Default values NumericFocus and ScaleFlag

Dear Gurobi experts,

I see some strange behaviour when using NumericFocus and ScaleFlag. I use two different sets of parameters (see [1]). The first set does not use NumericFocus and ScaleFlag. The second set sets NumericFocus and ScaleFlag to their default values, namely 0 and 1, respectively.

To my understanding their should be no difference in the two runs. However, I see huge differences (see [2]). Also the run time differs from 155.35 seconds to 75.75 seconds.

Do you have any explanation for this? Are the default values in my Gurobi version 8.0.0 different from those in the web documentation?

Thank you!
Henrik Büsing

[1]

Parameter set 1:
gurobi_cl seed=0 Crossover=-1 threads=48 method=2 NodeMethod=1 Cuts=-1 MipFocus=2 MILP_Binaer8regions_7typDays.mps

Parameter set 2:
gurobi_cl seed=0 Crossover=-1 threads=48 method=2 NodeMethod=1 Cuts=-1 MipFocus=2 NumericFocus=0 ScaleFlag=1 MILP_Binaer8regions_7typDays.mps

[2]

Parameter set 1:

(OK) Loading MATH environment
(OK) Loading gurobi 8.0.0
Set parameter seed to value 0
Set parameter Crossover to value -1
Set parameter threads to value 48
Set parameter method to value 2
Set parameter NodeMethod to value 1
Set parameter Cuts to value -1
Set parameter MipFocus to value 2

Gurobi Optimizer version 8.0.0 build v8.0.0rc0 (linux64)
Copyright (c) 2018, Gurobi Optimization, LLC

Read MPS format model from file MILP_Binaer8regions_7typDays.mps
Reading time = 0.73 seconds
unknown: 82777 rows, 53802 columns, 251889 nonzeros
Optimize a model with 82777 rows, 53802 columns and 251889 nonzeros
Variable types: 53679 continuous, 123 integer (123 binary)
Coefficient statistics:
Matrix range [8e-07, 5e+02]
Objective range [2e-06, 3e-01]
Bounds range [1e+00, 6e+04]
RHS range [4e-02, 2e+01]
Presolve removed 24632 rows and 16504 columns
Presolve time: 0.40s
Presolved: 58145 rows, 37298 columns, 196306 nonzeros
Variable types: 37233 continuous, 65 integer (65 binary)
Presolve removed 65 rows and 65 columns
Presolved: 58080 rows, 37233 columns, 196176 nonzeros

Root barrier log...

Ordering time: 0.83s

Barrier statistics:
Dense cols : 150
AA' NZ : 1.417e+06
Factor NZ : 6.194e+06 (roughly 90 MBytes of memory)
Factor Ops : 2.049e+09 (less than 1 second per iteration)
Threads : 48

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 2.07191146e+05 -1.48388905e+06 3.56e+05 2.44e-03 1.11e+03 2s
1 1.94219922e+05 -1.47590781e+06 2.56e+05 9.71e-02 7.37e+02 2s
2 9.98486673e+04 -1.22817999e+06 1.06e+05 8.74e-03 3.46e+02 2s
3 3.56441614e+04 -7.26786320e+05 3.54e+04 1.79e-04 1.02e+02 2s
4 1.87622166e+04 -4.40847970e+05 7.64e+03 1.06e-12 2.49e+01 2s
5 9.03443590e+03 -2.15460204e+05 2.67e+03 7.49e-13 8.59e+00 2s
6 4.10159558e+03 -8.75573213e+04 9.46e+02 7.50e-13 2.83e+00 3s
7 1.46077521e+03 -4.43101283e+04 1.67e+02 2.87e-13 7.43e-01 3s
8 7.85414472e+02 -2.09133281e+04 1.31e+01 6.74e-13 2.47e-01 3s
9 4.46340340e+02 -8.68158041e+03 7.91e-01 2.10e-13 9.70e-02 3s
10 2.99273108e+02 -4.11788974e+03 3.03e-01 1.37e-13 4.21e-02 3s
11 2.01805505e+02 -9.94606271e+02 3.43e-02 7.87e-13 1.03e-02 3s
12 1.67742720e+02 -4.45282910e+02 1.05e-02 3.81e-13 5.19e-03 3s
13 1.47252850e+02 -2.01950660e+02 5.25e-03 2.05e-13 2.95e-03 3s
14 1.40369300e+02 -1.92143822e+02 4.06e-03 1.96e-13 2.81e-03 3s
15 1.34352448e+02 -1.59104484e+02 3.26e-03 1.72e-13 2.48e-03 3s
16 1.25842815e+02 -1.39599191e+02 2.42e-03 1.56e-13 2.24e-03 3s
17 1.10712940e+02 -3.04724529e+01 1.60e-03 5.23e-14 1.19e-03 3s
18 9.59728238e+01 2.04359956e+01 9.18e-04 5.77e-14 6.37e-04 3s
19 8.72145372e+01 3.63504849e+01 5.42e-04 5.09e-14 4.29e-04 3s
20 8.26045387e+01 4.27669613e+01 3.53e-04 4.12e-14 3.36e-04 3s
21 7.97121768e+01 5.25305488e+01 2.35e-04 3.44e-14 2.29e-04 3s
22 7.83264173e+01 5.50593542e+01 1.83e-04 3.18e-14 1.96e-04 4s
23 7.72185567e+01 6.24231180e+01 1.41e-04 2.68e-14 1.25e-04 4s
24 7.63012912e+01 6.50581624e+01 1.09e-04 1.99e-14 9.48e-05 4s
25 7.55049173e+01 6.65356741e+01 8.12e-05 2.35e-14 7.56e-05 4s
26 7.50533085e+01 6.77867240e+01 6.44e-05 3.03e-14 6.13e-05 4s
27 7.47138607e+01 6.98861533e+01 5.21e-05 2.88e-14 4.07e-05 4s
28 7.41269017e+01 7.10722993e+01 2.58e-05 2.41e-14 2.57e-05 4s
29 7.39835719e+01 7.13440331e+01 2.06e-05 3.66e-14 2.22e-05 4s
30 7.37725532e+01 7.19336049e+01 1.22e-05 1.33e-14 1.55e-05 4s
31 7.37192721e+01 7.23390372e+01 9.88e-06 1.78e-14 1.16e-05 4s
32 7.37109290e+01 7.24397195e+01 9.53e-06 1.69e-14 1.07e-05 4s
33 7.36118380e+01 7.27085062e+01 5.64e-06 7.51e-15 7.61e-06 4s
34 7.35863396e+01 7.28368950e+01 4.67e-06 6.19e-15 6.32e-06 4s
35 7.35726751e+01 7.28923243e+01 4.14e-06 5.42e-15 5.73e-06 4s
36 7.35544484e+01 7.29445730e+01 3.25e-06 5.08e-15 5.14e-06 4s
37 7.35266207e+01 7.31255884e+01 1.87e-06 4.44e-15 3.38e-06 4s
38 7.35071381e+01 7.33158385e+01 1.03e-06 1.35e-14 1.61e-06 4s
39 7.34929789e+01 7.34034171e+01 4.33e-07 2.71e-13 7.55e-07 5s
40 7.34905453e+01 7.34327693e+01 3.48e-07 5.45e-13 4.87e-07 5s
41 7.34860943e+01 7.34553216e+01 1.99e-07 1.19e-12 2.59e-07 5s
42 7.34842822e+01 7.34626569e+01 1.45e-07 1.27e-12 1.82e-07 5s
43 7.34839166e+01 7.34651207e+01 1.34e-07 1.48e-12 1.58e-07 5s
44 7.34818868e+01 7.34671533e+01 7.33e-08 2.97e-12 1.24e-07 5s
45 7.34809433e+01 7.34712892e+01 4.65e-08 1.37e-11 8.14e-08 5s
46 7.34804257e+01 7.34729575e+01 3.59e-08 2.70e-11 6.29e-08 5s
47 7.34801003e+01 7.34741989e+01 3.71e-08 2.46e-11 4.97e-08 5s
48 7.34798717e+01 7.34750985e+01 3.28e-08 1.84e-11 4.02e-08 5s
49 7.34797575e+01 7.34764649e+01 2.77e-08 1.07e-11 2.78e-08 5s
50 7.34795537e+01 7.34769123e+01 1.89e-08 9.03e-12 2.23e-08 5s
51 7.34793798e+01 7.34773969e+01 1.06e-08 6.95e-12 1.67e-08 5s
52 7.34792717e+01 7.34778663e+01 6.60e-09 7.52e-12 1.19e-08 5s
53 7.34792030e+01 7.34785523e+01 3.91e-09 1.30e-11 5.49e-09 5s
54 7.34791903e+01 7.34786593e+01 6.34e-09 1.93e-11 4.49e-09 6s
55 7.34791847e+01 7.34787376e+01 2.37e-07 2.41e-11 3.79e-09 6s
56 7.34791102e+01 7.34790121e+01 3.35e-08 4.49e-11 8.68e-10 6s
57 7.34791053e+01 7.34790537e+01 8.19e-07 4.25e-11 4.69e-10 6s
58 7.34791028e+01 7.34790713e+01 8.44e-07 3.98e-11 2.94e-10 6s
59 7.34790985e+01 7.34790826e+01 5.38e-07 3.83e-11 1.60e-10 6s
60 7.34790974e+01 7.34790870e+01 6.51e-07 3.59e-11 1.11e-10 6s
61 7.34790974e+01 7.34790870e+01 1.13e-06 3.58e-11 1.11e-10 6s
62 7.34790973e+01 7.34790870e+01 1.13e-06 3.58e-11 1.11e-10 6s
63 7.34790973e+01 7.34790870e+01 1.13e-06 3.58e-11 1.11e-10 6s
64 7.34790973e+01 7.34790870e+01 1.13e-06 3.58e-11 1.11e-10 6s
65 7.34790957e+01 7.34790883e+01 5.90e-07 5.83e-09 8.47e-11 6s
66 7.34790939e+01 7.34790924e+01 1.46e-07 2.36e-09 3.35e-11 7s
67 7.34790939e+01 7.34790924e+01 1.46e-07 2.36e-09 3.35e-11 7s
68 7.34790939e+01 7.34790923e+01 2.54e-07 4.29e-09 3.34e-11 7s
69 7.34790939e+01 7.34790922e+01 2.38e-07 1.20e-07 3.16e-11 7s

Barrier solved model in 69 iterations and 6.88 seconds
Optimal objective 7.34790939e+01

Root crossover log...

11082 DPushes remaining with DInf 1.6892464e-04 7s
0 DPushes remaining with DInf 2.6494613e-14 8s

12875 PPushes remaining with PInf 9.2844638e-06 8s
0 PPushes remaining with PInf 1.8429318e-05 9s

Push phase complete: Pinf 1.8429318e-05, Dinf 5.6550335e-01 9s

Root simplex log...

Iteration Objective Primal Inf. Dual Inf. Time
18804 7.3479094e+01 0.000000e+00 5.655033e-01 9s
18837 7.3479094e+01 0.000000e+00 0.000000e+00 9s
18837 7.3479094e+01 0.000000e+00 0.000000e+00 9s

Root relaxation: objective 7.347909e+01, 18837 iterations, 8.74 seconds

Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

0 0 73.47909 0 32 - 73.47909 - - 10s
H 0 0 73.5089179 73.47909 0.04% - 12s
H 0 0 73.5051135 73.47909 0.04% - 24s
H 0 0 73.5051113 73.48296 0.03% - 24s
0 0 73.48447 0 25 73.50511 73.48447 0.03% - 25s
0 0 73.48641 0 22 73.50511 73.48641 0.03% - 37s
0 0 73.48776 0 20 73.50511 73.48776 0.02% - 49s
0 0 73.48931 0 21 73.50511 73.48931 0.02% - 68s
0 0 73.49046 0 17 73.50511 73.49046 0.02% - 83s
0 0 73.49081 0 17 73.50511 73.49081 0.02% - 100s
H 0 0 73.5046206 73.49081 0.02% - 103s
H 0 0 73.5042500 73.49081 0.02% - 111s
0 0 73.49114 0 15 73.50425 73.49114 0.02% - 111s
0 0 73.49134 0 16 73.50425 73.49134 0.02% - 125s
0 0 73.49140 0 15 73.50425 73.49140 0.02% - 139s
H 0 0 73.5020323 73.49140 0.01% - 139s
H 0 0 73.4987906 73.49140 0.01% - 155s
H 0 0 73.4944707 73.49140 0.00% - 155s
H 0 0 73.4944643 73.49140 0.00% - 155s
0 0 73.49140 0 16 73.49446 73.49140 0.00% - 155s

Cutting planes:
Gomory: 10
Implied bound: 144
MIR: 339
Flow cover: 2217

Explored 1 nodes (58736 simplex iterations) in 155.35 seconds
Thread count was 48 (of 48 available processors)

Solution count 9: 73.4945 73.4945 73.4988 ... 73.5089

Optimal solution found (tolerance 1.00e-04)
Warning: max constraint violation (5.1285e-06) exceeds tolerance
Best objective 7.349446428785e+01, best bound 7.349140350684e+01, gap 0.0042%

Parameter set 2:

(OK) Loading MATH environment
(OK) Loading gurobi 8.0.0
Set parameter seed to value 0
Set parameter Crossover to value -1
Set parameter threads to value 48
Set parameter method to value 2
Set parameter NodeMethod to value 1
Set parameter Cuts to value -1
Set parameter MipFocus to value 2
Set parameter NumericFocus to value 0
Set parameter ScaleFlag to value 1

Gurobi Optimizer version 8.0.0 build v8.0.0rc0 (linux64)
Copyright (c) 2018, Gurobi Optimization, LLC

Read MPS format model from file MILP_Binaer8regions_7typDays.mps
Reading time = 0.26 seconds
unknown: 82777 rows, 53802 columns, 251889 nonzeros
Optimize a model with 82777 rows, 53802 columns and 251889 nonzeros
Variable types: 53679 continuous, 123 integer (123 binary)
Coefficient statistics:
Matrix range [8e-07, 5e+02]
Objective range [2e-06, 3e-01]
Bounds range [1e+00, 6e+04]
RHS range [4e-02, 2e+01]
Presolve removed 24632 rows and 16504 columns
Presolve time: 0.40s
Presolved: 58145 rows, 37298 columns, 196306 nonzeros
Variable types: 37233 continuous, 65 integer (65 binary)
Presolve removed 65 rows and 65 columns
Presolved: 58080 rows, 37233 columns, 196176 nonzeros

Root barrier log...

Ordering time: 0.83s

Barrier statistics:
Dense cols : 150
AA' NZ : 1.417e+06
Factor NZ : 6.194e+06 (roughly 90 MBytes of memory)
Factor Ops : 2.049e+09 (less than 1 second per iteration)
Threads : 48

Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 2.86869147e+05 -2.78944512e+06 4.39e+05 4.95e-04 2.51e+03 2s
1 2.76845163e+05 -2.65785928e+06 2.82e+05 1.76e-02 1.45e+03 2s
2 1.21514857e+05 -1.97927738e+06 7.47e+04 4.18e-13 4.43e+02 2s
3 7.21189299e+04 -9.91413312e+05 1.89e+04 5.73e-13 1.23e+02 2s
4 2.90528649e+04 -5.74554206e+05 6.65e+03 3.65e-13 3.79e+01 2s
5 1.88657427e+04 -3.38763714e+05 4.15e+03 4.11e-13 1.98e+01 2s
6 9.24562448e+03 -1.59167168e+05 1.36e+03 2.10e-13 6.76e+00 2s
7 2.76975107e+03 -8.63504560e+04 2.58e+02 1.32e-13 1.69e+00 3s
8 1.23209751e+03 -2.88011206e+04 6.08e+01 1.50e-13 4.48e-01 3s
9 6.16794883e+02 -1.62749203e+04 8.09e+00 1.49e-13 1.83e-01 3s
10 4.87818115e+02 -1.05537911e+04 3.13e+00 7.98e-14 1.16e-01 3s
11 3.64440632e+02 -3.82945186e+03 1.81e+00 3.16e-14 4.35e-02 3s
12 2.59964643e+02 -1.56857622e+03 7.65e-01 1.36e-14 1.72e-02 3s
13 1.89053625e+02 -8.74936737e+02 2.27e-01 7.58e-15 9.31e-03 3s
14 1.73131885e+02 -6.25047809e+02 1.44e-01 5.61e-15 6.89e-03 3s
15 1.56947258e+02 -4.09185593e+02 8.24e-02 3.94e-15 4.84e-03 3s
16 1.36479365e+02 -2.25241692e+02 4.90e-02 2.44e-15 3.08e-03 3s
17 1.15617773e+02 -8.44114645e+01 2.79e-02 1.07e-15 1.70e-03 3s
18 1.01791269e+02 -1.28270711e+01 1.65e-02 6.66e-16 9.71e-04 3s
19 9.29206651e+01 2.79591290e+01 1.09e-02 3.61e-16 5.50e-04 3s
20 8.52163099e+01 3.93346957e+01 6.45e-03 3.82e-10 3.88e-04 3s
21 8.30266824e+01 4.85721056e+01 5.19e-03 3.06e-09 2.91e-04 3s
22 8.06521897e+01 5.23439105e+01 3.92e-03 4.26e-09 2.39e-04 3s
23 7.84330989e+01 6.21955728e+01 2.71e-03 6.14e-09 1.37e-04 3s
24 7.68831959e+01 6.42743346e+01 1.89e-03 6.11e-09 1.07e-04 4s
25 7.58937214e+01 6.72748229e+01 1.36e-03 5.37e-09 7.29e-05 4s
26 7.52737447e+01 6.91614837e+01 1.02e-03 4.47e-09 5.17e-05 4s
27 7.46455504e+01 7.11563702e+01 6.67e-04 2.86e-09 2.95e-05 4s
28 7.41079121e+01 7.22057370e+01 3.61e-04 2.00e-09 1.61e-05 4s
29 7.39297137e+01 7.26100545e+01 2.66e-04 1.42e-09 1.12e-05 4s
30 7.38391686e+01 7.28083291e+01 2.15e-04 1.12e-09 8.73e-06 4s
31 7.37893188e+01 7.29818758e+01 1.87e-04 8.39e-10 6.84e-06 4s
32 7.37146918e+01 7.31127453e+01 1.45e-04 6.21e-10 5.10e-06 4s
33 7.36516283e+01 7.32277970e+01 1.05e-04 4.43e-10 3.59e-06 4s
34 7.36239440e+01 7.32764579e+01 8.92e-05 3.71e-10 2.94e-06 4s
35 7.35703617e+01 7.33810824e+01 5.72e-05 2.10e-10 1.61e-06 4s
36 7.35442768e+01 7.34137410e+01 4.11e-05 1.53e-10 1.11e-06 4s
37 7.35249443e+01 7.34236008e+01 2.97e-05 1.32e-10 8.60e-07 4s
38 7.35082607e+01 7.34538957e+01 1.86e-05 5.14e-11 4.62e-07 4s
39 7.35019875e+01 7.34660758e+01 1.46e-05 1.26e-10 3.06e-07 4s
40 7.34992490e+01 7.34672934e+01 1.29e-05 1.36e-10 2.72e-07 4s
41 7.34943259e+01 7.34718885e+01 9.68e-06 1.52e-10 1.91e-07 5s
42 7.34910192e+01 7.34742640e+01 7.55e-06 1.91e-10 1.43e-07 5s
43 7.34883910e+01 7.34761713e+01 5.89e-06 2.21e-10 1.05e-07 5s
44 7.34866472e+01 7.34770376e+01 4.84e-06 2.26e-10 8.26e-08 5s
45 7.34824158e+01 7.34779471e+01 2.28e-06 2.50e-10 3.90e-08 5s
46 7.34817496e+01 7.34784206e+01 1.81e-06 1.88e-10 2.91e-08 5s
47 7.34815805e+01 7.34784360e+01 1.69e-06 1.85e-10 2.76e-08 5s
48 7.34811309e+01 7.34786104e+01 1.37e-06 1.77e-10 2.22e-08 5s
49 7.34805176e+01 7.34787444e+01 9.44e-07 1.55e-10 1.58e-08 5s
50 7.34798828e+01 7.34788985e+01 5.61e-07 1.72e-10 9.20e-09 5s
51 7.34795645e+01 7.34790305e+01 3.22e-07 1.88e-10 5.49e-09 5s
52 7.34793973e+01 7.34791671e+01 2.03e-07 1.84e-10 3.00e-09 5s
53 7.34793317e+01 7.34792132e+01 1.55e-07 1.83e-10 2.10e-09 5s
54 7.34791798e+01 7.34792426e+01 4.37e-08 1.81e-10 6.34e-10 5s
55 7.34791294e+01 7.34792578e+01 6.41e-08 1.77e-10 1.61e-10 5s
56 7.34791200e+01 7.34792603e+01 9.60e-07 1.76e-10 9.06e-11 5s
57 7.34791195e+01 7.34792603e+01 9.35e-07 1.76e-10 8.81e-11 6s
58 7.34791126e+01 7.34792598e+01 5.78e-07 1.76e-10 5.75e-11 6s
59 7.34791104e+01 7.34792597e+01 4.91e-07 1.76e-10 4.96e-11 6s
60 7.34791086e+01 7.34792605e+01 4.28e-07 1.74e-10 4.14e-11 6s
61 7.34791085e+01 7.34792594e+01 4.24e-07 1.72e-10 4.09e-11 6s
62 7.34791080e+01 7.34792438e+01 3.93e-07 1.48e-10 3.72e-11 6s
63 7.34791080e+01 7.34792438e+01 1.14e-06 1.48e-10 3.72e-11 6s
64 7.34791064e+01 7.34792522e+01 8.81e-07 9.09e-09 2.98e-11 6s
65 7.34791061e+01 7.34792479e+01 8.38e-07 8.55e-09 2.96e-11 6s
66 7.34791052e+01 7.34792438e+01 7.38e-07 7.74e-09 2.61e-11 6s
67 7.34791044e+01 7.34792416e+01 6.71e-07 4.17e-09 2.30e-11 6s
68 7.34791027e+01 7.34792413e+01 5.40e-07 3.38e-09 1.91e-11 6s
69 7.34791026e+01 7.34792339e+01 4.85e-07 3.05e-09 1.74e-11 6s
70 7.34791025e+01 7.34792263e+01 8.65e-07 2.74e-09 1.63e-11 6s
71 7.34791021e+01 7.34792255e+01 7.88e-07 2.69e-09 1.50e-11 7s
72 7.34791017e+01 7.34792276e+01 7.32e-07 2.43e-09 1.41e-11 7s

Barrier solved model in 72 iterations and 6.64 seconds
Optimal objective 7.34791080e+01

Root crossover log...

9137 DPushes remaining with DInf 1.0794260e-02 7s
0 DPushes remaining with DInf 4.8824961e-15 8s

14456 PPushes remaining with PInf 3.2760484e-01 8s
0 PPushes remaining with PInf 8.3441806e-05 9s

Push phase complete: Pinf 8.3441806e-05, Dinf 1.8644110e+00 9s

Root simplex log...

Iteration Objective Primal Inf. Dual Inf. Time
19401 7.3479422e+01 0.000000e+00 1.864411e+00 9s
19700 7.3479100e+01 0.000000e+00 0.000000e+00 10s
19700 7.3479100e+01 0.000000e+00 0.000000e+00 10s

Root relaxation: objective 7.347910e+01, 19700 iterations, 9.38 seconds
Total elapsed time = 10.16s

Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

0 0 73.47910 0 28 - 73.47910 - - 11s
H 0 0 73.5040862 73.47910 0.03% - 12s
H 0 0 73.5040856 73.47910 0.03% - 12s
H 0 0 73.4997918 73.48296 0.02% - 23s
0 0 73.48443 0 25 73.49979 73.48443 0.02% - 24s
0 0 73.48525 0 21 73.49979 73.48525 0.02% - 33s
0 0 73.48807 0 19 73.49979 73.48807 0.02% - 44s
0 0 73.48953 0 14 73.49979 73.48953 0.01% - 51s
0 0 73.49114 0 21 73.49979 73.49114 0.01% - 60s
0 0 73.49123 0 23 73.49979 73.49123 0.01% - 68s
0 0 73.49286 0 19 73.49979 73.49286 0.01% - 75s

Cutting planes:
Gomory: 7
Implied bound: 100
MIR: 373
Flow cover: 2285

Explored 1 nodes (41815 simplex iterations) in 75.75 seconds
Thread count was 48 (of 48 available processors)

Solution count 3: 73.4998 73.5041 73.5041

Optimal solution found (tolerance 1.00e-04)
Best objective 7.349979181492e+01, best bound 7.349285949007e+01, gap 0.0094%