MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance m6
Facility Layout
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 82.25687690 (ALPHAECP) 82.25687691 (ANTIGONE) 82.25687691 (BARON) 82.25687691 (BONMIN) 82.25687691 (COUENNE) 82.25687691 (LINDO) 82.25687691 (SCIP) 82.25687691 (SHOT) |
| Referencesⓘ | Westerlund, Tapio and Lundqvist, Kurt, Alpha-ECP, Version 5.01 An Interactive MINLP-Solver Based on the Extended Cutting Plane Method, Tech. Rep. 01-178-A, Process Design Laboratory at Abo University, 2001. |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 26 Oct 2004 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 86 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 12 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 8 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 157 |
| #Linear Constraintsⓘ | 145 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 12 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 626 |
| #Nonlinear Nonzeros in Jacobianⓘ | 12 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 12 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 12 |
| #Blocks in Hessian of Lagrangianⓘ | 12 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 2.5000e+01 |
| Infeasibility of initial pointⓘ | 5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 158 1 0 157 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 87 57 30 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 635 623 12 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,objvar,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;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30;
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,e153,e154,e155
,e156,e157,e158;
e1.. objvar - 2.4*x32 - 2.4*x33 - 12*x50 - 12*x51 - 12*x58 - 12*x59 - 6*x60
- 6*x61 =E= 0;
e2.. x76 - x77 =L= 0;
e3.. 0.5*x62 - x68 + x76 =L= 0;
e4.. 0.5*x62 - x76 =L= 0;
e5.. 0.5*x69 - x75 + x82 =L= 0;
e6.. 0.5*x69 - x82 =L= 0;
e7.. 0.5*x63 - x68 + x77 =L= 0;
e8.. 0.5*x63 - x77 =L= 0;
e9.. 0.5*x70 - x75 + x83 =L= 0;
e10.. 0.5*x70 - x83 =L= 0;
e11.. 0.5*x64 - x68 + x78 =L= 0;
e12.. 0.5*x64 - x78 =L= 0;
e13.. 0.5*x71 - x75 + x84 =L= 0;
e14.. 0.5*x71 - x84 =L= 0;
e15.. 0.5*x65 - x68 + x79 =L= 0;
e16.. 0.5*x65 - x79 =L= 0;
e17.. 0.5*x72 - x75 + x85 =L= 0;
e18.. 0.5*x72 - x85 =L= 0;
e19.. 0.5*x66 - x68 + x80 =L= 0;
e20.. 0.5*x66 - x80 =L= 0;
e21.. 0.5*x73 - x75 + x86 =L= 0;
e22.. 0.5*x73 - x86 =L= 0;
e23.. 0.5*x67 - x68 + x81 =L= 0;
e24.. 0.5*x67 - x81 =L= 0;
e25.. 0.5*x74 - x75 + x87 =L= 0;
e26.. 0.5*x74 - x87 =L= 0;
e27.. - x32 + x76 - x77 =L= 0;
e28.. - x32 - x76 + x77 =L= 0;
e29.. - x33 + x82 - x83 =L= 0;
e30.. - x33 - x82 + x83 =L= 0;
e31.. - 15*b1 - 15*b2 + 0.5*x62 + 0.5*x63 - x76 + x77 =L= 0;
e32.. - 15*b1 + 15*b2 + 0.5*x62 + 0.5*x63 + x76 - x77 =L= 15;
e33.. 5*b1 - 5*b2 + 0.5*x69 + 0.5*x70 - x82 + x83 =L= 5;
e34.. 5*b1 + 5*b2 + 0.5*x69 + 0.5*x70 + x82 - x83 =L= 10;
e35.. - x34 + x76 - x78 =L= 0;
e36.. - x34 - x76 + x78 =L= 0;
e37.. - x35 + x82 - x84 =L= 0;
e38.. - x35 - x82 + x84 =L= 0;
e39.. - 15*b3 - 15*b4 + 0.5*x62 + 0.5*x64 - x76 + x78 =L= 0;
e40.. - 15*b3 + 15*b4 + 0.5*x62 + 0.5*x64 + x76 - x78 =L= 15;
e41.. 5*b3 - 5*b4 + 0.5*x69 + 0.5*x71 - x82 + x84 =L= 5;
e42.. 5*b3 + 5*b4 + 0.5*x69 + 0.5*x71 + x82 - x84 =L= 10;
e43.. - x36 + x76 - x79 =L= 0;
e44.. - x36 - x76 + x79 =L= 0;
e45.. - x37 + x82 - x85 =L= 0;
e46.. - x37 - x82 + x85 =L= 0;
e47.. - 15*b5 - 15*b6 + 0.5*x62 + 0.5*x65 - x76 + x79 =L= 0;
e48.. - 15*b5 + 15*b6 + 0.5*x62 + 0.5*x65 + x76 - x79 =L= 15;
e49.. 5*b5 - 5*b6 + 0.5*x69 + 0.5*x72 - x82 + x85 =L= 5;
e50.. 5*b5 + 5*b6 + 0.5*x69 + 0.5*x72 + x82 - x85 =L= 10;
e51.. - x38 + x76 - x80 =L= 0;
e52.. - x38 - x76 + x80 =L= 0;
e53.. - x39 + x82 - x86 =L= 0;
e54.. - x39 - x82 + x86 =L= 0;
e55.. - 15*b7 - 15*b8 + 0.5*x62 + 0.5*x66 - x76 + x80 =L= 0;
e56.. - 15*b7 + 15*b8 + 0.5*x62 + 0.5*x66 + x76 - x80 =L= 15;
e57.. 5*b7 - 5*b8 + 0.5*x69 + 0.5*x73 - x82 + x86 =L= 5;
e58.. 5*b7 + 5*b8 + 0.5*x69 + 0.5*x73 + x82 - x86 =L= 10;
e59.. - x40 + x76 - x81 =L= 0;
e60.. - x40 - x76 + x81 =L= 0;
e61.. - x41 + x82 - x87 =L= 0;
e62.. - x41 - x82 + x87 =L= 0;
e63.. - 15*b9 - 15*b10 + 0.5*x62 + 0.5*x67 - x76 + x81 =L= 0;
e64.. - 15*b9 + 15*b10 + 0.5*x62 + 0.5*x67 + x76 - x81 =L= 15;
e65.. 5*b9 - 5*b10 + 0.5*x69 + 0.5*x74 - x82 + x87 =L= 5;
e66.. 5*b9 + 5*b10 + 0.5*x69 + 0.5*x74 + x82 - x87 =L= 10;
e67.. - x42 + x77 - x78 =L= 0;
e68.. - x42 - x77 + x78 =L= 0;
e69.. - x43 + x83 - x84 =L= 0;
e70.. - x43 - x83 + x84 =L= 0;
e71.. - 15*b11 - 15*b12 + 0.5*x63 + 0.5*x64 - x77 + x78 =L= 0;
e72.. - 15*b11 + 15*b12 + 0.5*x63 + 0.5*x64 + x77 - x78 =L= 15;
e73.. 5*b11 - 5*b12 + 0.5*x70 + 0.5*x71 - x83 + x84 =L= 5;
e74.. 5*b11 + 5*b12 + 0.5*x70 + 0.5*x71 + x83 - x84 =L= 10;
e75.. - x44 + x77 - x79 =L= 0;
e76.. - x44 - x77 + x79 =L= 0;
e77.. - x45 + x83 - x85 =L= 0;
e78.. - x45 - x83 + x85 =L= 0;
e79.. - 15*b13 - 15*b14 + 0.5*x63 + 0.5*x65 - x77 + x79 =L= 0;
e80.. - 15*b13 + 15*b14 + 0.5*x63 + 0.5*x65 + x77 - x79 =L= 15;
e81.. 5*b13 - 5*b14 + 0.5*x70 + 0.5*x72 - x83 + x85 =L= 5;
e82.. 5*b13 + 5*b14 + 0.5*x70 + 0.5*x72 + x83 - x85 =L= 10;
e83.. - x46 + x77 - x80 =L= 0;
e84.. - x46 - x77 + x80 =L= 0;
e85.. - x47 + x83 - x86 =L= 0;
e86.. - x47 - x83 + x86 =L= 0;
e87.. - 15*b15 - 15*b16 + 0.5*x63 + 0.5*x66 - x77 + x80 =L= 0;
e88.. - 15*b15 + 15*b16 + 0.5*x63 + 0.5*x66 + x77 - x80 =L= 15;
e89.. 5*b15 - 5*b16 + 0.5*x70 + 0.5*x73 - x83 + x86 =L= 5;
e90.. 5*b15 + 5*b16 + 0.5*x70 + 0.5*x73 + x83 - x86 =L= 10;
e91.. - x48 + x77 - x81 =L= 0;
e92.. - x48 - x77 + x81 =L= 0;
e93.. - x49 + x83 - x87 =L= 0;
e94.. - x49 - x83 + x87 =L= 0;
e95.. - 15*b17 - 15*b18 + 0.5*x63 + 0.5*x67 - x77 + x81 =L= 0;
e96.. - 15*b17 + 15*b18 + 0.5*x63 + 0.5*x67 + x77 - x81 =L= 15;
e97.. 5*b17 - 5*b18 + 0.5*x70 + 0.5*x74 - x83 + x87 =L= 5;
e98.. 5*b17 + 5*b18 + 0.5*x70 + 0.5*x74 + x83 - x87 =L= 10;
e99.. - x50 + x78 - x79 =L= 0;
e100.. - x50 - x78 + x79 =L= 0;
e101.. - x51 + x84 - x85 =L= 0;
e102.. - x51 - x84 + x85 =L= 0;
e103.. - 15*b19 - 15*b20 + 0.5*x64 + 0.5*x65 - x78 + x79 =L= 0;
e104.. - 15*b19 + 15*b20 + 0.5*x64 + 0.5*x65 + x78 - x79 =L= 15;
e105.. 5*b19 - 5*b20 + 0.5*x71 + 0.5*x72 - x84 + x85 =L= 5;
e106.. 5*b19 + 5*b20 + 0.5*x71 + 0.5*x72 + x84 - x85 =L= 10;
e107.. - x52 + x78 - x80 =L= 0;
e108.. - x52 - x78 + x80 =L= 0;
e109.. - x53 + x84 - x86 =L= 0;
e110.. - x53 - x84 + x86 =L= 0;
e111.. - 15*b21 - 15*b22 + 0.5*x64 + 0.5*x66 - x78 + x80 =L= 0;
e112.. - 15*b21 + 15*b22 + 0.5*x64 + 0.5*x66 + x78 - x80 =L= 15;
e113.. 5*b21 - 5*b22 + 0.5*x71 + 0.5*x73 - x84 + x86 =L= 5;
e114.. 5*b21 + 5*b22 + 0.5*x71 + 0.5*x73 + x84 - x86 =L= 10;
e115.. - x54 + x78 - x81 =L= 0;
e116.. - x54 - x78 + x81 =L= 0;
e117.. - x55 + x84 - x87 =L= 0;
e118.. - x55 - x84 + x87 =L= 0;
e119.. - 15*b23 - 15*b24 + 0.5*x64 + 0.5*x67 - x78 + x81 =L= 0;
e120.. - 15*b23 + 15*b24 + 0.5*x64 + 0.5*x67 + x78 - x81 =L= 15;
e121.. 5*b23 - 5*b24 + 0.5*x71 + 0.5*x74 - x84 + x87 =L= 5;
e122.. 5*b23 + 5*b24 + 0.5*x71 + 0.5*x74 + x84 - x87 =L= 10;
e123.. - x56 + x79 - x80 =L= 0;
e124.. - x56 - x79 + x80 =L= 0;
e125.. - x57 + x85 - x86 =L= 0;
e126.. - x57 - x85 + x86 =L= 0;
e127.. - 15*b25 - 15*b26 + 0.5*x65 + 0.5*x66 - x79 + x80 =L= 0;
e128.. - 15*b25 + 15*b26 + 0.5*x65 + 0.5*x66 + x79 - x80 =L= 15;
e129.. 5*b25 - 5*b26 + 0.5*x72 + 0.5*x73 - x85 + x86 =L= 5;
e130.. 5*b25 + 5*b26 + 0.5*x72 + 0.5*x73 + x85 - x86 =L= 10;
e131.. - x58 + x79 - x81 =L= 0;
e132.. - x58 - x79 + x81 =L= 0;
e133.. - x59 + x85 - x87 =L= 0;
e134.. - x59 - x85 + x87 =L= 0;
e135.. - 15*b27 - 15*b28 + 0.5*x65 + 0.5*x67 - x79 + x81 =L= 0;
e136.. - 15*b27 + 15*b28 + 0.5*x65 + 0.5*x67 + x79 - x81 =L= 15;
e137.. 5*b27 - 5*b28 + 0.5*x72 + 0.5*x74 - x85 + x87 =L= 5;
e138.. 5*b27 + 5*b28 + 0.5*x72 + 0.5*x74 + x85 - x87 =L= 10;
e139.. - x60 + x80 - x81 =L= 0;
e140.. - x60 - x80 + x81 =L= 0;
e141.. - x61 + x86 - x87 =L= 0;
e142.. - x61 - x86 + x87 =L= 0;
e143.. - 15*b29 - 15*b30 + 0.5*x66 + 0.5*x67 - x80 + x81 =L= 0;
e144.. - 15*b29 + 15*b30 + 0.5*x66 + 0.5*x67 + x80 - x81 =L= 15;
e145.. 5*b29 - 5*b30 + 0.5*x73 + 0.5*x74 - x86 + x87 =L= 5;
e146.. 5*b29 + 5*b30 + 0.5*x73 + 0.5*x74 + x86 - x87 =L= 10;
e147.. 14/x62 - x69 =L= 0;
e148.. 14/x69 - x62 =L= 0;
e149.. 10/x63 - x70 =L= 0;
e150.. 10/x70 - x63 =L= 0;
e151.. 9/x64 - x71 =L= 0;
e152.. 9/x71 - x64 =L= 0;
e153.. 6/x65 - x72 =L= 0;
e154.. 6/x72 - x65 =L= 0;
e155.. 10/x66 - x73 =L= 0;
e156.. 10/x73 - x66 =L= 0;
e157.. 25/x67 - x74 =L= 0;
e158.. 25/x74 - x67 =L= 0;
* set non-default bounds
x62.lo = 2.8; x62.up = 7.4833;
x63.lo = 2; x63.up = 6.3246;
x64.lo = 1.8; x64.up = 6;
x65.lo = 1.2247; x65.up = 4.899;
x66.lo = 2; x66.up = 6.3246;
x67.lo = 5; x67.up = 10;
x68.fx = 15;
x69.lo = 1.8708; x69.up = 5;
x70.lo = 1.5811; x70.up = 5;
x71.lo = 1.5; x71.up = 5;
x72.lo = 1.2247; x72.up = 4.899;
x73.lo = 1.5811; x73.up = 5;
x74.lo = 2.5; x74.up = 5;
x75.fx = 5;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc