff   14         0.40419    0.37123  8.15%  68.8    5s
H  460   281                       0.4041851    0.37769  6.56%  46.1    6s
  1084   510    0.38415   11   19    0.40419    0.37947  6.11%  40.2   10s
  1490   730    0.40222   17   13    0.40419    0.38078  5.79%  38.5   15s
  2093   928    0.38995   15   35    0.40419    0.38187  5.52%  35.9   21s
H 2104   888                       0.4041851    0.38187  5.52%  35.7   25s
  3083  1013    0.38978   28   17    0.40419    0.38301  5.24%  40.4   31s
  3387   993     cutoff   27         0.40419    0.38366  5.08%  40.2   35s
H 3604   938                       0.4041851    0.38399  5.00%  40.2   38s
  3979   927     cutoff   28         0.40419    0.38499  4.75%  39.8   40s
H 4170   853                       0.4041851    0.38534  4.66%  39.5   41s
  4238   857    0.39273   26   15    0.40419    0.38544  4.64%  39.7   45s
  4619   940    0.39800   25   14    0.40419    0.38595  4.51%  39.4   50s
  5388  1169    0.39922   30   14    0.40419    0.38653  4.37%  38.9   57s
H 5413  1169                       0.4041851    0.38653  4.37%  38.8   57s
H 5439  1169                       0.4041851    0.38653  4.37%  38.8   57s
  5635  1292    0.39187   30   14    0.40419    0.38679  4.30%  39.0   62s
  6155  1396    0.39858   24   17    0.40419    0.38715  4.21%  38.8   66s
H 6528  1443                       0.4041851    0.38747  4.13%  38.5   69s
  6566  1490    0.40302   28   10    0.40419    0.38750  4.13%  38.5   70s
  7397  1633    0.39175   18   22    0.40419    0.38817  3.96%  37.8   77s
  7719  1742    0.39543   27   14    0.40419    0.38835  3.92%  37.4   80s
  8712  1994    0.39883   28   10    0.40419    0.38900  3.76%  37.2   87s
H 9460  2086                       0.4041851    0.38926  3.69%  36.7   89s
  9718  2188    0.39624   31   13    0.40419    0.38944  3.65%  36.6   93s
 10263  2235    0.40075   30    9    0.40419    0.38976  3.57%  36.3   96s
 10525  2372    0.40004   28   12    0.40419    0.38990  3.53%  36.3  101s
 11996  2470    0.40245   24   15    0.40419    0.39046  3.39%  35.7  108s
 12450  2536    0.40408   26   13    0.40419    0.39050  3.38%  35.5  112s
 12938  2577    0.39730   27   10    0.40419    0.39079  3.31%  35.5  117s
 13290  2631     cutoff   32         0.40419    0.39103  3.26%  35.4  120s
 14466  2866     cutoff   32         0.40419    0.39141  3.16%  35.2  127s
 15536  2956    0.40185   23   18    0.40419    0.39175  3.08%  34.8  131s
 16470  3044    0.39564   25   20    0.40419    0.39208  3.00%  34.6  135s
 17612  3161    0.39929   32    9    0.40419    0.39243  2.91%  34.3  142s
 19284  3222    0.39909   27   10    0.40419    0.39289  2.79%  34.0  148s
 19946  3232    0.39481   23   16    0.40419    0.39301  2.76%  33.8  151s
 20561  3247     cutoff   20         0.40419    0.39325  2.70%  33.8  155s
 22736  3296     cutoff   32         0.40419    0.39368  2.60%  33.5  162s
 23631  3301    0.40258   27    9    0.40419    0.39394  2.54%  33.3  166s
 24794  3294     cutoff   27         0.40419    0.39429  2.45%  33.1  173s
 26462  3278    0.40404   36    7    0.40419    0.39466  2.36%  32.8  176s
 28116  3226 infeasible   26         0.40419    0.39496  2.28%  32.5  182s
 28663  3197    0.39864   30    9    0.40419    0.39517  2.23%  32.5  185s
 30659  3139    0.40284   31    6    0.40419    0.39563  2.12%  32.1  191s
H30990  3142                       0.4041851    0.39564  2.11%  32.1  194s
 31036  3109    0.39978   30    8    0.40419    0.39568  2.10%  32.1  197s
 31628  3045    0.40031   21   17    0.40419    0.39576  2.08%  32.0  200s
 32810  2966     cutoff   29         0.40419    0.39595  2.04%  31.8  206s
 33709  2874     cutoff   30         0.40419    0.39618  1.98%  31.7  210s
 34877  2743     cutoff   23         0.40419    0.39642  1.92%  31.6  216s
 36557  2619    0.40098   27   11    0.40419    0.39684  1.82%  31.4  223s
 36833  2574     cutoff   28         0.40419    0.39696  1.79%  31.4  225s
 38203  2407    0.39834   18   27    0.40419    0.39715  1.74%  31.2  230s
H38300  2407                       0.4041851    0.39715  1.74%  31.2  230s
 39658  2154    0.40385   28   11    0.40419    0.39758  1.63%  31.0  237s
 41264  1949    0.39889   28   13    0.40419    0.39796  1.54%  30.8  242s
 42168  1687     cutoff   27         0.40419    0.39826  1.47%  30.7  248s
 42647  1472     cutoff   31         0.40419    0.39842  1.43%  30.6  250s
H43730  1436                       0.4041851    0.39893  1.30%  30.5  253s
 43746  1310     cutoff   26         0.40419    0.39899  1.28%  30.5  255s
 45430   705    0.40275   26   13    0.40419    0.39993  1.05%  30.3  261s
 46080   469     cutoff   29         0.40419    0.40031  0.96%  30.2  265s

Cutting planes:
  Implied bound: 367
  MIR: 268
  Flow cover: 612
  RLT: 68
  Relax-and-lift: 158

Explored 47222 nodes (1415356 simplex iterations) in 266.69 seconds (293.74 work units)
Thread count was 4 (of 40 available processors)

Solution count 10: 0.404185 0.404185 0.404343 ... 0.597221

Optimal solution found (tolerance 1.00e-04)
Best objective 4.041851116267e-01, best bound 4.041851116267e-01, gap 0.0000%
The objective bound is 0.404185 while the objective upper bound is 0.404185

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.66 (ave)

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