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@ -127,7 +127,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": 1,
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"id": "22a67170-10b4-43d3-8708-014d91141e73",
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"metadata": {
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"ExecuteTime": {
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@ -163,7 +163,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"execution_count": 2,
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"id": "2f67032f-0d74-4317-b45c-19da0ec859e9",
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"metadata": {
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"ExecuteTime": {
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@ -213,7 +213,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": 3,
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"id": "2a896f47",
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"metadata": {
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"ExecuteTime": {
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@ -228,10 +228,10 @@
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"text": [
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"Restricted license - for non-production use only - expires 2024-10-28\n",
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"Set parameter QCPDual to value 1\n",
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"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
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"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
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"\n",
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"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
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"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n",
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"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
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"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
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"\n",
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"Optimize a model with 7 rows, 6 columns and 15 nonzeros\n",
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"Model fingerprint: 0x15c7a953\n",
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@ -257,7 +257,7 @@
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"* 0 0 0 1320.0000000 1320.00000 0.00% - 0s\n",
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"\n",
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"Explored 1 nodes (5 simplex iterations) in 0.01 seconds (0.00 work units)\n",
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"Thread count was 12 (of 12 available processors)\n",
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"Thread count was 20 (of 20 available processors)\n",
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"\n",
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"Solution count 2: 1320 1400 \n",
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"\n",
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@ -324,7 +324,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 4,
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"id": "5eb09fab",
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"metadata": {
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"ExecuteTime": {
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@ -370,7 +370,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"execution_count": 5,
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"id": "6156752c",
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"metadata": {
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"ExecuteTime": {
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@ -397,7 +397,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"execution_count": 6,
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"id": "7623f002",
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"metadata": {
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"ExecuteTime": {
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@ -438,7 +438,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 7,
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"id": "435f7bf8-4b09-4889-b1ec-b7b56e7d8ed2",
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"metadata": {
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"ExecuteTime": {
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@ -476,7 +476,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 8,
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"id": "9d13dd50-3dcf-4673-a757-6f44dcc0dedf",
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"metadata": {
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"ExecuteTime": {
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@ -490,10 +490,10 @@
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"output_type": "stream",
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"text": [
|
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|
"Set parameter QCPDual to value 1\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
|
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|
|
|
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
|
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|
|
"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
|
|
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|
|
"Model fingerprint: 0x5e67c6ee\n",
|
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@ -513,13 +513,13 @@
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"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
|
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|
|
"Optimal objective 8.290621916e+09\n",
|
|
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|
|
"Set parameter QCPDual to value 1\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
|
|
|
|
|
"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
|
|
|
|
|
"Model fingerprint: 0xa4a7961e\n",
|
|
|
|
|
"Model fingerprint: 0x4a7cfe2b\n",
|
|
|
|
|
"Variable types: 500 continuous, 500 integer (500 binary)\n",
|
|
|
|
|
"Coefficient statistics:\n",
|
|
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|
|
" Matrix range [1e+00, 2e+06]\n",
|
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|
@ -527,37 +527,48 @@
|
|
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|
" Bounds range [1e+00, 1e+00]\n",
|
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|
|
" RHS range [3e+08, 3e+08]\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.30129e+09 (0.01s)\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.29184e+09 (0.01s)\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.29146e+09 (0.01s)\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.29146e+09 (0.02s)\n",
|
|
|
|
|
"Loaded user MIP start with objective 8.29146e+09\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 time: 0.01s\n",
|
|
|
|
|
"Presolve time: 0.00s\n",
|
|
|
|
|
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
|
|
|
|
|
"Variable types: 500 continuous, 500 integer (500 binary)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Root relaxation: objective 8.290622e+09, 512 iterations, 0.01 seconds (0.00 work units)\n",
|
|
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|
|
"Root relaxation: objective 8.290622e+09, 512 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 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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Cutting planes:\n",
|
|
|
|
|
" Cover: 1\n",
|
|
|
|
|
" Gomory: 1\n",
|
|
|
|
|
" Flow cover: 2\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Explored 1 nodes (512 simplex iterations) in 0.09 seconds (0.01 work units)\n",
|
|
|
|
|
"Thread count was 12 (of 12 available processors)\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Solution count 3: 8.29146e+09 8.29184e+09 8.30129e+09 \n",
|
|
|
|
|
"Solution count 1: 8.29153e+09 \n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Optimal solution found (tolerance 1.00e-04)\n",
|
|
|
|
|
"Best objective 8.291459497797e+09, best bound 8.290645029670e+09, gap 0.0098%\n",
|
|
|
|
|
"Best objective 8.291528276179e+09, best bound 8.290733258025e+09, gap 0.0096%\n",
|
|
|
|
|
"WARNING: Cannot get reduced costs for MIP.\n",
|
|
|
|
|
"WARNING: Cannot get duals for MIP.\n"
|
|
|
|
|
]
|
|
|
|
|
},
|
|
|
|
|
{
|
|
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|
"data": {
|
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|
"text/plain": [
|
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|
"{}"
|
|
|
|
|
]
|
|
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|
|
},
|
|
|
|
|
"execution_count": 8,
|
|
|
|
|
"metadata": {},
|
|
|
|
|
"output_type": "execute_result"
|
|
|
|
|
}
|
|
|
|
|
],
|
|
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|
"source": [
|
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@ -578,7 +589,7 @@
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|
},
|
|
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|
{
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
"execution_count": 11,
|
|
|
|
|
"execution_count": 9,
|
|
|
|
|
"id": "2ff391ed-e855-4228-aa09-a7641d8c2893",
|
|
|
|
|
"metadata": {
|
|
|
|
|
"ExecuteTime": {
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|
@ -592,10 +603,10 @@
|
|
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|
"output_type": "stream",
|
|
|
|
|
"text": [
|
|
|
|
|
"Set parameter QCPDual to value 1\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
|
|
|
|
|
"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
|
|
|
|
|
"Model fingerprint: 0x5e67c6ee\n",
|
|
|
|
@ -605,7 +616,7 @@
|
|
|
|
|
" Bounds range [1e+00, 1e+00]\n",
|
|
|
|
|
" RHS range [3e+08, 3e+08]\n",
|
|
|
|
|
"Presolve removed 1000 rows and 500 columns\n",
|
|
|
|
|
"Presolve time: 0.01s\n",
|
|
|
|
|
"Presolve time: 0.00s\n",
|
|
|
|
|
"Presolved: 1 rows, 500 columns, 500 nonzeros\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Iteration Objective Primal Inf. Dual Inf. Time\n",
|
|
|
|
@ -615,10 +626,10 @@
|
|
|
|
|
"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
|
|
|
|
|
"Optimal objective 8.290621916e+09\n",
|
|
|
|
|
"Set parameter QCPDual to value 1\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
|
|
|
|
|
"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
|
|
|
|
|
"Model fingerprint: 0x8a0f9587\n",
|
|
|
|
@ -656,8 +667,8 @@
|
|
|
|
|
" Gomory: 2\n",
|
|
|
|
|
" MIR: 1\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Explored 1 nodes (1025 simplex iterations) in 0.08 seconds (0.03 work units)\n",
|
|
|
|
|
"Thread count was 12 (of 12 available processors)\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Solution count 4: 8.29147e+09 8.29398e+09 8.29827e+09 9.75713e+09 \n",
|
|
|
|
|
"\n",
|
|
|
|
@ -666,6 +677,16 @@
|
|
|
|
|
"WARNING: Cannot get reduced costs for MIP.\n",
|
|
|
|
|
"WARNING: Cannot get duals for MIP.\n"
|
|
|
|
|
]
|
|
|
|
|
},
|
|
|
|
|
{
|
|
|
|
|
"data": {
|
|
|
|
|
"text/plain": [
|
|
|
|
|
"{}"
|
|
|
|
|
]
|
|
|
|
|
},
|
|
|
|
|
"execution_count": 9,
|
|
|
|
|
"metadata": {},
|
|
|
|
|
"output_type": "execute_result"
|
|
|
|
|
}
|
|
|
|
|
],
|
|
|
|
|
"source": [
|
|
|
|
@ -696,7 +717,7 @@
|
|
|
|
|
},
|
|
|
|
|
{
|
|
|
|
|
"cell_type": "code",
|
|
|
|
|
"execution_count": 12,
|
|
|
|
|
"execution_count": 10,
|
|
|
|
|
"id": "67a6cd18",
|
|
|
|
|
"metadata": {
|
|
|
|
|
"ExecuteTime": {
|
|
|
|
@ -710,10 +731,10 @@
|
|
|
|
|
"output_type": "stream",
|
|
|
|
|
"text": [
|
|
|
|
|
"Set parameter QCPDual to value 1\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
|
|
|
|
|
"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
|
|
|
|
|
"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n",
|
|
|
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"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
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"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
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"\n",
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"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
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"Model fingerprint: 0x2dfe4e1c\n",
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@ -723,7 +744,7 @@
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" Bounds range [1e+00, 1e+00]\n",
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" RHS range [3e+08, 3e+08]\n",
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"Presolve removed 1000 rows and 500 columns\n",
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"Presolve time: 0.01s\n",
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"Presolve time: 0.00s\n",
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"Presolved: 1 rows, 500 columns, 500 nonzeros\n",
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"\n",
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"Iteration Objective Primal Inf. Dual Inf. Time\n",
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@ -733,13 +754,13 @@
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"Solved in 1 iterations and 0.01 seconds (0.00 work units)\n",
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"Optimal objective 8.253596777e+09\n",
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"Set parameter QCPDual to value 1\n",
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"Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)\n",
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"Gurobi Optimizer version 10.0.3 build v10.0.3rc0 (linux64)\n",
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"\n",
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"CPU model: Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz, instruction set [SSE2|AVX|AVX2]\n",
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"Thread count: 6 physical cores, 12 logical processors, using up to 12 threads\n",
|
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"CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]\n",
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"Thread count: 10 physical cores, 20 logical processors, using up to 20 threads\n",
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"\n",
|
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|
|
"Optimize a model with 1001 rows, 1000 columns and 2500 nonzeros\n",
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"Model fingerprint: 0x20637200\n",
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"Model fingerprint: 0x0f0924a1\n",
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"Variable types: 500 continuous, 500 integer (500 binary)\n",
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"Coefficient statistics:\n",
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" Matrix range [1e+00, 2e+06]\n",
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@ -747,13 +768,16 @@
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" Bounds range [1e+00, 1e+00]\n",
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" RHS range [3e+08, 3e+08]\n",
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"\n",
|
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|
"User MIP start produced solution with objective 8.25814e+09 (0.01s)\n",
|
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"User MIP start produced solution with objective 8.25814e+09 (0.00s)\n",
|
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"User MIP start produced solution with objective 8.25512e+09 (0.01s)\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.25459e+09 (0.04s)\n",
|
|
|
|
|
"User MIP start produced solution with objective 8.25459e+09 (0.04s)\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Presolve time: 0.01s\n",
|
|
|
|
|
"Presolve time: 0.00s\n",
|
|
|
|
|
"Presolved: 1001 rows, 1000 columns, 2500 nonzeros\n",
|
|
|
|
|
"Variable types: 500 continuous, 500 integer (500 binary)\n",
|
|
|
|
|
"\n",
|
|
|
|
@ -777,10 +801,10 @@
|
|
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|
|
" StrongCG: 1\n",
|
|
|
|
|
" Flow cover: 1\n",
|
|
|
|
|
"\n",
|
|
|
|
|
"Explored 1 nodes (575 simplex iterations) in 0.11 seconds (0.01 work units)\n",
|
|
|
|
|
"Thread count was 12 (of 12 available processors)\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",
|
|
|
|
|
"\n",
|
|
|
|
|
"Solution count 3: 8.25459e+09 8.25512e+09 8.25814e+09 \n",
|
|
|
|
|
"Solution count 4: 8.25459e+09 8.25483e+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",
|
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|
@ -788,7 +812,7 @@
|
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|
|
"WARNING: Cannot get duals for MIP.\n",
|
|
|
|
|
"obj = 8254590409.96973\n",
|
|
|
|
|
" x = [1.0, 1.0, 0.0, 1.0, 1.0]\n",
|
|
|
|
|
" y = [935662.0949263407, 1604270.0218116897, 0.0, 1369560.835229226, 602828.5321028307]\n"
|
|
|
|
|
" y = [935662.0949262811, 1604270.0218116897, 0.0, 1369560.835229226, 602828.5321028307]\n"
|
|
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|
|
]
|
|
|
|
|
}
|
|
|
|
|
],
|
|
|
|
@ -826,7 +850,7 @@
|
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|
|
"name": "python",
|
|
|
|
|
"nbconvert_exporter": "python",
|
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|
|
"pygments_lexer": "ipython3",
|
|
|
|
|
"version": "3.8.13"
|
|
|
|
|
"version": "3.11.7"
|
|
|
|
|
}
|
|
|
|
|
},
|
|
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|
|
"nbformat": 4,
|
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|