MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance acopf_caseactivsg70k_qcqp
AC Optimal Power Flow: Given an undirected network, where at every node electric power is generated or demanded and edges model transmission lines, the goal is to minimize the cost of power generation subject to network demand, the nonlinear physics of power flows, and operational constraints. Synthetic US power system model
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | |
| Referencesⓘ | Bienstock, Daniel and Villagra, Matias, Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF, Tech. Rep., 2024. Hua Wei, H. Sasaki, J. Kubokawa, R. Yokoyama, An interior point nonlinear programming for optimal power flow problems with a novel data structure. In Proceedings of the 20th International Conference on Power Industry Computer Applications, 1997, 134-141. Carpentier, J. L., Contribution a l'Etude du Dispatching Economique, Bulletin de la Societe Francoise des Electriciens, 8, 1962, 431-447. Birchfield, Adam B., Xu, Ti, Gegner, Kathleen M., Shetye, Komal S., and Overbye, Thomas J., Grid Structural Characteristics as Validation Criteria for Synthetic Networks, IEEE Transactions on Power Systems, 32:4, 2017, 3258-3265. Birchfield, Adam B., Xu, Ti, and Overbye, Thomas J., Power Flow Convergence and Reactive Power Planning in the Creation of Large Synthetic Grids, IEEE Transactions on Power Systems, 33:6, 2018, 6667-6674. |
| Applicationⓘ | Electricity Networks |
| Added to libraryⓘ | 04 Mar 2024 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 900023 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 418897 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 4430 |
| #Nonlinear Nonzeros in Objectiveⓘ | 4429 |
| #Constraintsⓘ | 1016476 |
| #Linear Constraintsⓘ | 632828 |
| #Quadratic Constraintsⓘ | 383648 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 3434923 |
| #Nonlinear Nonzeros in Jacobianⓘ | 1120124 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 1085441 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 418897 |
| #Blocks in Hessian of Lagrangianⓘ | 278898 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 140000 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.501972 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.9238e-04 |
| Maximal coefficientⓘ | 3.3927e+06 |
| Infeasibility of initial pointⓘ | 6.75e+04 |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1016477 879243 0 137234 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 900024 900024 0 0 0 0 0 0
* FX 133499
*
* Nonzero counts
* Total const NL
* 3439354 2314801 1124553
* Solve m using RMIQCP minimizing objvar;
Variables
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x1754,x1755,x1756,x1757,x1758,x1759,x1760,x1761,x1762,x1763,x1764,x1765,
x1766,x1767,x1768,x1769,x1770,x1771,x1772,x1773,x1774,x1775,x1776,x1777,
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x127422,x127423,x127424,x127425,x127426,x127427,x127428,x127429,x127430,
x127431,x127432,x127433,x127434,x127435,x127436,x127437,x127438,x127439,
x127440,x127441,x127442,x127443,x127444,x127445,x127446,x127447,x127448,
x127449,x127450,x127451,x127452,x127453,x127454,x127455,x127456,x127457,
x127458,x127459,x127460,x127461,x127462,x127463,x127464,x127465,x127466,
x127467,x127468,x127469,x127470,x127471,x127472,x127473,x127474,x127475,
x127476,x127477,x127478,x127479,x127480,x127481,x127482,x127483,x127484,
x127485,x127486,x127487,x127488,x127489,x127490,x127491,x127492,x127493,
x127494,x127495,x127496,x127497,x127498,x127499,x127500,x127501,x127502,
x127503,x127504,x127505,x127506,x127507,x127508,x127509,x127510,x127511,
x127512,x127513,x127514,x127515,x127516,x127517,x127518,x127519,x127520,
x127521,x127522,x127523,x127524,x127525,x127526,x127527,x127528,x127529,
x127530,x127531,x127532,x127533,x127534,x127535,x127536,x127537,x127538,
x127539,x127540,x127541,x127542,x127543,x127544,x127545,x127546,x127547,
x127548,x127549,x127550,x127551,x127552,x127553,x127554,x127555,x127556,
x127557,x127558,x127559,x127560,x127561,x127562,x127563,x127564,x127565,
x127566,x127567,x127568,x127569,x127570,x127571,x127572,x127573,x127574,
x127575,x127576,x127577,x127578,x127579,x127580,x127581,x127582,x127583,
x127584,x127585,x127586,x127587,x127588,x127589,x127590,x127591,x127592,
x127593,x127594,x127595,x127596,x127597,x127598,x127599,x127600,x127601,
x127602,x127603,x127604,x127605,x127606,x127607,x127608,x127609,x127610,
x127611,x127612,x127613,x127614,x127615,x127616,x127617,x127618,x127619,
x127620,x127621,x127622,x127623,x127624,x127625,x127626,x127627,x127628,
x127629,x127630,x127631,x127632,x127633,x127634,x127635,x127636,x127637,
x127638,x127639,x127640,x127641,x127642,x127643,x127644,x127645,x127646,
x127647,x127648,x127649,x127650,x127651,x127652,x127653,x127654,x127655,
x127656,x127657,x127658,x127659,x127660,x127661,x127662,x127663,x127664,
x127665,x127666,x127667,x127668,x127669,x127670,x127671,x127672,x127673,
x127674,x127675,x127676,x127677,x127678,x127679,x127680,x127681,x127682,
x127683,x127684,x127685,x127686,x127687,x127688,x127689,x127690,x127691,
x127692,x127693,x127694,x127695,x127696,x127697,x127698,x127699,x127700,
x127701,x127702,x127703,x127704,x127705,x127706,x127707,x127708,x127709,
x127710,x127711,x127712,x127713,x127714,x127715,x127716,x127717,x127718,
x127719,x127720,x127721,x127722,x127723,x127724,x127725,x127726,x127727,
x127728,x127729,x127730,x127731,x127732,x127733,x127734,x127735,x127736,
x127737,x127738,x127739,x127740,x127741,x127742,x127743,x127744,x127745,
x127746,x127747,x127748,x127749,x127750,x127751,x127752,x127753,x127754,
x127755,x127756,x127757,x127758,x127759,x127760,x127761,x127762,x127763,
x127764,x127765,x127766,x127767,x127768,x127769,x127770,x127771,x127772,
x127773,x127774,x127775,x127776,x127777,x127778,x127779,x127780,x127781,
x127782,x127783,x127784,x127785,x127786,x127787,x127788,x127789,x127790,
x127791,x127792,x127793,x127794,x127795,x127796,x127797,x127798,x127799,
x127800,x127801,x127802,x127803,x127804,x127805,x127806,x127807,x127808,
x127809,x127810,x127811,x127812,x127813,x127814,x127815,x127816,x127817,
x127818,x127819,x127820,x127821,x127822,x127823,x127824,x127825,x127826,
x127827,x127828,x127829,x127830,x127831,x127832,x127833,x127834,x127835,
x127836,x127837,x127838,x127839,x127840,x127841,x127842,x127843,x127844,
x127845,x127846,x127847,x127848,x127849,x127850,x127851,x127852,x127853,
x127854,x127855,x127856,x127857,x127858,x127859,x127860,x127861,x127862,
x127863,x127864,x127865,x127866,x127867,x127868,x127869,x127870,x127871,
x127872,x127873,x127874,x127875,x127876,x127877,x127878,x127879,x127880,
x127881,x127882,x127883,x127884,x127885,x127886,x127887,x127888,x127889,
x127890,x127891,x127892,x127893,x127894,x127895,x127896,x127897,x127898,
x127899,x127900,x127901,x127902,x127903,x127904,x127905,x127906,x127907,
x127908,x127909,x127910,x127911,x127912,x127913,x127914,x127915,x127916,
x127917,x127918,x127919,x127920,x127921,x127922,x127923,x127924,x127925,
x127926,x127927,x127928,x127929,x127930,x127931,x127932,x127933,x127934,
x127935,x127936,x127937,x127938,x127939,x127940,x127941,x127942,x127943,
x127944,x127945,x127946,x127947,x127948,x127949,x127950,x127951,x127952,
x127953,x127954,x127955,x127956,x127957,x127958,x127959,x127960,x127961,
x127962,x127963,x127964,x127965,x127966,x127967,x127968,x127969,x127970,
x127971,x127972,x127973,x127974,x127975,x127976,x127977,x127978,x127979,
x127980,x127981,x127982,x127983,x127984,x127985,x127986,x127987,x127988,
x127989,x127990,x127991,x127992,x127993,x127994,x127995,x127996,x127997,
x127998,x127999,x128000,x128001,x128002,x128003,x128004,x128005,x128006,
x128007,x128008,x128009,x128010,x128011,x128012,x128013,x128014,x128015,
x128016,x128017,x128018,x128019,x128020,x128021,x128022,x128023,x128024,
x128025,x128026,x128027,x128028,x128029,x128030,x128031,x128032,x128033,
x128034,x128035,x128036,x128037,x128038,x128039,x128040,x128041,x128042,
x128043,x128044,x128045,x128046,x128047,x128048,x128049,x128050,x128051,
x128052,x128053,x128054,x128055,x128056,x128057,x128058,x128059,x128060,
x128061,x128062,x128063,x128064,x128065,x128066,x128067,x128068,x128069,
x128070,x128071,x128072,x128073,x128074,x128075,x128076,x128077,x128078,
x128079,x128080,x128081,x128082,x128083,x128084,x128085,x128086,x128087,
x128088,x128089,x128090,x128091,x128092,x128093,x128094,x128095,x128096,
x128097,x128098,x128099,x128100,x128101,x128102,x128103,x128104,x128105,
x128106,x128107,x128108,x128109,x128110,x128111,x128112,x128113,x128114,
x128115,x128116,x128117,x128118,x128119,x128120,x128121,x128122,x128123,
x128124,x128125,x128126,x128127,x128128,x128129,x128130,x128131,x128132,
x128133,x128134,x128135,x128136,x128137,x128138,x128139,x128140,x128141,
x128142,x128143,x128144,x128145,x128146,x128147,x128148,x128149,x128150,
x128151,x128152,x128153,x128154,x128155,x128156,x128157,x128158,x128159,
x128160,x128161,x128162,x128163,x128164,x128165,x128166,x128167,x128168,
x128169,x128170,x128171,x128172,x128173,x128174,x128175,x128176,x128177,
x128178,x128179,x128180,x128181,x128182,x128183,x128184,x128185,x128186,
x128187,x128188,x128189,x128190,x128191,x128192,x128193,x128194,x128195,
x128196,x128197,x128198,x128199,x128200,x128201,x128202,x128203,x128204,
x128205,x128206,x128207,x128208,x128209,x128210,x128211,x128212,x128213,
x128214,x128215,x128216,x128217,x128218,x128219,x128220,x128221,x128222,
x128223,x128224,x128225,x128226,x128227,x128228,x128229,x128230,x128231,
x128232,x128233,x128234,x128235,x128236,x128237,x128238,x128239,x128240,
x128241,x128242,x128243,x128244,x128245,x128246,x128247,x128248,x128249,
x128250,x128251,x128252,x128253,x128254,x128255,x128256,x128257,x128258,
x128259,x128260,x128261,x128262,x128263,x128264,x128265,x128266,x128267,
x128268,x128269,x128270,x128271,x128272,x128273,x128274,x128275,x128276,
x128277,x128278,x128279,x128280,x128281,x128282,x128283,x128284,x128285,
x128286,x128287,x128288,x128289,x128290,x128291,x128292,x128293,x128294,
x128295,x128296,x128297,x128298,x128299,x128300,x128301,x128302,x128303,
x128304,x128305,x128306,x128307,x128308,x128309,x128310,x128311,x128312,
x128313,x128314,x128315,x128316,x128317,x128318,x128319,x128320,x128321,
x128322,x128323,x128324,x128325,x128326,x128327,x128328,x128329,x128330,
x128331,x128332,x128333,x128334,x128335,x128336,x128337,x128338,x128339,
x128340,x128341,x128342,x128343,x128344,x128345,x128346,x128347,x128348,
x128349,x128350,x128351,x128352,x128353,x128354,x128355,x128356,x128357,
x128358,x128359,x128360,x128361,x128362,x128363,x128364,x128365,x128366,
x128367,x128368,x128369,x128370,x128371,x128372,x128373,x128374,x128375,
x128376,x128377,x128378,x128379,x128380,x128381,x128382,x128383,x128384,
x128385,x128386,x128387,x128388,x128389,x128390,x128391,x128392,x128393,
x128394,x128395,x128396,x128397,x128398,x128399,x128400,x128401,x128402,
x128403,x128404,x128405,x128406,x128407,x128408,x128409,x128410,x128411,
x128412,x128413,x128414,x128415,x128416,x128417,x128418,x128419,x128420,
x128421,x128422,x128423,x128424,x128425,x128426,x128427,x128428,x128429,
x128430,x128431,x128432,x128433,x128434,x128435,x128436,x128437,x128438,
x128439,x128440,x128441,x128442,x128443,x128444,x128445,x128446,x128447,
x128448,x128449,x128450,x128451,x128452,x128453,x128454,x128455,x128456,
x128457,x128458,x128459,x128460,x128461,x128462,x128463,x128464,x128465,
x128466,x128467,x128468,x128469,x128470,x128471,x128472,x128473,x128474,
x128475,x128476,x128477,x128478,x128479,x128480,x128481,x128482,x128483,
x128484,x128485,x128486,x128487,x128488,x128489,x128490,x128491,x128492,
x128493,x128494,x128495,x128496,x128497,x128498,x128499,x128500,x128501,
x128502,x128503,x128504,x128505,x128506,x128507,x128508,x128509,x128510,
x128511,x128512,x128513,x128514,x128515,x128516,x128517,x128518,x128519,
x128520,x128521,x128522,x128523,x128524,x128525,x128526,x128527,x128528,
x128529,x128530,x128531,x128532,x128533,x128534,x128535,x128536,x128537,
x128538,x128539,x128540,x128541,x128542,x128543,x128544,x128545,x128546,
x128547,x128548,x128549,x128550,x128551,x128552,x128553,x128554,x128555,
x128556,x128557,x128558,x128559,x128560,x128561,x128562,x128563,x128564,
x128565,x128566,x128567,x128568,x128569,x128570,x128571,x128572,x128573,
x128574,x128575,x128576,x128577,x128578,x128579,x128580,x128581,x128582,
x128583,x128584,x128585,x128586,x128587,x128588,x128589,x128590,x128591,
x128592,x128593,x128594,x128595,x128596,x128597,x128598,x128599,x128600,
x128601,x128602,x128603,x128604,x128605,x128606,x128607,x128608,x128609,
x128610,x128611,x128612,x128613,x128614,x128615,x128616,x128617,x128618,
x128619,x128620,x128621,x128622,x128623,x128624,x128625,x128626,x128627,
x128628,x128629,x128630,x128631,x128632,x128633,x128634,x128635,x128636,
x128637,x128638,x128639,x128640,x128641,x128642,x128643,x128644,x128645,
x128646,x128647,x128648,x128649,x128650,x128651,x128652,x128653,x128654,
x128655,x128656,x128657,x128658,x128659,x128660,x128661,x128662,x128663,
x128664,x128665,x128666,x128667,x128668,x128669,x128670,x128671,x128672,
x128673,x128674,x128675,x128676,x128677,x128678,x128679,x128680,x128681,
x128682,x128683,x128684,x128685,x128686,x128687,x128688,x128689,x128690,
x128691,x128692,x128693,x128694,x128695,x128696,x128697,x128698,x128699,
x128700,x128701,x128702,x128703,x128704,x128705,x128706,x128707,x128708,
x128709,x128710,x128711,x128712,x128713,x128714,x128715,x128716,x128717,
x128718,x128719,x128720,x128721,x128722,x128723,x128724,x128725,x128726,
x128727,x128728,x128729,x128730,x128731,x128732,x128733,x128734,x128735,
x128736,x128737,x128738,x128739,x128740,x128741,x128742,x128743,x128744,
x128745,x128746,x128747,x128748,x128749,x128750,x128751,x128752,x128753,
x128754,x128755,x128756,x128757,x128758,x128759,x128760,x128761,x128762,
x128763,x128764,x128765,x128766,x128767,x128768,x128769,x128770,x128771,
x128772,x128773,x128774,x128775,x128776,x128777,x128778,x128779,x128780,
x128781,x128782,x128783,x128784,x128785,x128786,x128787,x128788,x128789,
x128790,x128791,x128792,x128793,x128794,x128795,x128796,x128797,x128798,
x128799,x128800,x128801,x128802,x128803,x128804,x128805,x128806,x128807,
x128808,x128809,x128810,x128811,x128812,x128813,x128814,x128815,x128816,
x128817,x128818,x128819,x128820,x128821,x128822,x128823,x128824,x128825,
x128826,x128827,x128828,x128829,x128830,x128831,x128832,x128833,x128834,
x128835,x128836,x128837,x128838,x128839,x128840,x128841,x128842,x128843,
x128844,x128845,x128846,x128847,x128848,x128849,x128850,x128851,x128852,
x128853,x128854,x128855,x128856,x128857,x128858,x128859,x128860,x128861,
x128862,x128863,x128864,x128865,x128866,x128867,x128868,x128869,x128870,
x128871,x128872,x128873,x128874,x128875,x128876,x128877,x128878,x128879,
x128880,x128881,x128882,x128883,x128884,x128885,x128886,x128887,x128888,
x128889,x128890,x128891,x128892,x128893,x128894,x128895,x128896,x128897,
x128898,x128899,x128900,x128901,x128902,x128903,x128904,x128905,x128906,
x128907,x128908,x128909,x128910,x128911,x128912,x128913,x128914,x128915,
x128916,x128917,x128918,x128919,x128920,x128921,x128922,x128923,x128924,
x128925,x128926,x128927,x128928,x128929,x128930,x128931,x128932,x128933,
x128934,x128935,x128936,x128937,x128938,x128939,x128940,x128941,x128942,
x128943,x128944,x128945,x128946,x128947,x128948,x128949,x128950,x128951,
x128952,x128953,x128954,x128955,x128956,x128957,x128958,x128959,x128960,
x128961,x128962,x128963,x128964,x128965,x128966,x128967,x128968,x128969,
x128970,x128971,x128972,x128973,x128974,x128975,x128976,x128977,x128978,
x128979,x128980,x128981,x128982,x128983,x128984,x128985,x128986,x128987,
x128988,x128989,x128990,x128991,x128992,x128993,x128994,x128995,x128996,
x128997,x128998,x128999,x129000,x129001,x129002,x129003,x129004,x129005,
x129006,x129007,x129008,x129009,x129010,x129011,x129012,x129013,x129014,
x129015,x129016,x129017,x129018,x129019,x129020,x129021,x129022,x129023,
x129024,x129025,x129026,x129027,x129028,x129029,x129030,x129031,x129032,
x129033,x129034,x129035,x129036,x129037,x129038,x129039,x129040,x129041,
x129042,x129043,x129044,x129045,x129046,x129047,x129048,x129049,x129050,
x129051,x129052,x129053,x129054,x129055,x129056,x129057,x129058,x129059,
x129060,x129061,x129062,x129063,x129064,x129065,x129066,x129067,x129068,
x129069,x129070,x129071,x129072,x129073,x129074,x129075,x129076,x129077,
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