MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance flay03h
Determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 48.98894200 (ALPHAECP) 48.98979257 (ANTIGONE) 48.98979272 (BARON) 48.98979486 (BONMIN) 48.98978636 (COUENNE) 48.98979352 (LINDO) 48.98979322 (SCIP) 48.98974379 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | FLay03H.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 122 |
| #Binary Variablesⓘ | 12 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 3 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 2 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 144 |
| #Linear Constraintsⓘ | 141 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 3 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 384 |
| #Nonlinear Nonzeros in Jacobianⓘ | 3 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 3 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 3 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| 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ⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 6.0000e+01 |
| Infeasibility of initial pointⓘ | 59 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 145 28 6 111 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 123 111 12 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 387 384 3 0
*
* Solve m using MINLP 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,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,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;
Binary Variables b111,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122;
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;
e1.. - 2*x13 - 2*x14 + objvar =E= 0;
e2.. - x1 - x7 + x13 =G= 0;
e3.. - x2 - x8 + x13 =G= 0;
e4.. - x3 - x9 + x13 =G= 0;
e5.. - x4 - x10 + x14 =G= 0;
e6.. - x5 - x11 + x14 =G= 0;
e7.. - x6 - x12 + x14 =G= 0;
e8.. 40/x10 - x7 =L= 0;
e9.. 50/x11 - x8 =L= 0;
e10.. 60/x12 - x9 =L= 0;
e11.. x1 - x15 - x17 - x19 - x21 =E= 0;
e12.. x1 - x16 - x18 - x20 - x22 =E= 0;
e13.. x2 - x23 - x25 - x27 - x29 =E= 0;
e14.. x2 - x24 - x26 - x28 - x30 =E= 0;
e15.. x3 - x31 - x33 - x35 - x37 =E= 0;
e16.. x3 - x32 - x34 - x36 - x38 =E= 0;
e17.. x4 - x39 - x41 - x43 - x45 =E= 0;
e18.. x4 - x40 - x42 - x44 - x46 =E= 0;
e19.. x5 - x47 - x49 - x51 - x53 =E= 0;
e20.. x5 - x48 - x50 - x52 - x54 =E= 0;
e21.. x6 - x55 - x57 - x59 - x61 =E= 0;
e22.. x6 - x56 - x58 - x60 - x62 =E= 0;
e23.. x7 - x63 - x65 - x67 - x69 =E= 0;
e24.. x7 - x64 - x66 - x68 - x70 =E= 0;
e25.. x8 - x71 - x73 - x75 - x77 =E= 0;
e26.. x8 - x72 - x74 - x76 - x78 =E= 0;
e27.. x9 - x79 - x81 - x83 - x85 =E= 0;
e28.. x9 - x80 - x82 - x84 - x86 =E= 0;
e29.. x10 - x87 - x89 - x91 - x93 =E= 0;
e30.. x10 - x88 - x90 - x92 - x94 =E= 0;
e31.. x11 - x95 - x97 - x99 - x101 =E= 0;
e32.. x11 - x96 - x98 - x100 - x102 =E= 0;
e33.. x12 - x103 - x105 - x107 - x109 =E= 0;
e34.. x12 - x104 - x106 - x108 - x110 =E= 0;
e35.. x15 - 29*b111 =L= 0;
e36.. x16 - 29*b112 =L= 0;
e37.. x17 - 29*b114 =L= 0;
e38.. x18 - 29*b115 =L= 0;
e39.. x19 - 29*b117 =L= 0;
e40.. x20 - 29*b118 =L= 0;
e41.. x21 - 29*b120 =L= 0;
e42.. x22 - 29*b121 =L= 0;
e43.. x23 - 29*b111 =L= 0;
e44.. x24 - 29*b113 =L= 0;
e45.. x25 - 29*b114 =L= 0;
e46.. x26 - 29*b116 =L= 0;
e47.. x27 - 29*b117 =L= 0;
e48.. x28 - 29*b119 =L= 0;
e49.. x29 - 29*b120 =L= 0;
e50.. x30 - 29*b122 =L= 0;
e51.. x31 - 29*b112 =L= 0;
e52.. x32 - 29*b113 =L= 0;
e53.. x33 - 29*b115 =L= 0;
e54.. x34 - 29*b116 =L= 0;
e55.. x35 - 29*b118 =L= 0;
e56.. x36 - 29*b119 =L= 0;
e57.. x37 - 29*b121 =L= 0;
e58.. x38 - 29*b122 =L= 0;
e59.. x39 - 29*b111 =L= 0;
e60.. x40 - 29*b112 =L= 0;
e61.. x41 - 29*b114 =L= 0;
e62.. x42 - 29*b115 =L= 0;
e63.. x43 - 29*b117 =L= 0;
e64.. x44 - 29*b118 =L= 0;
e65.. x45 - 29*b120 =L= 0;
e66.. x46 - 29*b121 =L= 0;
e67.. x47 - 29*b111 =L= 0;
e68.. x48 - 29*b113 =L= 0;
e69.. x49 - 29*b114 =L= 0;
e70.. x50 - 29*b116 =L= 0;
e71.. x51 - 29*b117 =L= 0;
e72.. x52 - 29*b119 =L= 0;
e73.. x53 - 29*b120 =L= 0;
e74.. x54 - 29*b122 =L= 0;
e75.. x55 - 29*b112 =L= 0;
e76.. x56 - 29*b113 =L= 0;
e77.. x57 - 29*b115 =L= 0;
e78.. x58 - 29*b116 =L= 0;
e79.. x59 - 29*b118 =L= 0;
e80.. x60 - 29*b119 =L= 0;
e81.. x61 - 29*b121 =L= 0;
e82.. x62 - 29*b122 =L= 0;
e83.. x63 - 40*b111 =L= 0;
e84.. x64 - 40*b112 =L= 0;
e85.. x65 - 40*b114 =L= 0;
e86.. x66 - 40*b115 =L= 0;
e87.. x67 - 40*b117 =L= 0;
e88.. x68 - 40*b118 =L= 0;
e89.. x69 - 40*b120 =L= 0;
e90.. x70 - 40*b121 =L= 0;
e91.. x71 - 40*b111 =L= 0;
e92.. x72 - 50*b113 =L= 0;
e93.. x73 - 40*b114 =L= 0;
e94.. x74 - 50*b116 =L= 0;
e95.. x75 - 40*b117 =L= 0;
e96.. x76 - 50*b119 =L= 0;
e97.. x77 - 40*b120 =L= 0;
e98.. x78 - 50*b122 =L= 0;
e99.. x79 - 40*b112 =L= 0;
e100.. x80 - 50*b113 =L= 0;
e101.. x81 - 40*b115 =L= 0;
e102.. x82 - 50*b116 =L= 0;
e103.. x83 - 40*b118 =L= 0;
e104.. x84 - 50*b119 =L= 0;
e105.. x85 - 40*b121 =L= 0;
e106.. x86 - 50*b122 =L= 0;
e107.. x87 - 40*b111 =L= 0;
e108.. x88 - 40*b112 =L= 0;
e109.. x89 - 40*b114 =L= 0;
e110.. x90 - 40*b115 =L= 0;
e111.. x91 - 40*b117 =L= 0;
e112.. x92 - 40*b118 =L= 0;
e113.. x93 - 40*b120 =L= 0;
e114.. x94 - 40*b121 =L= 0;
e115.. x95 - 40*b111 =L= 0;
e116.. x96 - 50*b113 =L= 0;
e117.. x97 - 40*b114 =L= 0;
e118.. x98 - 50*b116 =L= 0;
e119.. x99 - 40*b117 =L= 0;
e120.. x100 - 50*b119 =L= 0;
e121.. x101 - 40*b120 =L= 0;
e122.. x102 - 50*b122 =L= 0;
e123.. x103 - 40*b112 =L= 0;
e124.. x104 - 50*b113 =L= 0;
e125.. x105 - 40*b115 =L= 0;
e126.. x106 - 50*b116 =L= 0;
e127.. x107 - 40*b118 =L= 0;
e128.. x108 - 50*b119 =L= 0;
e129.. x109 - 40*b121 =L= 0;
e130.. x110 - 50*b122 =L= 0;
e131.. x15 - x23 + x63 =L= 0;
e132.. x16 - x31 + x64 =L= 0;
e133.. x24 - x32 + x72 =L= 0;
e134.. - x17 + x25 + x73 =L= 0;
e135.. - x18 + x33 + x81 =L= 0;
e136.. - x26 + x34 + x82 =L= 0;
e137.. x43 - x51 + x91 =L= 0;
e138.. x44 - x59 + x92 =L= 0;
e139.. x52 - x60 + x100 =L= 0;
e140.. - x45 + x53 + x101 =L= 0;
e141.. - x46 + x61 + x109 =L= 0;
e142.. - x54 + x62 + x110 =L= 0;
e143.. b111 + b114 + b117 + b120 =E= 1;
e144.. b112 + b115 + b118 + b121 =E= 1;
e145.. b113 + b116 + b119 + b122 =E= 1;
* set non-default bounds
x1.up = 29;
x2.up = 29;
x3.up = 29;
x4.up = 29;
x5.up = 29;
x6.up = 29;
x7.lo = 1; x7.up = 40;
x8.lo = 1; x8.up = 50;
x9.lo = 1; x9.up = 60;
x10.lo = 1; x10.up = 40;
x11.lo = 1; x11.up = 50;
x12.lo = 1; x12.up = 60;
x13.up = 30;
x14.up = 30;
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