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 0.231513 seconds.
    local lower bound updated to 0.236429
    local upper bound updated to 0.461082

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.248317 seconds.
    local lower bound updated to 0.436308
    local upper bound updated to 0.436308
The Primal step takes 0.482222 (S)
lower bound updated to 0.436308

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.666865
    local lower bound updated to 0.594368

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.641133
    local lower bound updated to 0.641133
The Dual step takes 0.0473965 (S)
upper bound updated to 0.641133
*** OUTER ITERATION 1 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 0.456924 seconds.
    local lower bound updated to 0.277454
    local upper bound updated to 0.448053

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.642753 seconds.
    local lower bound updated to 0.435036
    local upper bound updated to 0.436308

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 0.325364 seconds.
    local lower bound updated to 0.436308
    local upper bound updated to 0.436308
The Primal step takes 1.43128 (S)
lower bound updated to 0.436308

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.531889
    local lower bound updated to 0.453519

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.468329
    local lower bound updated to 0.463107

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.466847
    local lower bound updated to 0.464296

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.464296
    local lower bound updated to 0.464296
The Dual step takes 0.512017 (S)
upper bound updated to 0.464296
*** OUTER ITERATION 2 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.39591 seconds.
    local lower bound updated to 0.352543
    local upper bound updated to 0.462106

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 0.612311 seconds.
    local lower bound updated to 0.398466
    local upper bound updated to 0.444401

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 1.21515 seconds.
    local lower bound updated to 0.440746
    local upper bound updated to 0.443123

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 1.46835 seconds.
    local lower bound updated to 0.440746
    local upper bound updated to 0.442584

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 1.15454 seconds.
    local lower bound updated to 0.44101
    local upper bound updated to 0.441848

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 1.50109 seconds.
    local lower bound updated to 0.44101
    local upper bound updated to 0.441819

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 2.16296 seconds.
    local lower bound updated to 0.44101
    local upper bound updated to 0.441809

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 1.42331 seconds.
    local lower bound updated to 0.441035
    local upper bound updated to 0.44172

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 2.03221 seconds.
    local lower bound updated to 0.441584
    local upper bound updated to 0.441702

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 2.23496 seconds.
    local lower bound updated to 0.441701
    local upper bound updated to 0.441701
The Primal step takes 16.2333 (S)
lower bound updated to 0.441701

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.48704
    local lower bound updated to 0.443986

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.461028
    local lower bound updated to 0.455634

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.461028
    local lower bound updated to 0.456148

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.460114
    local lower bound updated to 0.456257

    ++ RESTRICTED DUAL ITERATION 5 ++
    local upper bound updated to 0.456878
    local lower bound updated to 0.456299

    ++ RESTRICTED DUAL ITERATION 6 ++
    local upper bound updated to 0.456299
    local lower bound updated to 0.456299
The Dual step takes 1.85972 (S)
upper bound updated to 0.456299
*** OUTER ITERATION 3 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 2.76518 seconds.
    local lower bound updated to 0.381225
    local upper bound updated to 0.456299

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 1.14193 seconds.
    local lower bound updated to 0.407605
    local upper bound updated to 0.448039

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 3.8637 seconds.
    local lower bound updated to 0.444324
    local upper bound updated to 0.447516

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 5.12915 seconds.
    local lower bound updated to 0.446163
    local upper bound updated to 0.44747

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 3.48395 seconds.
    local lower bound updated to 0.446163
    local upper bound updated to 0.447287

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 3.72017 seconds.
    local lower bound updated to 0.446163
    local upper bound updated to 0.447269

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 4.28243 seconds.
    local lower bound updated to 0.446316
    local upper bound updated to 0.447013

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 4.14364 seconds.
    local lower bound updated to 0.447013
    local upper bound updated to 0.447013
The Primal step takes 28.5706 (S)
lower bound updated to 0.447013

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.469168
    local lower bound updated to 0.447013

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.45372
    local lower bound updated to 0.448937

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.450839
    local lower bound updated to 0.4507

    ++ RESTRICTED DUAL ITERATION 4 ++
    local upper bound updated to 0.4507
    local lower bound updated to 0.4507
The Dual step takes 5.13466 (S)
upper bound updated to 0.4507
*** OUTER ITERATION 4 ***

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 4.19046 seconds.
    local lower bound updated to 0.39128
    local upper bound updated to 0.4507

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 2.51192 seconds.
    local lower bound updated to 0.430963
    local upper bound updated to 0.449772

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 5.50505 seconds.
    local lower bound updated to 0.444582
    local upper bound updated to 0.449414

    ++ RESTRICTED PRIMAL ITERATION 4 ++
One worst-case parameter optimization takes 12.5312 seconds.
    local lower bound updated to 0.447206
    local upper bound updated to 0.449368

    ++ RESTRICTED PRIMAL ITERATION 5 ++
One worst-case parameter optimization takes 6.98303 seconds.
    local lower bound updated to 0.448498
    local upper bound updated to 0.449293

    ++ RESTRICTED PRIMAL ITERATION 6 ++
One worst-case parameter optimization takes 8.08653 seconds.
    local lower bound updated to 0.448498
    local upper bound updated to 0.44926

    ++ RESTRICTED PRIMAL ITERATION 7 ++
One worst-case parameter optimization takes 11.7094 seconds.
    local lower bound updated to 0.448498
    local upper bound updated to 0.44921

    ++ RESTRICTED PRIMAL ITERATION 8 ++
One worst-case parameter optimization takes 9.25198 seconds.
    local lower bound updated to 0.448942
    local upper bound updated to 0.449193

    ++ RESTRICTED PRIMAL ITERATION 9 ++
One worst-case parameter optimization takes 11.1589 seconds.
    local lower bound updated to 0.44901
    local upper bound updated to 0.449189

    ++ RESTRICTED PRIMAL ITERATION 10 ++
One worst-case parameter optimization takes 11.5887 seconds.
    local lower bound updated to 0.449017
    local upper bound updated to 0.44918

    ++ RESTRICTED PRIMAL ITERATION 11 ++
One worst-case parameter optimization takes 9.36934 seconds.
    local lower bound updated to 0.449144
    local upper bound updated to 0.449169

    ++ RESTRICTED PRIMAL ITERATION 12 ++
One worst-case parameter optimization takes 9.00801 seconds.
    local lower bound updated to 0.449169
    local upper bound updated to 0.449169
The Primal step takes 101.982 (S)
lower bound updated to 0.449169

    ++ RESTRICTED DUAL ITERATION 1 ++
    local upper bound updated to 0.468674
    local lower bound updated to 0.449169

    ++ RESTRICTED DUAL ITERATION 2 ++
    local upper bound updated to 0.459724
    local lower bound updated to 0.449173

    ++ RESTRICTED DUAL ITERATION 3 ++
    local upper bound updated to 0.449173
    local lower bound updated to 0.449173
The Dual step takes 7.7725 (S)
upper bound updated to 0.449173
This is to get the final optimal randomized assortment

    ++ RESTRICTED PRIMAL ITERATION 1 ++
One worst-case parameter optimization takes 3.53795 seconds.
    local lower bound updated to 0.390296
    local upper bound updated to 0.449173

    ++ RESTRICTED PRIMAL ITERATION 2 ++
One worst-case parameter optimization takes 14.0609 seconds.
    local lower bound updated to 0.449119
    local upper bound updated to 0.449169

    ++ RESTRICTED PRIMAL ITERATION 3 ++
One worst-case parameter optimization takes 11.4968 seconds.
    local lower bound updated to 0.449169
    local upper bound updated to 0.449169
The time obtain the optimal randomized assortment is 193.143 (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_69916.log"
The computation time limit for a lower bound is 85803
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 2496 rows, 2008 columns and 8025 nonzeros
Model fingerprint: 0x7c708d3d
Variable types: 1951 continuous, 57 integer (57 binary)
Coefficient statistics:
  Matrix range     [2e-03, 1e+00]
  Objective range  [1e+00, 1e+00]
  Bounds range     [1e+00, 1e+00]
  RHS range        [4e-01, 1e+00]
Presolve removed 671 rows and 1209 columns
Presolve time: 0.03s
Presolved: 1825 rows, 799 columns, 7056 nonzeros
Variable types: 744 continuous, 55 integer (55 binary)
Found heuristic solution: objective 0.5547804
Found heuristic solution: objective 0.5040623

Root relaxation: objective 3.393806e-01, 241 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    0.33938    0   22    0.50406    0.33938  32.7%     -    0s
     0     0    0.34726    0   26    0.50406    0.34726  31.1%     -    0s
     0     0    0.38803    0   23    0.50406    0.38803  23.0%     -    0s
H    0     0                       0.4675574    0.38803  17.0%     -    0s
     0     0    0.38901    0   23    0.46756    0.38901  16.8%     -    0s
H    0     0                       0.4634122    0.38901  16.1%     -    0s
H    0     0                       0.4547751    0.39850  12.4%     -    0s
     0     0    0.39850    0   23    0.45478    0.39850  12.4%     -    0s
     0     0    0.39959    0   22    0.45478    0.39959  12.1%     -    0s
H    0     0                       0.4546484    0.39959  12.1%     -    0s
H    0     0                       0.4545171    0.39959  12.1%     -    0s
     0     0    0.40609    0   23    0.45452    0.40609  10.7%     -    0s
     0     0    0.40695    0   23    0.45452    0.40695  10.5%     -    0s
     0     0    0.40885    0   24    0.45452    0.40885  10.0%     -    0s
H    0     0                       0.4534312    0.40885  9.83%     -    0s
H    0     0                       0.4505089    0.40885  9.25%     -    1s
     0     2    0.40885    0   24    0.45051    0.40885  9.25%     -    1s
H  300   148                       0.4491693    0.41608  7.37%  38.2    2s
H  731   212                       0.4491693    0.42406  5.59%  33.4    4s
  1300   292    0.43421    8   12    0.44917    0.42793  4.73%  31.8    5s
H 1303   292                       0.4491693    0.42793  4.73%  31.8    5s
  3761   297    0.44256   10    8    0.44917    0.43732  2.64%  26.8   10s

Cutting planes:
  Implied bound: 292
  MIR: 112
  Flow cover: 284
  RLT: 20
  Relax-and-lift: 115

Explored 5047 nodes (127332 simplex iterations) in 11.30 seconds (7.70 work units)
Thread count was 4 (of 48 available processors)

Solution count 10: 0.449169 0.449169 0.449169 ... 0.467557

Optimal solution found (tolerance 1.00e-04)
Best objective 4.491693117277e-01, best bound 4.491693117277e-01, gap 0.0000%
The objective bound is 0.449169 while the objective upper bound is 0.449169

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

        Job resource usage summary 

                 Memory (GB)    NCPUs
 Requested  :        12             4
 Used       :         0 (peak)   3.15 (ave)

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