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Instance slay04h
Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 9859.65940000 (ALPHAECP) 9859.65938400 (ANTIGONE) 9859.65970000 (BARON) 9859.65970000 (BONMIN) 9859.65948700 (COUENNE) 9859.65970800 (CPLEX) 9859.65970800 (GUROBI) 9859.65970000 (LINDO) 9859.65970700 (SCIP) 9859.65970800 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay04H.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 140 |
| #Binary Variablesⓘ | 24 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 8 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 20 |
| #Nonlinear Nonzeros in Objectiveⓘ | 8 |
| #Constraintsⓘ | 174 |
| #Linear Constraintsⓘ | 174 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 480 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 8 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 8 |
| #Blocks in Hessian of Lagrangianⓘ | 8 |
| 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ⓘ | 3.9000e+02 |
| Infeasibility of initial pointⓘ | 3.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 175 31 24 120 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 141 117 24 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 501 493 8 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,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,x129
,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,objvar;
Positive Variables 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,x129,x130
,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140;
Binary Variables b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128;
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,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x5)) + 390*(sqr((-10) + x2) + sqr((-15
) + x6)) + 240*(sqr((-7) + x3) + sqr((-9) + x7)) + 70*(sqr((-3) + x4) +
sqr((-3) + x8))) - 300*x129 - 240*x130 - 210*x131 - 100*x132 - 150*x133
- 120*x134 - 300*x135 - 240*x136 - 210*x137 - 100*x138 - 150*x139
- 120*x140 + objvar =E= 0;
e2.. - x1 + x2 + x129 =G= 0;
e3.. - x1 + x3 + x130 =G= 0;
e4.. - x1 + x4 + x131 =G= 0;
e5.. - x2 + x3 + x132 =G= 0;
e6.. - x2 + x4 + x133 =G= 0;
e7.. - x3 + x4 + x134 =G= 0;
e8.. x1 - x2 + x129 =G= 0;
e9.. x1 - x3 + x130 =G= 0;
e10.. x1 - x4 + x131 =G= 0;
e11.. x2 - x3 + x132 =G= 0;
e12.. x2 - x4 + x133 =G= 0;
e13.. x3 - x4 + x134 =G= 0;
e14.. - x5 + x6 + x135 =G= 0;
e15.. - x5 + x7 + x136 =G= 0;
e16.. - x5 + x8 + x137 =G= 0;
e17.. - x6 + x7 + x138 =G= 0;
e18.. - x6 + x8 + x139 =G= 0;
e19.. - x7 + x8 + x140 =G= 0;
e20.. x5 - x6 + x135 =G= 0;
e21.. x5 - x7 + x136 =G= 0;
e22.. x5 - x8 + x137 =G= 0;
e23.. x6 - x7 + x138 =G= 0;
e24.. x6 - x8 + x139 =G= 0;
e25.. x7 - x8 + x140 =G= 0;
e26.. x1 - x9 - x12 - x15 - x18 =E= 0;
e27.. x1 - x10 - x13 - x16 - x19 =E= 0;
e28.. x1 - x11 - x14 - x17 - x20 =E= 0;
e29.. x2 - x21 - x24 - x27 - x30 =E= 0;
e30.. x2 - x22 - x25 - x28 - x31 =E= 0;
e31.. x2 - x23 - x26 - x29 - x32 =E= 0;
e32.. x3 - x33 - x36 - x39 - x42 =E= 0;
e33.. x3 - x34 - x37 - x40 - x43 =E= 0;
e34.. x3 - x35 - x38 - x41 - x44 =E= 0;
e35.. x4 - x45 - x48 - x51 - x54 =E= 0;
e36.. x4 - x46 - x49 - x52 - x55 =E= 0;
e37.. x4 - x47 - x50 - x53 - x56 =E= 0;
e38.. x5 - x57 - x60 - x63 - x66 =E= 0;
e39.. x5 - x58 - x61 - x64 - x67 =E= 0;
e40.. x5 - x59 - x62 - x65 - x68 =E= 0;
e41.. x6 - x69 - x72 - x75 - x78 =E= 0;
e42.. x6 - x70 - x73 - x76 - x79 =E= 0;
e43.. x6 - x71 - x74 - x77 - x80 =E= 0;
e44.. x7 - x81 - x84 - x87 - x90 =E= 0;
e45.. x7 - x82 - x85 - x88 - x91 =E= 0;
e46.. x7 - x83 - x86 - x89 - x92 =E= 0;
e47.. x8 - x93 - x96 - x99 - x102 =E= 0;
e48.. x8 - x94 - x97 - x100 - x103 =E= 0;
e49.. x8 - x95 - x98 - x101 - x104 =E= 0;
e50.. x9 - 27.5*b105 =L= 0;
e51.. x10 - 27.5*b106 =L= 0;
e52.. x11 - 27.5*b107 =L= 0;
e53.. x12 - 27.5*b111 =L= 0;
e54.. x13 - 27.5*b112 =L= 0;
e55.. x14 - 27.5*b113 =L= 0;
e56.. x15 - 27.5*b117 =L= 0;
e57.. x16 - 27.5*b118 =L= 0;
e58.. x17 - 27.5*b119 =L= 0;
e59.. x18 - 27.5*b123 =L= 0;
e60.. x19 - 27.5*b124 =L= 0;
e61.. x20 - 27.5*b125 =L= 0;
e62.. x21 - 27.5*b105 =L= 0;
e63.. x22 - 26.5*b108 =L= 0;
e64.. x23 - 26.5*b109 =L= 0;
e65.. x24 - 27.5*b111 =L= 0;
e66.. x25 - 26.5*b114 =L= 0;
e67.. x26 - 26.5*b115 =L= 0;
e68.. x27 - 27.5*b117 =L= 0;
e69.. x28 - 26.5*b120 =L= 0;
e70.. x29 - 26.5*b121 =L= 0;
e71.. x30 - 27.5*b123 =L= 0;
e72.. x31 - 26.5*b126 =L= 0;
e73.. x32 - 26.5*b127 =L= 0;
e74.. x33 - 27.5*b106 =L= 0;
e75.. x34 - 26.5*b108 =L= 0;
e76.. x35 - 28.5*b110 =L= 0;
e77.. x36 - 27.5*b112 =L= 0;
e78.. x37 - 26.5*b114 =L= 0;
e79.. x38 - 28.5*b116 =L= 0;
e80.. x39 - 27.5*b118 =L= 0;
e81.. x40 - 26.5*b120 =L= 0;
e82.. x41 - 28.5*b122 =L= 0;
e83.. x42 - 27.5*b124 =L= 0;
e84.. x43 - 26.5*b126 =L= 0;
e85.. x44 - 28.5*b128 =L= 0;
e86.. x45 - 27.5*b107 =L= 0;
e87.. x46 - 26.5*b109 =L= 0;
e88.. x47 - 28.5*b110 =L= 0;
e89.. x48 - 27.5*b113 =L= 0;
e90.. x49 - 26.5*b115 =L= 0;
e91.. x50 - 28.5*b116 =L= 0;
e92.. x51 - 27.5*b119 =L= 0;
e93.. x52 - 26.5*b121 =L= 0;
e94.. x53 - 28.5*b122 =L= 0;
e95.. x54 - 27.5*b125 =L= 0;
e96.. x55 - 26.5*b127 =L= 0;
e97.. x56 - 28.5*b128 =L= 0;
e98.. x57 - 27*b105 =L= 0;
e99.. x58 - 27*b106 =L= 0;
e100.. x59 - 27*b107 =L= 0;
e101.. x60 - 27*b111 =L= 0;
e102.. x61 - 27*b112 =L= 0;
e103.. x62 - 27*b113 =L= 0;
e104.. x63 - 27*b117 =L= 0;
e105.. x64 - 27*b118 =L= 0;
e106.. x65 - 27*b119 =L= 0;
e107.. x66 - 27*b123 =L= 0;
e108.. x67 - 27*b124 =L= 0;
e109.. x68 - 27*b125 =L= 0;
e110.. x69 - 27*b105 =L= 0;
e111.. x70 - 27.5*b108 =L= 0;
e112.. x71 - 27.5*b109 =L= 0;
e113.. x72 - 27*b111 =L= 0;
e114.. x73 - 27.5*b114 =L= 0;
e115.. x74 - 27.5*b115 =L= 0;
e116.. x75 - 27*b117 =L= 0;
e117.. x76 - 27.5*b120 =L= 0;
e118.. x77 - 27.5*b121 =L= 0;
e119.. x78 - 27*b123 =L= 0;
e120.. x79 - 27.5*b126 =L= 0;
e121.. x80 - 27.5*b127 =L= 0;
e122.. x81 - 27*b106 =L= 0;
e123.. x82 - 27.5*b108 =L= 0;
e124.. x83 - 28.5*b110 =L= 0;
e125.. x84 - 27*b112 =L= 0;
e126.. x85 - 27.5*b114 =L= 0;
e127.. x86 - 28.5*b116 =L= 0;
e128.. x87 - 27*b118 =L= 0;
e129.. x88 - 27.5*b120 =L= 0;
e130.. x89 - 28.5*b122 =L= 0;
e131.. x90 - 27*b124 =L= 0;
e132.. x91 - 27.5*b126 =L= 0;
e133.. x92 - 28.5*b128 =L= 0;
e134.. x93 - 27*b107 =L= 0;
e135.. x94 - 27.5*b109 =L= 0;
e136.. x95 - 28.5*b110 =L= 0;
e137.. x96 - 27*b113 =L= 0;
e138.. x97 - 27.5*b115 =L= 0;
e139.. x98 - 28.5*b116 =L= 0;
e140.. x99 - 27*b119 =L= 0;
e141.. x100 - 27.5*b121 =L= 0;
e142.. x101 - 28.5*b122 =L= 0;
e143.. x102 - 27*b125 =L= 0;
e144.. x103 - 27.5*b127 =L= 0;
e145.. x104 - 28.5*b128 =L= 0;
e146.. x9 - x21 + 6*b105 =L= 0;
e147.. x10 - x33 + 4*b106 =L= 0;
e148.. x11 - x45 + 3.5*b107 =L= 0;
e149.. x22 - x34 + 5*b108 =L= 0;
e150.. x23 - x46 + 4.5*b109 =L= 0;
e151.. x35 - x47 + 2.5*b110 =L= 0;
e152.. - x12 + x24 + 6*b111 =L= 0;
e153.. - x13 + x36 + 4*b112 =L= 0;
e154.. - x14 + x48 + 3.5*b113 =L= 0;
e155.. - x25 + x37 + 5*b114 =L= 0;
e156.. - x26 + x49 + 4.5*b115 =L= 0;
e157.. - x38 + x50 + 2.5*b116 =L= 0;
e158.. x63 - x75 + 5.5*b117 =L= 0;
e159.. x64 - x87 + 4.5*b118 =L= 0;
e160.. x65 - x99 + 4.5*b119 =L= 0;
e161.. x76 - x88 + 4*b120 =L= 0;
e162.. x77 - x100 + 4*b121 =L= 0;
e163.. x89 - x101 + 3*b122 =L= 0;
e164.. - x66 + x78 + 5.5*b123 =L= 0;
e165.. - x67 + x90 + 4.5*b124 =L= 0;
e166.. - x68 + x102 + 4.5*b125 =L= 0;
e167.. - x79 + x91 + 4*b126 =L= 0;
e168.. - x80 + x103 + 4*b127 =L= 0;
e169.. - x92 + x104 + 3*b128 =L= 0;
e170.. b105 + b111 + b117 + b123 =E= 1;
e171.. b106 + b112 + b118 + b124 =E= 1;
e172.. b107 + b113 + b119 + b125 =E= 1;
e173.. b108 + b114 + b120 + b126 =E= 1;
e174.. b109 + b115 + b121 + b127 =E= 1;
e175.. b110 + b116 + b122 + b128 =E= 1;
* set non-default bounds
x1.lo = 2.5; x1.up = 27.5;
x2.lo = 3.5; x2.up = 26.5;
x3.lo = 1.5; x3.up = 28.5;
x4.lo = 1; x4.up = 29;
x5.lo = 3; x5.up = 27;
x6.lo = 2.5; x6.up = 27.5;
x7.lo = 1.5; x7.up = 28.5;
x8.lo = 1.5; x8.up = 28.5;
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