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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance wastewater05m2
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 229.70083910 (ANTIGONE) 229.70083910 (BARON) 149.93470460 (COUENNE) 229.70083940 (GUROBI) 229.70083930 (LINDO) 229.70083940 (SCIP) |
| Referencesⓘ | Castro, Pedro M, Matos, Henrique A, and Novais, Augusto Q, An efficient heuristic procedure for the optimal design of wastewater treatment systems, Resources, Conservation and Recycling, 50:2, 2007, 158-185. Castro, Pedro M, Teles, João P, and Novais, Augusto Q, Linear program-based algorithm for the optimal design of wastewater treatment systems, Clean Technologies and Environmental Policy, 11:1, 2009, 83-93. |
| Sourceⓘ | ANTIGONE test library model Other_MIQCQP/castro_etal_2007_wts_Ex05_M2.gms |
| Applicationⓘ | Waste Water Treatment |
| Added to libraryⓘ | 15 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 133 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 24 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 3 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 151 |
| #Linear Constraintsⓘ | 103 |
| #Quadratic Constraintsⓘ | 48 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 547 |
| #Nonlinear Nonzeros in Jacobianⓘ | 96 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 96 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 8 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 8.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 5.4871e+05 |
| Infeasibility of initial pointⓘ | 5.487e+05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 152 140 0 12 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 134 134 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 551 455 96 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
,x130,x131,x132,x133,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
,x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68
,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85
,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101
,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114
,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127
,x128,x129,x130,x131,x132,x133;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152;
e1.. - x26 - x27 - x28 + objvar =E= 0;
e2.. - x10 - x16 - x17 - x18 =E= -13.1;
e3.. - x11 - x19 - x20 - x21 =E= -32.7;
e4.. - x12 - x22 - x23 - x24 =E= -56.5;
e5.. - x1 - x4 - x7 - x16 - x19 - x22 + x26 =E= 0;
e6.. - x2 - x5 - x8 - x17 - x20 - x23 + x27 =E= 0;
e7.. - x3 - x6 - x9 - x18 - x21 - x24 + x28 =E= 0;
e8.. - x1 - x2 - x3 - x13 + x26 =E= 0;
e9.. - x4 - x5 - x6 - x14 + x27 =E= 0;
e10.. - x7 - x8 - x9 - x15 + x28 =E= 0;
e11.. - x10 - x11 - x12 - x13 - x14 - x15 + x25 =E= 0;
e12.. - x56 - x74 - x77 - x80 =E= -131;
e13.. - x57 - x75 - x78 - x81 =E= -5109;
e14.. - x58 - x76 - x79 - x82 =E= -327.5;
e15.. - x59 - x83 - x86 - x89 =E= -3597;
e16.. - x60 - x84 - x87 - x90 =E= -548706;
e17.. - x61 - x85 - x88 - x91 =E= -1308;
e18.. - x62 - x92 - x95 - x98 =E= -5650;
e19.. - x63 - x93 - x96 - x99 =E= -1412.5;
e20.. - x64 - x94 - x97 - x100 =E= -1977.5;
e21.. - x74 + 131*x125 =E= 0;
e22.. - x75 + 5109*x125 =E= 0;
e23.. - x76 + 327.5*x125 =E= 0;
e24.. - x77 + 131*x126 =E= 0;
e25.. - x78 + 5109*x126 =E= 0;
e26.. - x79 + 327.5*x126 =E= 0;
e27.. - x80 + 131*x127 =E= 0;
e28.. - x81 + 5109*x127 =E= 0;
e29.. - x82 + 327.5*x127 =E= 0;
e30.. - x83 + 3597*x128 =E= 0;
e31.. - x84 + 548706*x128 =E= 0;
e32.. - x85 + 1308*x128 =E= 0;
e33.. - x86 + 3597*x129 =E= 0;
e34.. - x87 + 548706*x129 =E= 0;
e35.. - x88 + 1308*x129 =E= 0;
e36.. - x89 + 3597*x130 =E= 0;
e37.. - x90 + 548706*x130 =E= 0;
e38.. - x91 + 1308*x130 =E= 0;
e39.. - x92 + 5650*x131 =E= 0;
e40.. - x93 + 1412.5*x131 =E= 0;
e41.. - x94 + 1977.5*x131 =E= 0;
e42.. - x95 + 5650*x132 =E= 0;
e43.. - x96 + 1412.5*x132 =E= 0;
e44.. - x97 + 1977.5*x132 =E= 0;
e45.. - x98 + 5650*x133 =E= 0;
e46.. - x99 + 1412.5*x133 =E= 0;
e47.. - x100 + 1977.5*x133 =E= 0;
e48.. - x56 + 131*x119 =E= 0;
e49.. - x57 + 5109*x119 =E= 0;
e50.. - x58 + 327.5*x119 =E= 0;
e51.. - x59 + 3597*x120 =E= 0;
e52.. - x60 + 548706*x120 =E= 0;
e53.. - x61 + 1308*x120 =E= 0;
e54.. - x62 + 5650*x121 =E= 0;
e55.. - x63 + 1412.5*x121 =E= 0;
e56.. - x64 + 1977.5*x121 =E= 0;
e57.. - x16 + 13.1*x125 =E= 0;
e58.. - x17 + 13.1*x126 =E= 0;
e59.. - x18 + 13.1*x127 =E= 0;
e60.. - x19 + 32.7*x128 =E= 0;
e61.. - x20 + 32.7*x129 =E= 0;
e62.. - x21 + 32.7*x130 =E= 0;
e63.. - x22 + 56.5*x131 =E= 0;
e64.. - x23 + 56.5*x132 =E= 0;
e65.. - x24 + 56.5*x133 =E= 0;
e66.. - x10 + 13.1*x119 =E= 0;
e67.. - x11 + 32.7*x120 =E= 0;
e68.. - x12 + 56.5*x121 =E= 0;
e69.. x119 + x125 + x126 + x127 =E= 1;
e70.. x120 + x128 + x129 + x130 =E= 1;
e71.. x121 + x131 + x132 + x133 =E= 1;
e72.. - 20000*x26 + x29 + x38 + x47 + x74 + x83 + x92 =L= 0;
e73.. - 20000*x26 + x30 + x39 + x48 + x75 + x84 + x93 =L= 0;
e74.. - 20000*x26 + x31 + x40 + x49 + x76 + x85 + x94 =L= 0;
e75.. - 20000*x27 + x32 + x41 + x50 + x77 + x86 + x95 =L= 0;
e76.. - 20000*x27 + x33 + x42 + x51 + x78 + x87 + x96 =L= 0;
e77.. - 20000*x27 + x34 + x43 + x52 + x79 + x88 + x97 =L= 0;
e78.. - 20000*x28 + x35 + x44 + x53 + x80 + x89 + x98 =L= 0;
e79.. - 20000*x28 + x36 + x45 + x54 + x81 + x90 + x99 =L= 0;
e80.. - 20000*x28 + x37 + x46 + x55 + x82 + x91 + x100 =L= 0;
e81.. x29 + x38 + x47 + x74 + x83 + x92 - x101 =E= 0;
e82.. 0.001*x30 + 0.001*x39 + 0.001*x48 + 0.001*x75 + 0.001*x84 + 0.001*x93
- x102 =E= 0;
e83.. x31 + x40 + x49 + x76 + x85 + x94 - x103 =E= 0;
e84.. 0.1*x32 + 0.1*x41 + 0.1*x50 + 0.1*x77 + 0.1*x86 + 0.1*x95 - x104 =E= 0
;
e85.. 0.1*x33 + 0.1*x42 + 0.1*x51 + 0.1*x78 + 0.1*x87 + 0.1*x96 - x105 =E= 0
;
e86.. 0.03*x34 + 0.03*x43 + 0.03*x52 + 0.03*x79 + 0.03*x88 + 0.03*x97 - x106
=E= 0;
e87.. 0.05*x35 + 0.05*x44 + 0.05*x53 + 0.05*x80 + 0.05*x89 + 0.05*x98 - x107
=E= 0;
e88.. x36 + x45 + x54 + x81 + x90 + x99 - x108 =E= 0;
e89.. 0.8*x37 + 0.8*x46 + 0.8*x55 + 0.8*x82 + 0.8*x91 + 0.8*x100 - x109
=E= 0;
e90.. - x29 - x32 - x35 - x65 + x101 =E= 0;
e91.. - x30 - x33 - x36 - x66 + x102 =E= 0;
e92.. - x31 - x34 - x37 - x67 + x103 =E= 0;
e93.. - x38 - x41 - x44 - x68 + x104 =E= 0;
e94.. - x39 - x42 - x45 - x69 + x105 =E= 0;
e95.. - x40 - x43 - x46 - x70 + x106 =E= 0;
e96.. - x47 - x50 - x53 - x71 + x107 =E= 0;
e97.. - x48 - x51 - x54 - x72 + x108 =E= 0;
e98.. - x49 - x52 - x55 - x73 + x109 =E= 0;
e99.. x101*x110 - x29 =E= 0;
e100.. x102*x110 - x30 =E= 0;
e101.. x103*x110 - x31 =E= 0;
e102.. x101*x111 - x32 =E= 0;
e103.. x102*x111 - x33 =E= 0;
e104.. x103*x111 - x34 =E= 0;
e105.. x101*x112 - x35 =E= 0;
e106.. x102*x112 - x36 =E= 0;
e107.. x103*x112 - x37 =E= 0;
e108.. x104*x113 - x38 =E= 0;
e109.. x105*x113 - x39 =E= 0;
e110.. x106*x113 - x40 =E= 0;
e111.. x104*x114 - x41 =E= 0;
e112.. x105*x114 - x42 =E= 0;
e113.. x106*x114 - x43 =E= 0;
e114.. x104*x115 - x44 =E= 0;
e115.. x105*x115 - x45 =E= 0;
e116.. x106*x115 - x46 =E= 0;
e117.. x107*x116 - x47 =E= 0;
e118.. x108*x116 - x48 =E= 0;
e119.. x109*x116 - x49 =E= 0;
e120.. x107*x117 - x50 =E= 0;
e121.. x108*x117 - x51 =E= 0;
e122.. x109*x117 - x52 =E= 0;
e123.. x107*x118 - x53 =E= 0;
e124.. x108*x118 - x54 =E= 0;
e125.. x109*x118 - x55 =E= 0;
e126.. x101*x122 - x65 =E= 0;
e127.. x102*x122 - x66 =E= 0;
e128.. x103*x122 - x67 =E= 0;
e129.. x104*x123 - x68 =E= 0;
e130.. x105*x123 - x69 =E= 0;
e131.. x106*x123 - x70 =E= 0;
e132.. x107*x124 - x71 =E= 0;
e133.. x108*x124 - x72 =E= 0;
e134.. x109*x124 - x73 =E= 0;
e135.. x26*x110 - x1 =E= 0;
e136.. x26*x111 - x2 =E= 0;
e137.. x26*x112 - x3 =E= 0;
e138.. x27*x113 - x4 =E= 0;
e139.. x27*x114 - x5 =E= 0;
e140.. x27*x115 - x6 =E= 0;
e141.. x28*x116 - x7 =E= 0;
e142.. x28*x117 - x8 =E= 0;
e143.. x28*x118 - x9 =E= 0;
e144.. x26*x122 - x13 =E= 0;
e145.. x27*x123 - x14 =E= 0;
e146.. x28*x124 - x15 =E= 0;
e147.. x110 + x111 + x112 + x122 =E= 1;
e148.. x113 + x114 + x115 + x123 =E= 1;
e149.. x116 + x117 + x118 + x124 =E= 1;
e150.. - 2*x25 + x56 + x59 + x62 + x65 + x68 + x71 =L= 0;
e151.. - 2*x25 + x57 + x60 + x63 + x66 + x69 + x72 =L= 0;
e152.. - 5*x25 + x58 + x61 + x64 + x67 + x70 + x73 =L= 0;
* set non-default bounds
x1.up = 1000000;
x2.up = 1000000;
x3.up = 1000000;
x4.up = 1000000;
x5.up = 1000000;
x6.up = 1000000;
x7.up = 1000000;
x8.up = 1000000;
x9.up = 1000000;
x10.up = 1000000;
x11.up = 1000000;
x12.up = 1000000;
x13.up = 1000000;
x14.up = 1000000;
x15.up = 1000000;
x16.up = 1000000;
x17.up = 1000000;
x18.up = 1000000;
x19.up = 1000000;
x20.up = 1000000;
x21.up = 1000000;
x22.up = 1000000;
x23.up = 1000000;
x24.up = 1000000;
x25.up = 1000000;
x26.up = 1000000;
x27.up = 1000000;
x28.up = 1000000;
x29.up = 1000000;
x30.up = 1000000;
x31.up = 1000000;
x32.up = 1000000;
x33.up = 1000000;
x34.up = 1000000;
x35.up = 1000000;
x36.up = 1000000;
x37.up = 1000000;
x38.up = 1000000;
x39.up = 1000000;
x40.up = 1000000;
x41.up = 1000000;
x42.up = 1000000;
x43.up = 1000000;
x44.up = 1000000;
x45.up = 1000000;
x46.up = 1000000;
x47.up = 1000000;
x48.up = 1000000;
x49.up = 1000000;
x50.up = 1000000;
x51.up = 1000000;
x52.up = 1000000;
x53.up = 1000000;
x54.up = 1000000;
x55.up = 1000000;
x56.up = 1000000;
x57.up = 1000000;
x58.up = 1000000;
x59.up = 1000000;
x60.up = 1000000;
x61.up = 1000000;
x62.up = 1000000;
x63.up = 1000000;
x64.up = 1000000;
x65.up = 1000000;
x66.up = 1000000;
x67.up = 1000000;
x68.up = 1000000;
x69.up = 1000000;
x70.up = 1000000;
x71.up = 1000000;
x72.up = 1000000;
x73.up = 1000000;
x74.up = 1000000;
x75.up = 1000000;
x76.up = 1000000;
x77.up = 1000000;
x78.up = 1000000;
x79.up = 1000000;
x80.up = 1000000;
x81.up = 1000000;
x82.up = 1000000;
x83.up = 1000000;
x84.up = 1000000;
x85.up = 1000000;
x86.up = 1000000;
x87.up = 1000000;
x88.up = 1000000;
x89.up = 1000000;
x90.up = 1000000;
x91.up = 1000000;
x92.up = 1000000;
x93.up = 1000000;
x94.up = 1000000;
x95.up = 1000000;
x96.up = 1000000;
x97.up = 1000000;
x98.up = 1000000;
x99.up = 1000000;
x100.up = 1000000;
x101.up = 1000000;
x102.up = 1000000;
x103.up = 1000000;
x104.up = 1000000;
x105.up = 1000000;
x106.up = 1000000;
x107.up = 1000000;
x108.up = 1000000;
x109.up = 1000000;
x110.up = 1000000;
x111.up = 1000000;
x112.up = 1000000;
x113.up = 1000000;
x114.up = 1000000;
x115.up = 1000000;
x116.up = 1000000;
x117.up = 1000000;
x118.up = 1000000;
x119.up = 1000000;
x120.up = 1000000;
x121.up = 1000000;
x122.up = 1000000;
x123.up = 1000000;
x124.up = 1000000;
x125.up = 1000000;
x126.up = 1000000;
x127.up = 1000000;
x128.up = 1000000;
x129.up = 1000000;
x130.up = 1000000;
x131.up = 1000000;
x132.up = 1000000;
x133.up = 1000000;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2024-08-26 Git hash: 6cc1607f