Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.06 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Statistics for model UNKNOWN:
Linear constraint matrix : 365 Constrs, 311 Vars, 5668 NZs
Variable types : 260 Continuous,
51 Integer
Quadratic constraints : 2 Constrs, 104 NZs
Matrix coefficient range : [ 7.93393e-06, 1.19315 ]
Objective coefficient range : [ 1, 1 ]
Variable bound range : [ 0, 0 ]
RHS coefficient range : [ 0.2, 11 ]MISOCP Example with Portfolio Optimization
Gurobi Live Barcelona
Pierre Bonami - Gurobi
Portfolio optimization
- Model proposed by Markowitz in 1952
- Foundation of modern portfolio optimization
\[ \begin{aligned} & \max \mu^T x - \gamma \frac{x^T \Sigma x}{2} \\ & \text{s.t.}\\ & \sum_{i=1}^n x_i = 1\\ & x \ge 0 \end{aligned} \]
- \(\mu\): vector of expected returns, \(\Sigma\): return covariance matrix
- \(x\) represents the fraction of wealth invested in each asset
- \(\gamma \geq 0\) is the risk aversion coefficient (fixed parameter)
Robust portfolio optimization with cardinality constraint
The basic problem has many variants used in practice and is one of the main applications for MISOCP.
Here we use in particular an instance constructed by Vielma (2008) with:
- A cardinality constraint on the number of assets that can be held in the portfolio
- A second order cone constraint to mitigate errors in estimation of variance.
Statistics of the model
(note: formulation is slightly different and objective is put in constraints)
Solve the model with QCP branch-and-bound
Set MIQCPMethod to 0 and optimize
Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.03 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Set parameter MIQCPMethod to value 0
Gurobi Optimizer version 11.0.0 build v11.0.0beta2 (mac64[x86] - macOS 13.6 22G120)
CPU model: Intel(R) Core(TM) i5-1038NG7 CPU @ 2.00GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 365 rows, 311 columns and 5668 nonzeros
Model fingerprint: 0x97dee3ae
Model has 2 quadratic constraints
Variable types: 260 continuous, 51 integer (0 binary)
Coefficient statistics:
Matrix range [8e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-01, 1e+01]
Presolve removed 211 rows and 108 columns
Presolve time: 0.02s
Presolved: 156 rows, 303 columns, 5447 nonzeros
Presolved model has 100 quadratic constraint(s)
Variable types: 252 continuous, 51 integer (51 binary)
Root relaxation presolve removed 51 rows and 51 columns
Root relaxation presolve time: 0.03s
Root relaxation presolved: 484 rows, 452 columns, 6024 nonzeros
Root relaxation presolved model has 100 second-order cone constraints
Root barrier log...
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 1.132e+04
Factor NZ : 1.700e+04 (roughly 1 MB of memory)
Factor Ops : 1.523e+06 (less than 1 second per iteration)
Threads : 4
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -8.14250076e+00 -2.35798354e+01 3.97e+02 1.38e-01 7.21e-01 0s
1 -5.02961303e-01 -2.00521636e+01 1.65e+02 4.16e-05 2.81e-01 0s
2 -3.52687244e-02 -8.78839737e+00 5.94e+00 4.58e-11 1.92e-02 0s
3 -5.09534423e-02 -1.49533942e+00 4.13e-01 4.16e-12 2.21e-03 0s
4 -6.33437696e-02 -3.92751355e-01 4.98e-02 6.75e-13 4.48e-04 0s
5 -7.49835377e-02 -1.75071373e-01 3.63e-03 1.84e-13 1.29e-04 0s
6 -8.19839145e-02 -1.22785145e-01 6.12e-04 7.35e-14 5.21e-05 0s
7 -8.50406435e-02 -8.91071375e-02 7.18e-05 4.77e-15 5.20e-06 0s
8 -8.58100110e-02 -8.60277556e-02 7.90e-11 1.58e-15 2.77e-07 0s
9 -8.58566172e-02 -8.58659752e-02 3.07e-11 2.80e-14 1.19e-08 0s
10 -8.58618793e-02 -8.58624582e-02 2.84e-09 4.91e-13 7.37e-10 0s
Barrier solved model in 10 iterations and 0.07 seconds (0.03 work units)
Optimal objective -8.58618793e-02
Root relaxation: objective -8.586188e-02, 0 iterations, 0.04 seconds (0.01 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 -0.08586 0 13 - -0.08586 - - 0s
0 0 -0.08586 0 51 - -0.08586 - - 0s
0 0 -0.08586 0 51 - -0.08586 - - 0s
0 0 -0.08586 0 51 - -0.08586 - - 0s
0 2 -0.08586 0 51 - -0.08586 - - 0s
H 194 202 0.0000000 -0.08586 - 0.0 1s
H 204 200 -0.0573676 -0.08586 49.7% 0.0 1s
H 242 221 -0.0835976 -0.08586 2.71% 0.0 1s
H 288 192 -0.0836875 -0.08586 2.60% 0.0 1s
H 289 192 -0.0854908 -0.08586 0.43% 0.0 1s
H 290 192 -0.0854909 -0.08586 0.43% 0.0 1s
* 316 173 14 -0.0854910 -0.08586 0.43% 0.0 1s
H 359 162 -0.0856168 -0.08586 0.29% 0.0 1s
* 390 137 14 -0.0856169 -0.08586 0.29% 0.0 2s
* 447 127 18 -0.0856170 -0.08586 0.29% 0.0 2s
* 478 127 15 -0.0856173 -0.08586 0.29% 0.0 2s
* 482 127 34 -0.0856889 -0.08586 0.20% 0.0 2s
* 506 107 35 -0.0856930 -0.08586 0.20% 0.0 2s
* 511 107 35 -0.0856950 -0.08586 0.19% 0.0 2s
Cutting planes:
MIR: 4
Flow cover: 4
Explored 618 nodes (0 simplex iterations) in 2.47 seconds (3.55 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: -0.085695 -0.085693 -0.0856889 ... -0.0836875
Optimal solution found (tolerance 1.00e-04)
Warning: max constraint violation (1.1084e-06) exceeds tolerance
Best objective -8.569500013891e-02, best bound -8.569500013891e-02, gap 0.0000%Remarks
- Initial relaxation value is
-0.08586 - Not improved during the root
- Solution has a violation slightly above the default
1.1084e-06
Solve the model with OA branch-and-cut
Set MIQCPMethod to 1 and optimize
Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.03 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Set parameter MIQCPMethod to value 1
Gurobi Optimizer version 11.0.0 build v11.0.0beta2 (mac64[x86] - macOS 13.6 22G120)
CPU model: Intel(R) Core(TM) i5-1038NG7 CPU @ 2.00GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 365 rows, 311 columns and 5668 nonzeros
Model fingerprint: 0x97dee3ae
Model has 2 quadratic constraints
Variable types: 260 continuous, 51 integer (0 binary)
Coefficient statistics:
Matrix range [8e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-01, 1e+01]
Presolve removed 211 rows and 108 columns
Presolve time: 0.01s
Presolved: 156 rows, 303 columns, 5447 nonzeros
Presolved model has 100 quadratic constraint(s)
Variable types: 252 continuous, 51 integer (51 binary)
Root relaxation: objective -2.020047e-01, 108 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 -0.20200 0 - - -0.20200 - - 0s
0 0 -0.14578 0 - - -0.14578 - - 0s
0 0 -0.11167 0 2 - -0.11167 - - 0s
0 0 -0.09372 0 3 - -0.09372 - - 0s
0 0 -0.09372 0 3 - -0.09372 - - 0s
0 0 -0.08864 0 4 - -0.08864 - - 0s
0 0 -0.08863 0 4 - -0.08863 - - 0s
0 0 -0.08812 0 5 - -0.08812 - - 0s
0 0 -0.08808 0 6 - -0.08808 - - 0s
0 0 -0.08784 0 5 - -0.08784 - - 0s
0 0 -0.08784 0 5 - -0.08784 - - 0s
0 0 -0.08783 0 5 - -0.08783 - - 0s
H 0 0 -0.0828927 -0.08783 5.96% - 0s
0 0 -0.08783 0 5 -0.08289 -0.08783 5.96% - 0s
H 0 0 -0.0856874 -0.08783 2.50% - 0s
0 2 -0.08656 0 5 -0.08569 -0.08656 1.01% - 0s
H 7 4 -0.0856928 -0.08646 0.90% 9.9 0s
* 7 4 4 -0.0856928 -0.08646 0.90% 10.1 0s
H 29 0 -0.0856947 -0.08579 0.11% 18.0 0s
* 29 0 8 -0.0856947 -0.08578 0.10% 18.8 0s
* 41 0 8 -0.0856983 -0.08571 0.01% 15.0 0s
Cutting planes:
Implied bound: 1
MIR: 3
Flow cover: 1
Explored 42 nodes (1019 simplex iterations) in 0.49 seconds (0.38 work units)
Thread count was 8 (of 8 available processors)
Solution count 4: -0.0856983 -0.0856947 -0.0856928 -0.0828927
Optimal solution found (tolerance 1.00e-04)
Warning: max constraint violation (1.8144e-06) exceeds tolerance
Best objective -8.569825332774e-02, best bound -8.570543461248e-02, gap 0.0084%Remarks
- Initial relaxation value is weaker
-0.20200(LP relaxation) - Improved during the root to be similar to QCP:
-0.08656 - Overall solution time, much faster: 0.44 seconds vs 2.33
- Solution still has a violation slightly above the default
1.8144e-06 - If we had left MIQCPMethod to default settings we would have the same for this model.
Try to get a more feasible solution
Decrease FeasibilityTol.
Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.03 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Set parameter FeasibilityTol to value 1e-07
Gurobi Optimizer version 11.0.0 build v11.0.0beta2 (mac64[x86] - macOS 13.6 22G120)
CPU model: Intel(R) Core(TM) i5-1038NG7 CPU @ 2.00GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 365 rows, 311 columns and 5668 nonzeros
Model fingerprint: 0x97dee3ae
Model has 2 quadratic constraints
Variable types: 260 continuous, 51 integer (0 binary)
Coefficient statistics:
Matrix range [8e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-01, 1e+01]
Presolve removed 211 rows and 108 columns
Presolve time: 0.01s
Presolved: 156 rows, 303 columns, 5447 nonzeros
Presolved model has 100 quadratic constraint(s)
Variable types: 252 continuous, 51 integer (51 binary)
Root relaxation: objective -2.020047e-01, 108 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 -0.20200 0 - - -0.20200 - - 0s
0 0 -0.14578 0 - - -0.14578 - - 0s
0 0 -0.11167 0 2 - -0.11167 - - 0s
0 0 -0.09372 0 3 - -0.09372 - - 0s
0 0 -0.09372 0 3 - -0.09372 - - 0s
0 0 -0.08864 0 4 - -0.08864 - - 0s
0 0 -0.08863 0 4 - -0.08863 - - 0s
0 0 -0.08812 0 5 - -0.08812 - - 0s
0 0 -0.08808 0 6 - -0.08808 - - 0s
0 0 -0.08784 0 5 - -0.08784 - - 0s
0 0 -0.08784 0 5 - -0.08784 - - 0s
0 0 -0.08783 0 5 - -0.08783 - - 0s
H 0 0 -0.0856874 -0.08783 2.50% - 0s
0 1 -0.08656 0 5 -0.08569 -0.08656 1.01% - 0s
H 8 4 -0.0856947 -0.08646 0.90% 7.6 0s
* 8 4 5 -0.0856947 -0.08646 0.90% 8.5 0s
Cutting planes:
Implied bound: 1
MIR: 3
Flow cover: 1
Explored 35 nodes (1169 simplex iterations) in 0.42 seconds (0.38 work units)
Thread count was 8 (of 8 available processors)
Solution count 2: -0.0856947 -0.0856874
Optimal solution found (tolerance 1.00e-04)
Best objective -8.569474489716e-02, best bound -8.570145202443e-02, gap 0.0078%Remarks
- That worked and it was not even really slower (it’s pure luck!)
- We can get the maximal violation of the solution with the attribute
MaxVio
Disable cone disaggregation
This model has long quadratic constraints. Cone disaggregation is usually performed on these.
It’s good for performance but in this case it was the cause for the small violation.
We can disable the disaggregation with the parameter PreMIQCPForm
Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.03 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Set parameter PreMIQCPForm to value 1
Gurobi Optimizer version 11.0.0 build v11.0.0beta2 (mac64[x86] - macOS 13.6 22G120)
CPU model: Intel(R) Core(TM) i5-1038NG7 CPU @ 2.00GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 365 rows, 311 columns and 5668 nonzeros
Model fingerprint: 0x97dee3ae
Model has 2 quadratic constraints
Variable types: 260 continuous, 51 integer (0 binary)
Coefficient statistics:
Matrix range [8e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-01, 1e+01]
Presolve removed 211 rows and 108 columns
Presolve time: 0.01s
Presolved: 256 rows, 305 columns, 5549 nonzeros
Presolved model has 2 quadratic constraint(s)
Variable types: 254 continuous, 51 integer (51 binary)
Root relaxation presolve removed 151 rows and 151 columns
Root relaxation presolve time: 0.03s
Root relaxation presolved: 282 rows, 155 columns, 5425 nonzeros
Root relaxation presolved model has 2 second-order cone constraints
Root barrier log...
Ordering time: 0.00s
Barrier statistics:
AA' NZ : 2.205e+04
Factor NZ : 2.678e+04
Factor Ops : 3.145e+06 (less than 1 second per iteration)
Threads : 4
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 -2.15743096e+00 -1.10900378e+01 9.98e+01 5.75e-01 8.29e-01 0s
1 -3.81184924e-01 -1.43739011e+01 1.78e+01 6.33e-07 1.62e-01 0s
2 -9.11593201e-02 -5.38835630e+00 1.77e+00 6.97e-13 2.26e-02 0s
3 -3.65086440e-02 -1.05640189e+00 1.95e-06 4.10e-14 2.64e-03 0s
4 -5.65249132e-02 -2.96792390e-01 1.04e-07 8.24e-15 6.22e-04 0s
5 -7.01928841e-02 -1.26961320e-01 1.14e-13 1.39e-15 1.47e-04 0s
6 -8.44475308e-02 -8.93648693e-02 1.24e-14 2.22e-16 1.27e-05 0s
7 -8.56738257e-02 -8.64257570e-02 1.33e-14 2.22e-16 1.95e-06 0s
8 -8.58587744e-02 -8.58809223e-02 2.74e-14 2.22e-16 5.74e-08 0s
9 -8.58621945e-02 -8.58632060e-02 5.27e-13 4.00e-15 2.62e-09 0s
Barrier solved model in 9 iterations and 0.06 seconds (0.03 work units)
Optimal objective -8.58621945e-02
Root relaxation: objective -8.586219e-02, 0 iterations, 0.03 seconds (0.01 work units)
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 -0.08586 0 13 - -0.08586 - - 0s
0 0 -0.08586 0 51 - -0.08586 - - 0s
0 0 -0.08586 0 51 - -0.08586 - - 0s
H 0 0 0.0000000 -0.08586 - - 0s
H 0 0 -0.0458804 -0.08586 87.1% - 0s
0 2 -0.08586 0 50 -0.04588 -0.08586 87.1% - 0s
H 28 32 -0.0458804 -0.08586 87.1% 0.0 0s
H 29 32 -0.0501315 -0.08586 71.3% 0.0 0s
H 53 56 -0.0520809 -0.08586 64.9% 0.0 0s
H 59 64 -0.0536589 -0.08586 60.0% 0.0 0s
H 59 64 -0.0536589 -0.08586 60.0% 0.0 0s
H 60 64 -0.0599932 -0.08586 43.1% 0.0 0s
H 61 64 -0.0692581 -0.08586 24.0% 0.0 0s
H 69 72 -0.0711611 -0.08586 20.7% 0.0 1s
* 78 74 13 -0.0770387 -0.08586 11.5% 0.0 1s
H 93 78 -0.0770387 -0.08586 11.5% 0.0 1s
* 216 204 49 -0.0802887 -0.08586 6.94% 0.0 1s
* 217 204 49 -0.0808685 -0.08586 6.17% 0.0 1s
* 243 204 49 -0.0808687 -0.08586 6.17% 0.0 1s
* 245 204 49 -0.0809975 -0.08586 6.01% 0.0 1s
* 246 204 49 -0.0810161 -0.08586 5.98% 0.0 1s
H 385 226 -0.0811462 -0.08586 5.81% 0.0 2s
H 450 216 -0.0839754 -0.08586 2.25% 0.0 2s
* 452 216 49 -0.0839755 -0.08586 2.25% 0.0 2s
H 636 47 -0.0856947 -0.08586 0.19% 0.0 3s
705 42 -0.08586 20 40 -0.08569 -0.08586 0.19% 0.0 5s
2316 591 -0.08578 37 23 -0.08569 -0.08586 0.19% 0.0 10s
3934 407 cutoff 36 -0.08569 -0.08578 0.10% 0.0 15s
Cutting planes:
Implied bound: 4
MIR: 7
Flow cover: 2
Explored 4817 nodes (0 simplex iterations) in 17.60 seconds (19.80 work units)
Thread count was 8 (of 8 available processors)
Solution count 10: -0.0856947 -0.0839755 -0.0811462 ... -0.0770387
Optimal solution found (tolerance 1.00e-04)
Best objective -8.569474447765e-02, best bound -8.569476214813e-02, gap 0.0000%Remarks
- This was considerably slower!
- Root bound is actually good but it takes a lot of nodes to close the small gap
- Violation looks OK
Disable cone disaggregation again
We had set PreMIQCPForm to 1 that still reformulate quadratic constraints as second-order-cone.
Gurobi actually chose to use QCP branch-and-bound.
We can try to set it to 0.
Read MPS format model from file models/robust_50_1.cbf.mps.bz2
Reading time = 0.04 seconds
UNKNOWN: 365 rows, 311 columns, 5668 nonzeros
Set parameter PreMIQCPForm to value 0
Gurobi Optimizer version 11.0.0 build v11.0.0beta2 (mac64[x86] - macOS 13.6 22G120)
CPU model: Intel(R) Core(TM) i5-1038NG7 CPU @ 2.00GHz
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 365 rows, 311 columns and 5668 nonzeros
Model fingerprint: 0x97dee3ae
Model has 2 quadratic constraints
Variable types: 260 continuous, 51 integer (0 binary)
Coefficient statistics:
Matrix range [8e-06, 1e+00]
QMatrix range [1e+00, 1e+00]
Objective range [1e+00, 1e+00]
Bounds range [0e+00, 0e+00]
RHS range [2e-01, 1e+01]
Presolve removed 211 rows and 108 columns
Presolve time: 0.02s
Presolved: 154 rows, 203 columns, 5346 nonzeros
Presolved model has 2 quadratic constraint(s)
Variable types: 152 continuous, 51 integer (51 binary)
Root relaxation: objective -2.020047e-01, 108 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 -0.20200 0 - - -0.20200 - - 0s
0 0 -0.13924 0 - - -0.13924 - - 0s
0 0 -0.12183 0 - - -0.12183 - - 0s
0 0 -0.11835 0 - - -0.11835 - - 0s
0 0 -0.11289 0 - - -0.11289 - - 0s
0 0 -0.11085 0 2 - -0.11085 - - 0s
0 0 -0.09449 0 2 - -0.09449 - - 0s
0 0 -0.09449 0 - - -0.09449 - - 0s
0 0 -0.09449 0 2 - -0.09449 - - 0s
0 0 -0.09449 0 - - -0.09449 - - 0s
0 0 -0.09449 0 2 - -0.09449 - - 0s
0 0 -0.09424 0 3 - -0.09424 - - 0s
0 0 -0.09424 0 3 - -0.09424 - - 0s
0 0 -0.09383 0 3 - -0.09383 - - 0s
0 0 -0.09357 0 3 - -0.09357 - - 0s
0 0 -0.09356 0 3 - -0.09356 - - 0s
0 0 -0.09269 0 3 - -0.09269 - - 0s
0 0 -0.09231 0 3 - -0.09231 - - 0s
0 0 -0.09193 0 2 - -0.09193 - - 0s
0 0 -0.09172 0 3 - -0.09172 - - 0s
0 0 -0.09160 0 4 - -0.09160 - - 0s
0 0 -0.09124 0 2 - -0.09124 - - 0s
0 0 -0.09116 0 3 - -0.09116 - - 0s
0 0 -0.09100 0 3 - -0.09100 - - 0s
0 0 -0.09075 0 3 - -0.09075 - - 0s
0 0 -0.09069 0 4 - -0.09069 - - 0s
0 0 -0.09058 0 4 - -0.09058 - - 0s
0 0 -0.09033 0 3 - -0.09033 - - 0s
0 0 -0.08986 0 2 - -0.08986 - - 0s
0 0 -0.08966 0 2 - -0.08966 - - 0s
0 0 -0.08939 0 3 - -0.08939 - - 0s
0 0 -0.08909 0 3 - -0.08909 - - 0s
0 0 -0.08906 0 2 - -0.08906 - - 0s
0 0 -0.08906 0 3 - -0.08906 - - 0s
0 0 -0.08881 0 3 - -0.08881 - - 0s
0 0 -0.08866 0 3 - -0.08866 - - 0s
0 0 -0.08865 0 3 - -0.08865 - - 0s
0 0 -0.08865 0 3 - -0.08865 - - 0s
H 0 0 -0.0856928 -0.08865 3.45% - 0s
0 2 -0.08858 0 3 -0.08569 -0.08858 3.37% - 0s
H 132 44 -0.0856947 -0.08783 2.49% 5.6 0s
* 132 44 11 -0.0856947 -0.08783 2.49% 5.6 0s
* 555 1 10 -0.0856981 -0.08570 0.01% 4.8 0s
Cutting planes:
Implied bound: 3
Explored 557 nodes (2976 simplex iterations) in 0.95 seconds (0.95 work units)
Thread count was 8 (of 8 available processors)
Solution count 2: -0.0856981 -0.0856947
Optimal solution found (tolerance 1.00e-04)
Best objective -8.569808216221e-02, best bound -8.570418404331e-02, gap 0.0071%Remarks
- Now OA was used
- It’s as fast as defaults without the violations
- But it’s a small model and it is misleading. On larger models this would usually be much slower.
©️ Gurobi Optimization