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Update docs dependencies; re-run notebooks

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This commit is contained in:
Alinson S. Xavier
2025-06-10 12:28:39 -05:00
parent e0b4181579
commit a306f0df26
10 changed files with 388 additions and 302 deletions
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94
docs/tutorials/cuts-gurobipy.ipynb
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@@ -286,12 +286,16 @@
"output_type": "stream",
"text": [
"Set parameter Threads to value 1\n",
"Restricted license - for non-production use only - expires 2024-10-28\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Read parameters from file gurobi.env\n",
"Restricted license - for non-production use only - expires 2026-11-23\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 50 rows, 1225 columns and 2450 nonzeros\n",
"Model fingerprint: 0x04d7bec1\n",
"Coefficient statistics:\n",
@@ -309,7 +313,7 @@
"Solved in 66 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 5.588000000e+03\n",
"\n",
"User-callback calls 107, time in user-callback 0.00 sec\n"
"User-callback calls 110, time in user-callback 0.00 sec\n"
]
},
{
@@ -327,11 +331,16 @@
"Enforcing 19 subtour elimination constraints\n",
"Set parameter PreCrush to value 1\n",
"Set parameter LazyConstraints to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"PreCrush 1\n",
"Threads 1\n",
"LazyConstraints 1\n",
"\n",
"Optimize a model with 69 rows, 1225 columns and 6091 nonzeros\n",
"Model fingerprint: 0x09bd34d6\n",
"Variable types: 0 continuous, 1225 integer (1225 binary)\n",
@@ -356,23 +365,29 @@
"Enforcing 3 subtour elimination constraints\n",
" 0 0 6165.50000 0 6 6390.00000 6165.50000 3.51% - 0s\n",
" 0 0 6198.50000 0 16 6390.00000 6198.50000 3.00% - 0s\n",
" 0 0 6210.50000 0 6 6390.00000 6210.50000 2.81% - 0s\n",
" 0 0 6212.60000 0 31 6390.00000 6212.60000 2.78% - 0s\n",
"H 0 0 6241.0000000 6212.60000 0.46% - 0s\n",
"* 0 0 0 6219.0000000 6219.00000 0.00% - 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 11\n",
" Gomory: 6\n",
" Clique: 1\n",
" MIR: 1\n",
" StrongCG: 1\n",
" Zero half: 4\n",
" RLT: 1\n",
" Lazy constraints: 3\n",
"\n",
"Explored 1 nodes (222 simplex iterations) in 0.03 seconds (0.02 work units)\n",
"Explored 1 nodes (219 simplex iterations) in 0.04 seconds (0.03 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 3: 6219 6390 29853 \n",
"Solution count 4: 6219 6241 6390 29853 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 6.219000000000e+03, best bound 6.219000000000e+03, gap 0.0000%\n",
"\n",
"User-callback calls 141, time in user-callback 0.00 sec\n"
"User-callback calls 163, time in user-callback 0.00 sec\n"
]
}
],
@@ -402,11 +417,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 50 rows, 1225 columns and 2450 nonzeros\n",
"Model fingerprint: 0x04d7bec1\n",
"Coefficient statistics:\n",
@@ -424,14 +442,19 @@
"Solved in 66 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 5.588000000e+03\n",
"\n",
"User-callback calls 107, time in user-callback 0.00 sec\n",
"User-callback calls 110, time in user-callback 0.00 sec\n",
"Set parameter PreCrush to value 1\n",
"Set parameter LazyConstraints to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"PreCrush 1\n",
"Threads 1\n",
"LazyConstraints 1\n",
"\n",
"Optimize a model with 50 rows, 1225 columns and 2450 nonzeros\n",
"Model fingerprint: 0x77a94572\n",
"Variable types: 0 continuous, 1225 integer (1225 binary)\n",
@@ -452,39 +475,46 @@
"\n",
" 0 0 5588.00000 0 12 29695.0000 5588.00000 81.2% - 0s\n",
"Enforcing 9 subtour elimination constraints\n",
"Enforcing 11 subtour elimination constraints\n",
"H 0 0 27241.000000 5588.00000 79.5% - 0s\n",
" 0 0 5898.00000 0 8 27241.0000 5898.00000 78.3% - 0s\n",
"Enforcing 4 subtour elimination constraints\n",
"Enforcing 9 subtour elimination constraints\n",
"H 0 0 24919.000000 5588.00000 77.6% - 0s\n",
" 0 0 5847.50000 0 14 24919.0000 5847.50000 76.5% - 0s\n",
"Enforcing 5 subtour elimination constraints\n",
"Enforcing 5 subtour elimination constraints\n",
"Enforcing 3 subtour elimination constraints\n",
" 0 0 6066.00000 0 - 27241.0000 6066.00000 77.7% - 0s\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6128.00000 0 - 27241.0000 6128.00000 77.5% - 0s\n",
" 0 0 6139.00000 0 6 27241.0000 6139.00000 77.5% - 0s\n",
"H 0 0 6368.0000000 6139.00000 3.60% - 0s\n",
" 0 0 6154.75000 0 15 6368.00000 6154.75000 3.35% - 0s\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6154.75000 0 6 6368.00000 6154.75000 3.35% - 0s\n",
" 0 0 6165.75000 0 11 6368.00000 6165.75000 3.18% - 0s\n",
"H 0 0 7764.0000000 5847.50000 24.7% - 0s\n",
"H 0 0 6684.0000000 5847.50000 12.5% - 0s\n",
" 0 0 6013.75000 0 11 6684.00000 6013.75000 10.0% - 0s\n",
"H 0 0 6340.0000000 6013.75000 5.15% - 0s\n",
"Enforcing 3 subtour elimination constraints\n",
" 0 0 6204.00000 0 6 6368.00000 6204.00000 2.58% - 0s\n",
"* 0 0 0 6219.0000000 6219.00000 0.00% - 0s\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6095.00000 0 10 6340.00000 6095.00000 3.86% - 0s\n",
"Enforcing 3 subtour elimination constraints\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6128.00000 0 - 6340.00000 6128.00000 3.34% - 0s\n",
" 0 0 6139.00000 0 6 6340.00000 6139.00000 3.17% - 0s\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6187.25000 0 17 6340.00000 6187.25000 2.41% - 0s\n",
"Enforcing 2 subtour elimination constraints\n",
"Enforcing 2 subtour elimination constraints\n",
" 0 0 6201.00000 0 15 6340.00000 6201.00000 2.19% - 0s\n",
" 0 0 6201.00000 0 15 6340.00000 6201.00000 2.19% - 0s\n",
"H 0 0 6219.0000000 6201.00000 0.29% - 0s\n",
"Enforcing 3 subtour elimination constraints\n",
" 0 0 infeasible 0 6219.00000 6219.00000 0.00% - 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 5\n",
" MIR: 1\n",
" Zero half: 4\n",
" Lazy constraints: 4\n",
" Lazy constraints: 2\n",
"\n",
"Explored 1 nodes (224 simplex iterations) in 0.10 seconds (0.03 work units)\n",
"Explored 1 nodes (217 simplex iterations) in 0.12 seconds (0.05 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 4: 6219 6368 27241 29695 \n",
"Solution count 6: 6219 6340 6684 ... 29695\n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 6.219000000000e+03, best bound 6.219000000000e+03, gap 0.0000%\n",
"\n",
"User-callback calls 170, time in user-callback 0.01 sec\n"
"User-callback calls 216, time in user-callback 0.06 sec\n"
]
}
],

181
docs/tutorials/getting-started-gurobipy.ipynb
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@@ -215,12 +215,16 @@
"output_type": "stream",
"text": [
"Set parameter Threads to value 1\n",
"Restricted license - for non-production use only - expires 2024-10-28\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Read parameters from file gurobi.env\n",
"Restricted license - for non-production use only - expires 2026-11-23\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 7 rows, 6 columns and 15 nonzeros\n",
"Model fingerprint: 0x58dfdd53\n",
"Variable types: 3 continuous, 3 integer (3 binary)\n",
@@ -229,30 +233,28 @@
" Objective range [2e+00, 7e+02]\n",
" Bounds range [1e+00, 1e+00]\n",
" RHS range [1e+02, 1e+02]\n",
"Presolve removed 2 rows and 1 columns\n",
"Presolve removed 6 rows and 3 columns\n",
"Presolve time: 0.00s\n",
"Presolved: 5 rows, 5 columns, 13 nonzeros\n",
"Variable types: 0 continuous, 5 integer (3 binary)\n",
"Found heuristic solution: objective 1400.0000000\n",
"Presolved: 1 rows, 3 columns, 3 nonzeros\n",
"Variable types: 0 continuous, 3 integer (1 binary)\n",
"Found heuristic solution: objective 1990.0000000\n",
"\n",
"Root relaxation: objective 1.035000e+03, 3 iterations, 0.00 seconds (0.00 work units)\n",
"Root relaxation: objective 1.320000e+03, 0 iterations, 0.00 seconds (0.00 work units)\n",
"\n",
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
"\n",
" 0 0 1035.00000 0 1 1400.00000 1035.00000 26.1% - 0s\n",
" 0 0 1105.71429 0 1 1400.00000 1105.71429 21.0% - 0s\n",
"* 0 0 0 1320.0000000 1320.00000 0.00% - 0s\n",
"\n",
"Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)\n",
"Explored 1 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 2: 1320 1400 \n",
"Solution count 2: 1320 1990 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 1.320000000000e+03, best bound 1.320000000000e+03, gap 0.0000%\n",
"\n",
"User-callback calls 371, time in user-callback 0.00 sec\n",
"User-callback calls 541, time in user-callback 0.00 sec\n",
"obj = 1320.0\n",
"x = [-0.0, 1.0, 1.0]\n",
"y = [0.0, 60.0, 40.0]\n"
@@ -477,11 +479,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0xa8b70287\n",
"Coefficient statistics:\n",
@@ -497,15 +502,18 @@
" 0 6.6166537e+09 5.648803e+04 0.000000e+00 0s\n",
" 1 8.2906219e+09 0.000000e+00 0.000000e+00 0s\n",
"\n",
"Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
"Solved in 1 iterations and 0.02 seconds (0.00 work units)\n",
"Optimal objective 8.290621916e+09\n",
"\n",
"User-callback calls 56, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"User-callback calls 59, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x892e56b2\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
@@ -515,15 +523,18 @@
" Bounds range [1e+00, 1e+00]\n",
" RHS range [3e+08, 3e+08]\n",
"\n",
"User MIP start produced solution with objective 8.29824e+09 (0.00s)\n",
"User MIP start produced solution with objective 8.29398e+09 (0.00s)\n",
"User MIP start produced solution with objective 8.29153e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.29153e+09 (0.01s)\n",
"Loaded user MIP start with objective 8.29153e+09\n",
"\n",
"Presolve removed 500 rows and 0 columns\n",
"Presolve time: 0.00s\n",
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
"Presolved: 501 rows, 1000 columns, 2000 nonzeros\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
"\n",
"Root relaxation: objective 8.290622e+09, 512 iterations, 0.00 seconds (0.00 work units)\n",
"Root relaxation: objective 8.290622e+09, 501 iterations, 0.00 seconds (0.02 work units)\n",
"\n",
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
@@ -531,27 +542,29 @@
" 0 0 8.2906e+09 0 1 8.2915e+09 8.2906e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 - 0 8.2915e+09 8.2907e+09 0.01% - 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 1\n",
" Flow cover: 2\n",
" RLT: 2\n",
"\n",
"Explored 1 nodes (565 simplex iterations) in 0.02 seconds (0.01 work units)\n",
"Explored 1 nodes (550 simplex iterations) in 0.04 seconds (0.04 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 1: 8.29153e+09 \n",
"Solution count 4: 8.29153e+09 8.29398e+09 8.29695e+09 8.29824e+09 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.291528276179e+09, best bound 8.290733258025e+09, gap 0.0096%\n",
"Best objective 8.291528276179e+09, best bound 8.290709658754e+09, gap 0.0099%\n",
"\n",
"User-callback calls 193, time in user-callback 0.00 sec\n"
"User-callback calls 799, time in user-callback 0.00 sec\n"
]
},
{
"data": {
"text/plain": [
"{'WS: Count': 1, 'WS: Number of variables set': 477.0}"
"(<miplearn.solvers.gurobi.GurobiModel at 0x7f2bcd72cfd0>,\n",
" {'WS: Count': 1, 'WS: Number of variables set': 477.0})"
]
},
"execution_count": 8,
@@ -590,11 +603,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0xa8b70287\n",
"Coefficient statistics:\n",
@@ -613,12 +629,15 @@
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 8.290621916e+09\n",
"\n",
"User-callback calls 56, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"User-callback calls 59, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x4cbbf7c7\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
@@ -627,48 +646,52 @@
" Objective range [1e+00, 6e+07]\n",
" Bounds range [1e+00, 1e+00]\n",
" RHS range [3e+08, 3e+08]\n",
"Presolve removed 500 rows and 0 columns\n",
"Presolve time: 0.00s\n",
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
"Presolved: 501 rows, 1000 columns, 2000 nonzeros\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
"Found heuristic solution: objective 9.757128e+09\n",
"Found heuristic solution: objective 1.729688e+10\n",
"\n",
"Root relaxation: objective 8.290622e+09, 512 iterations, 0.00 seconds (0.00 work units)\n",
"Root relaxation: objective 8.290622e+09, 501 iterations, 0.00 seconds (0.02 work units)\n",
"\n",
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
"\n",
" 0 0 8.2906e+09 0 1 9.7571e+09 8.2906e+09 15.0% - 0s\n",
"H 0 0 8.298273e+09 8.2906e+09 0.09% - 0s\n",
" 0 0 8.2907e+09 0 4 8.2983e+09 8.2907e+09 0.09% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2983e+09 8.2907e+09 0.09% - 0s\n",
" 0 0 8.2907e+09 0 4 8.2983e+09 8.2907e+09 0.09% - 0s\n",
" 0 0 8.2906e+09 0 1 1.7297e+10 8.2906e+09 52.1% - 0s\n",
"H 0 0 8.298243e+09 8.2906e+09 0.09% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2982e+09 8.2907e+09 0.09% - 0s\n",
"H 0 0 8.293980e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 5 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 2 8.2908e+09 0 2 8.2940e+09 8.2908e+09 0.04% - 0s\n",
"H 9 9 8.292131e+09 8.2908e+09 0.02% 1.0 0s\n",
"H 132 88 8.292121e+09 8.2908e+09 0.02% 2.0 0s\n",
"* 133 88 28 8.292121e+09 8.2908e+09 0.02% 2.2 0s\n",
"H 216 136 8.291918e+09 8.2909e+09 0.01% 2.4 0s\n",
"* 232 136 28 8.291664e+09 8.2909e+09 0.01% 2.4 0s\n",
" 0 0 8.2907e+09 0 1 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 4 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 4 8.2940e+09 8.2907e+09 0.04% - 0s\n",
"H 0 0 8.291961e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2920e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2920e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 4 8.2920e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2920e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2908e+09 0 3 8.2920e+09 8.2908e+09 0.01% - 0s\n",
" 0 0 8.2908e+09 0 5 8.2920e+09 8.2908e+09 0.01% - 0s\n",
" 0 0 8.2908e+09 0 5 8.2920e+09 8.2908e+09 0.01% - 0s\n",
" 0 2 8.2908e+09 0 5 8.2920e+09 8.2908e+09 0.01% - 0s\n",
"H 9 9 8.291298e+09 8.2908e+09 0.01% 1.4 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 2\n",
" Cover: 1\n",
" MIR: 1\n",
" Inf proof: 3\n",
" MIR: 2\n",
"\n",
"Explored 233 nodes (1577 simplex iterations) in 0.09 seconds (0.06 work units)\n",
"Explored 10 nodes (759 simplex iterations) in 0.09 seconds (0.11 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 7: 8.29166e+09 8.29192e+09 8.29212e+09 ... 9.75713e+09\n",
"Solution count 6: 8.2913e+09 8.29196e+09 8.29398e+09 ... 1.72969e+10\n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.291663722826e+09, best bound 8.290885027548e+09, gap 0.0094%\n",
"Best objective 8.291298126440e+09, best bound 8.290812450252e+09, gap 0.0059%\n",
"\n",
"User-callback calls 708, time in user-callback 0.00 sec\n"
"User-callback calls 910, time in user-callback 0.00 sec\n"
]
}
],
@@ -713,11 +736,14 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x19042f12\n",
"Coefficient statistics:\n",
@@ -733,15 +759,18 @@
" 0 6.5917580e+09 5.627453e+04 0.000000e+00 0s\n",
" 1 8.2535968e+09 0.000000e+00 0.000000e+00 0s\n",
"\n",
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
"Solved in 1 iterations and 0.00 seconds (0.00 work units)\n",
"Optimal objective 8.253596777e+09\n",
"\n",
"User-callback calls 56, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"User-callback calls 59, time in user-callback 0.00 sec\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x6926c32f\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
@@ -751,44 +780,44 @@
" Bounds range [1e+00, 1e+00]\n",
" RHS range [3e+08, 3e+08]\n",
"\n",
"User MIP start produced solution with objective 8.25814e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25512e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.2551e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25508e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25508e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25499e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25448e+09 (0.02s)\n",
"User MIP start produced solution with objective 8.25448e+09 (0.02s)\n",
"User MIP start produced solution with objective 8.25989e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25699e+09 (0.05s)\n",
"User MIP start produced solution with objective 8.25678e+09 (0.05s)\n",
"User MIP start produced solution with objective 8.25668e+09 (0.05s)\n",
"User MIP start produced solution with objective 8.2554e+09 (0.05s)\n",
"User MIP start produced solution with objective 8.25448e+09 (0.05s)\n",
"User MIP start produced solution with objective 8.25448e+09 (0.05s)\n",
"Loaded user MIP start with objective 8.25448e+09\n",
"\n",
"Presolve removed 500 rows and 0 columns\n",
"Presolve time: 0.00s\n",
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
"Presolved: 501 rows, 1000 columns, 2000 nonzeros\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
"\n",
"Root relaxation: objective 8.253597e+09, 512 iterations, 0.00 seconds (0.00 work units)\n",
"Root relaxation: objective 8.253597e+09, 501 iterations, 0.00 seconds (0.02 work units)\n",
"\n",
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
"\n",
" 0 0 8.2536e+09 0 1 8.2545e+09 8.2536e+09 0.01% - 0s\n",
" 0 0 8.2537e+09 0 3 8.2545e+09 8.2537e+09 0.01% - 0s\n",
"H 0 0 8.254435e+09 8.2536e+09 0.01% - 0s\n",
" 0 0 - 0 8.2544e+09 8.2537e+09 0.01% - 0s\n",
"\n",
"Cutting planes:\n",
" Cover: 1\n",
" Flow cover: 2\n",
" RLT: 2\n",
"\n",
"Explored 1 nodes (515 simplex iterations) in 0.03 seconds (0.02 work units)\n",
"Explored 1 nodes (503 simplex iterations) in 0.07 seconds (0.03 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 6: 8.25448e+09 8.25499e+09 8.25508e+09 ... 8.25814e+09\n",
"Solution count 7: 8.25443e+09 8.25448e+09 8.2554e+09 ... 8.25989e+09\n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.254479145594e+09, best bound 8.253689731796e+09, gap 0.0096%\n",
"Best objective 8.254434593504e+09, best bound 8.253676932849e+09, gap 0.0092%\n",
"\n",
"User-callback calls 203, time in user-callback 0.00 sec\n",
"obj = 8254479145.594168\n",
"User-callback calls 787, time in user-callback 0.00 sec\n",
"obj = 8254434593.503945\n",
"x = [1.0, 1.0, 0.0]\n",
"y = [935662.0949262811, 1604270.0218116897, 0.0]\n"
"y = [935662.09492646, 1604270.0218116897, 0.0]\n"
]
}
],

162
docs/tutorials/getting-started-pyomo.ipynb
View File

@@ -220,12 +220,19 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Restricted license - for non-production use only - expires 2024-10-28\n",
"Set parameter Threads to value 1\n",
"Read parameters from file gurobi.env\n",
"Restricted license - for non-production use only - expires 2026-11-23\n",
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 7 rows, 6 columns and 15 nonzeros\n",
"Model fingerprint: 0x15c7a953\n",
@@ -235,25 +242,23 @@
" Objective range [2e+00, 7e+02]\n",
" Bounds range [1e+00, 1e+00]\n",
" RHS range [1e+02, 1e+02]\n",
"Presolve removed 2 rows and 1 columns\n",
"Presolve removed 6 rows and 3 columns\n",
"Presolve time: 0.00s\n",
"Presolved: 5 rows, 5 columns, 13 nonzeros\n",
"Variable types: 0 continuous, 5 integer (3 binary)\n",
"Found heuristic solution: objective 1400.0000000\n",
"Presolved: 1 rows, 3 columns, 3 nonzeros\n",
"Variable types: 0 continuous, 3 integer (1 binary)\n",
"Found heuristic solution: objective 1990.0000000\n",
"\n",
"Root relaxation: objective 1.035000e+03, 3 iterations, 0.00 seconds (0.00 work units)\n",
"Root relaxation: objective 1.320000e+03, 0 iterations, 0.00 seconds (0.00 work units)\n",
"\n",
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
"\n",
" 0 0 1035.00000 0 1 1400.00000 1035.00000 26.1% - 0s\n",
" 0 0 1105.71429 0 1 1400.00000 1105.71429 21.0% - 0s\n",
"* 0 0 0 1320.0000000 1320.00000 0.00% - 0s\n",
"\n",
"Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)\n",
"Thread count was 20 (of 20 available processors)\n",
"Explored 1 nodes (0 simplex iterations) in 0.01 seconds (0.00 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 2: 1320 1400 \n",
"Solution count 2: 1320 1990 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 1.320000000000e+03, best bound 1.320000000000e+03, gap 0.0000%\n",
@@ -483,11 +488,16 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x5e67c6ee\n",
@@ -506,14 +516,19 @@
"\n",
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 8.290621916e+09\n",
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x4a7cfe2b\n",
"Model fingerprint: 0xff6a55c5\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
"Coefficient statistics:\n",
" Matrix range [1e+00, 2e+06]\n",
@@ -521,8 +536,8 @@
" Bounds range [1e+00, 1e+00]\n",
" RHS range [3e+08, 3e+08]\n",
"\n",
"User MIP start produced solution with objective 8.29153e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.29153e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.29153e+09 (0.00s)\n",
"User MIP start produced solution with objective 8.29153e+09 (0.00s)\n",
"Loaded user MIP start with objective 8.29153e+09\n",
"\n",
"Presolve time: 0.00s\n",
@@ -537,19 +552,20 @@
" 0 0 8.2906e+09 0 1 8.2915e+09 8.2906e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 3 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2915e+09 8.2907e+09 0.01% - 0s\n",
" 0 0 - 0 8.2915e+09 8.2907e+09 0.01% - 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 1\n",
" Cover: 1\n",
" Flow cover: 2\n",
"\n",
"Explored 1 nodes (565 simplex iterations) in 0.04 seconds (0.01 work units)\n",
"Thread count was 20 (of 20 available processors)\n",
"Explored 1 nodes (564 simplex iterations) in 0.03 seconds (0.01 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 1: 8.29153e+09 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.291528276179e+09, best bound 8.290733258025e+09, gap 0.0096%\n",
"Best objective 8.291528276179e+09, best bound 8.290729173948e+09, gap 0.0096%\n",
"WARNING: Cannot get reduced costs for MIP.\n",
"WARNING: Cannot get duals for MIP.\n"
]
@@ -557,7 +573,7 @@
{
"data": {
"text/plain": [
"{}"
"(<miplearn.solvers.pyomo.PyomoModel at 0x7fdb38952450>, {})"
]
},
"execution_count": 8,
@@ -596,11 +612,16 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x5e67c6ee\n",
@@ -619,11 +640,16 @@
"\n",
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 8.290621916e+09\n",
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x8a0f9587\n",
@@ -652,22 +678,25 @@
" 0 0 8.2907e+09 0 5 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 1 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2907e+09 0 2 8.2940e+09 8.2907e+09 0.04% - 0s\n",
" 0 0 8.2908e+09 0 1 8.2940e+09 8.2908e+09 0.04% - 0s\n",
" 0 0 8.2908e+09 0 4 8.2940e+09 8.2908e+09 0.04% - 0s\n",
" 0 0 8.2908e+09 0 4 8.2940e+09 8.2908e+09 0.04% - 0s\n",
"H 0 0 8.291465e+09 8.2908e+09 0.01% - 0s\n",
" 0 0 8.2908e+09 0 3 8.2940e+09 8.2908e+09 0.04% - 0s\n",
" 0 0 8.2908e+09 0 3 8.2940e+09 8.2908e+09 0.04% - 0s\n",
" 0 2 8.2908e+09 0 3 8.2940e+09 8.2908e+09 0.04% - 0s\n",
"H 9 9 8.292471e+09 8.2908e+09 0.02% 1.3 0s\n",
"* 90 41 44 8.291525e+09 8.2908e+09 0.01% 1.5 0s\n",
"\n",
"Cutting planes:\n",
" Gomory: 2\n",
" MIR: 1\n",
" Gomory: 1\n",
" Cover: 1\n",
" MIR: 2\n",
"\n",
"Explored 1 nodes (1025 simplex iterations) in 0.12 seconds (0.03 work units)\n",
"Thread count was 20 (of 20 available processors)\n",
"Explored 91 nodes (1166 simplex iterations) in 0.06 seconds (0.05 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 4: 8.29147e+09 8.29398e+09 8.29827e+09 9.75713e+09 \n",
"Solution count 7: 8.29152e+09 8.29247e+09 8.29398e+09 ... 1.0319e+10\n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.291465302389e+09, best bound 8.290781665333e+09, gap 0.0082%\n",
"Best objective 8.291524908632e+09, best bound 8.290823611882e+09, gap 0.0085%\n",
"WARNING: Cannot get reduced costs for MIP.\n",
"WARNING: Cannot get duals for MIP.\n"
]
@@ -675,7 +704,7 @@
{
"data": {
"text/plain": [
"{}"
"(<miplearn.solvers.pyomo.PyomoModel at 0x7fdb2f563f50>, {})"
]
},
"execution_count": 9,
@@ -724,11 +753,16 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x2dfe4e1c\n",
@@ -747,14 +781,19 @@
"\n",
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
"Optimal objective 8.253596777e+09\n",
"Set parameter OutputFlag to value 1\n",
"Set parameter QCPDual to value 1\n",
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
"Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - \"Ubuntu 22.04.4 LTS\")\n",
"\n",
"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
"Thread count: 10 physical cores, 20 logical processors, using up to 1 threads\n",
"\n",
"Non-default parameters:\n",
"QCPDual 1\n",
"Threads 1\n",
"\n",
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
"Model fingerprint: 0x0f0924a1\n",
"Model fingerprint: 0xd941f1ed\n",
"Variable types: 500 continuous, 500 integer (500 binary)\n",
"Coefficient statistics:\n",
" Matrix range [1e+00, 2e+06]\n",
@@ -762,14 +801,11 @@
" Bounds range [1e+00, 1e+00]\n",
" RHS range [3e+08, 3e+08]\n",
"\n",
"User MIP start produced solution with objective 8.25814e+09 (0.00s)\n",
"User MIP start produced solution with objective 8.25814e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25512e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25483e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25483e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25483e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25459e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25459e+09 (0.01s)\n",
"Loaded user MIP start with objective 8.25459e+09\n",
"User MIP start produced solution with objective 8.25448e+09 (0.01s)\n",
"User MIP start produced solution with objective 8.25448e+09 (0.02s)\n",
"Loaded user MIP start with objective 8.25448e+09\n",
"\n",
"Presolve time: 0.00s\n",
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
@@ -780,31 +816,23 @@
" Nodes | Current Node | Objective Bounds | Work\n",
" Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time\n",
"\n",
" 0 0 8.2536e+09 0 1 8.2546e+09 8.2536e+09 0.01% - 0s\n",
" 0 0 8.2537e+09 0 3 8.2546e+09 8.2537e+09 0.01% - 0s\n",
" 0 0 8.2537e+09 0 1 8.2546e+09 8.2537e+09 0.01% - 0s\n",
" 0 0 8.2537e+09 0 4 8.2546e+09 8.2537e+09 0.01% - 0s\n",
" 0 0 8.2537e+09 0 4 8.2546e+09 8.2537e+09 0.01% - 0s\n",
" 0 0 8.2538e+09 0 4 8.2546e+09 8.2538e+09 0.01% - 0s\n",
" 0 0 8.2538e+09 0 5 8.2546e+09 8.2538e+09 0.01% - 0s\n",
" 0 0 8.2538e+09 0 6 8.2546e+09 8.2538e+09 0.01% - 0s\n",
" 0 0 8.2536e+09 0 1 8.2545e+09 8.2536e+09 0.01% - 0s\n",
" 0 0 - 0 8.2545e+09 8.2537e+09 0.01% - 0s\n",
"\n",
"Cutting planes:\n",
" Cover: 1\n",
" MIR: 2\n",
" StrongCG: 1\n",
" Flow cover: 1\n",
" Flow cover: 2\n",
"\n",
"Explored 1 nodes (575 simplex iterations) in 0.09 seconds (0.01 work units)\n",
"Thread count was 20 (of 20 available processors)\n",
"Explored 1 nodes (514 simplex iterations) in 0.03 seconds (0.01 work units)\n",
"Thread count was 1 (of 20 available processors)\n",
"\n",
"Solution count 4: 8.25459e+09 8.25483e+09 8.25512e+09 8.25814e+09 \n",
"Solution count 3: 8.25448e+09 8.25512e+09 8.25814e+09 \n",
"\n",
"Optimal solution found (tolerance 1.00e-04)\n",
"Best objective 8.254590409970e+09, best bound 8.253768093811e+09, gap 0.0100%\n",
"Best objective 8.254479145594e+09, best bound 8.253676932849e+09, gap 0.0097%\n",
"WARNING: Cannot get reduced costs for MIP.\n",
"WARNING: Cannot get duals for MIP.\n",
"obj = 8254590409.96973\n",
"obj = 8254479145.594172\n",
" x = [1.0, 1.0, 0.0, 1.0, 1.0]\n",
" y = [935662.0949262811, 1604270.0218116897, 0.0, 1369560.835229226, 602828.5321028307]\n"
]