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Instance slay07m
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ⓘ | 34119.82700000 (ALPHAECP) 64748.82251000 (ANTIGONE) 64748.82523000 (BARON) 64748.82500000 (BONMIN) 64748.82500000 (COUENNE) 64748.82529000 (CPLEX) 64748.82529000 (GUROBI) 64748.82529000 (LINDO) 64748.82529000 (SCIP) 64748.82529000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay07M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 140 |
| #Binary Variablesⓘ | 84 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 14 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 56 |
| #Nonlinear Nonzeros in Objectiveⓘ | 14 |
| #Constraintsⓘ | 189 |
| #Linear Constraintsⓘ | 189 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 588 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 14 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 14 |
| #Blocks in Hessian of Lagrangianⓘ | 14 |
| 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 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 190 22 84 84 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 141 57 84 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 645 631 14 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,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,x134,x135,x136,x137,x138,x139,x140,objvar;
Positive Variables 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,x134,x135,x136
,x137,x138,x139,x140;
Binary Variables b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29
,b30,b31,b32,b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46
,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63
,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80
,b81,b82,b83,b84,b85,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97
,b98;
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,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x8)) + 390*(sqr((-10) + x2) + sqr((-15
) + x9)) + 240*(sqr((-7) + x3) + sqr((-9) + x10)) + 70*(sqr((-3) + x4) +
sqr((-3) + x11)) + 165*(sqr((-20) + x5) + sqr((-17) + x12)) + 100*(sqr((-
18) + x6) + sqr((-8) + x13)) + 200*(sqr((-30) + x7) + sqr((-20) + x14)))
- 300*x99 - 240*x100 - 210*x101 - 140*x102 - 300*x103 - 250*x104
- 100*x105 - 150*x106 - 220*x107 - 200*x108 - 300*x109 - 120*x110
- 300*x111 - 150*x112 - 150*x113 - 100*x114 - 120*x115 - 180*x116
- 130*x117 - 190*x118 - 220*x119 - 300*x120 - 240*x121 - 210*x122
- 140*x123 - 300*x124 - 250*x125 - 100*x126 - 150*x127 - 220*x128
- 200*x129 - 300*x130 - 120*x131 - 300*x132 - 150*x133 - 150*x134
- 100*x135 - 120*x136 - 180*x137 - 130*x138 - 190*x139 - 220*x140
+ objvar =E= 0;
e2.. - x1 + x2 + x99 =G= 0;
e3.. - x1 + x3 + x100 =G= 0;
e4.. - x1 + x4 + x101 =G= 0;
e5.. - x1 + x5 + x102 =G= 0;
e6.. - x1 + x6 + x103 =G= 0;
e7.. - x1 + x7 + x104 =G= 0;
e8.. - x2 + x3 + x105 =G= 0;
e9.. - x2 + x4 + x106 =G= 0;
e10.. - x2 + x5 + x107 =G= 0;
e11.. - x2 + x6 + x108 =G= 0;
e12.. - x2 + x7 + x109 =G= 0;
e13.. - x3 + x4 + x110 =G= 0;
e14.. - x3 + x5 + x111 =G= 0;
e15.. - x3 + x6 + x112 =G= 0;
e16.. - x3 + x7 + x113 =G= 0;
e17.. - x4 + x5 + x114 =G= 0;
e18.. - x4 + x6 + x115 =G= 0;
e19.. - x4 + x7 + x116 =G= 0;
e20.. - x5 + x6 + x117 =G= 0;
e21.. - x5 + x7 + x118 =G= 0;
e22.. - x6 + x7 + x119 =G= 0;
e23.. x1 - x2 + x99 =G= 0;
e24.. x1 - x3 + x100 =G= 0;
e25.. x1 - x4 + x101 =G= 0;
e26.. x1 - x5 + x102 =G= 0;
e27.. x1 - x6 + x103 =G= 0;
e28.. x1 - x7 + x104 =G= 0;
e29.. x2 - x3 + x105 =G= 0;
e30.. x2 - x4 + x106 =G= 0;
e31.. x2 - x5 + x107 =G= 0;
e32.. x2 - x6 + x108 =G= 0;
e33.. x2 - x7 + x109 =G= 0;
e34.. x3 - x4 + x110 =G= 0;
e35.. x3 - x5 + x111 =G= 0;
e36.. x3 - x6 + x112 =G= 0;
e37.. x3 - x7 + x113 =G= 0;
e38.. x4 - x5 + x114 =G= 0;
e39.. x4 - x6 + x115 =G= 0;
e40.. x4 - x7 + x116 =G= 0;
e41.. x5 - x6 + x117 =G= 0;
e42.. x5 - x7 + x118 =G= 0;
e43.. x6 - x7 + x119 =G= 0;
e44.. - x8 + x9 + x120 =G= 0;
e45.. - x8 + x10 + x121 =G= 0;
e46.. - x8 + x11 + x122 =G= 0;
e47.. - x8 + x12 + x123 =G= 0;
e48.. - x8 + x13 + x124 =G= 0;
e49.. - x8 + x14 + x125 =G= 0;
e50.. - x9 + x10 + x126 =G= 0;
e51.. - x9 + x11 + x127 =G= 0;
e52.. - x9 + x12 + x128 =G= 0;
e53.. - x9 + x13 + x129 =G= 0;
e54.. - x9 + x14 + x130 =G= 0;
e55.. - x10 + x11 + x131 =G= 0;
e56.. - x10 + x12 + x132 =G= 0;
e57.. - x10 + x13 + x133 =G= 0;
e58.. - x10 + x14 + x134 =G= 0;
e59.. - x11 + x12 + x135 =G= 0;
e60.. - x11 + x13 + x136 =G= 0;
e61.. - x11 + x14 + x137 =G= 0;
e62.. - x12 + x13 + x138 =G= 0;
e63.. - x12 + x14 + x139 =G= 0;
e64.. - x13 + x14 + x140 =G= 0;
e65.. x8 - x9 + x120 =G= 0;
e66.. x8 - x10 + x121 =G= 0;
e67.. x8 - x11 + x122 =G= 0;
e68.. x8 - x12 + x123 =G= 0;
e69.. x8 - x13 + x124 =G= 0;
e70.. x8 - x14 + x125 =G= 0;
e71.. x9 - x10 + x126 =G= 0;
e72.. x9 - x11 + x127 =G= 0;
e73.. x9 - x12 + x128 =G= 0;
e74.. x9 - x13 + x129 =G= 0;
e75.. x9 - x14 + x130 =G= 0;
e76.. x10 - x11 + x131 =G= 0;
e77.. x10 - x12 + x132 =G= 0;
e78.. x10 - x13 + x133 =G= 0;
e79.. x10 - x14 + x134 =G= 0;
e80.. x11 - x12 + x135 =G= 0;
e81.. x11 - x13 + x136 =G= 0;
e82.. x11 - x14 + x137 =G= 0;
e83.. x12 - x13 + x138 =G= 0;
e84.. x12 - x14 + x139 =G= 0;
e85.. x13 - x14 + x140 =G= 0;
e86.. x1 - x2 + 40*b15 =L= 34;
e87.. x1 - x3 + 40*b16 =L= 36;
e88.. x1 - x4 + 40*b17 =L= 36.5;
e89.. x1 - x5 + 40*b18 =L= 35.5;
e90.. x1 - x6 + 40*b19 =L= 35;
e91.. x1 - x7 + 40*b20 =L= 33.5;
e92.. x2 - x3 + 40*b21 =L= 35;
e93.. x2 - x4 + 40*b22 =L= 35.5;
e94.. x2 - x5 + 40*b23 =L= 34.5;
e95.. x2 - x6 + 40*b24 =L= 34;
e96.. x2 - x7 + 40*b25 =L= 32.5;
e97.. x3 - x4 + 40*b26 =L= 37.5;
e98.. x3 - x5 + 40*b27 =L= 36.5;
e99.. x3 - x6 + 40*b28 =L= 36;
e100.. x3 - x7 + 40*b29 =L= 34.5;
e101.. x4 - x5 + 40*b30 =L= 37;
e102.. x4 - x6 + 40*b31 =L= 36.5;
e103.. x4 - x7 + 40*b32 =L= 35;
e104.. x5 - x6 + 40*b33 =L= 35.5;
e105.. x5 - x7 + 40*b34 =L= 34;
e106.. x6 - x7 + 40*b35 =L= 33.5;
e107.. - x1 + x2 + 40*b36 =L= 34;
e108.. - x1 + x3 + 40*b37 =L= 36;
e109.. - x1 + x4 + 40*b38 =L= 36.5;
e110.. - x1 + x5 + 40*b39 =L= 35.5;
e111.. - x1 + x6 + 40*b40 =L= 35;
e112.. - x1 + x7 + 40*b41 =L= 33.5;
e113.. - x2 + x3 + 40*b42 =L= 35;
e114.. - x2 + x4 + 40*b43 =L= 35.5;
e115.. - x2 + x5 + 40*b44 =L= 34.5;
e116.. - x2 + x6 + 40*b45 =L= 34;
e117.. - x2 + x7 + 40*b46 =L= 32.5;
e118.. - x3 + x4 + 40*b47 =L= 37.5;
e119.. - x3 + x5 + 40*b48 =L= 36.5;
e120.. - x3 + x6 + 40*b49 =L= 36;
e121.. - x3 + x7 + 40*b50 =L= 34.5;
e122.. - x4 + x5 + 40*b51 =L= 37;
e123.. - x4 + x6 + 40*b52 =L= 36.5;
e124.. - x4 + x7 + 40*b53 =L= 35;
e125.. - x5 + x6 + 40*b54 =L= 35.5;
e126.. - x5 + x7 + 40*b55 =L= 34;
e127.. - x6 + x7 + 40*b56 =L= 33.5;
e128.. x8 - x9 + 40*b57 =L= 34.5;
e129.. x8 - x10 + 40*b58 =L= 35.5;
e130.. x8 - x11 + 40*b59 =L= 35.5;
e131.. x8 - x12 + 40*b60 =L= 35;
e132.. x8 - x13 + 40*b61 =L= 36;
e133.. x8 - x14 + 40*b62 =L= 34;
e134.. x9 - x10 + 40*b63 =L= 36;
e135.. x9 - x11 + 40*b64 =L= 36;
e136.. x9 - x12 + 40*b65 =L= 35.5;
e137.. x9 - x13 + 40*b66 =L= 36.5;
e138.. x9 - x14 + 40*b67 =L= 34.5;
e139.. x10 - x11 + 40*b68 =L= 37;
e140.. x10 - x12 + 40*b69 =L= 36.5;
e141.. x10 - x13 + 40*b70 =L= 37.5;
e142.. x10 - x14 + 40*b71 =L= 35.5;
e143.. x11 - x12 + 40*b72 =L= 36.5;
e144.. x11 - x13 + 40*b73 =L= 37.5;
e145.. x11 - x14 + 40*b74 =L= 35.5;
e146.. x12 - x13 + 40*b75 =L= 37;
e147.. x12 - x14 + 40*b76 =L= 35;
e148.. x13 - x14 + 40*b77 =L= 36;
e149.. - x8 + x9 + 40*b78 =L= 34.5;
e150.. - x8 + x10 + 40*b79 =L= 35.5;
e151.. - x8 + x11 + 40*b80 =L= 35.5;
e152.. - x8 + x12 + 40*b81 =L= 35;
e153.. - x8 + x13 + 40*b82 =L= 36;
e154.. - x8 + x14 + 40*b83 =L= 34;
e155.. - x9 + x10 + 40*b84 =L= 36;
e156.. - x9 + x11 + 40*b85 =L= 36;
e157.. - x9 + x12 + 40*b86 =L= 35.5;
e158.. - x9 + x13 + 40*b87 =L= 36.5;
e159.. - x9 + x14 + 40*b88 =L= 34.5;
e160.. - x10 + x11 + 40*b89 =L= 37;
e161.. - x10 + x12 + 40*b90 =L= 36.5;
e162.. - x10 + x13 + 40*b91 =L= 37.5;
e163.. - x10 + x14 + 40*b92 =L= 35.5;
e164.. - x11 + x12 + 40*b93 =L= 36.5;
e165.. - x11 + x13 + 40*b94 =L= 37.5;
e166.. - x11 + x14 + 40*b95 =L= 35.5;
e167.. - x12 + x13 + 40*b96 =L= 37;
e168.. - x12 + x14 + 40*b97 =L= 35;
e169.. - x13 + x14 + 40*b98 =L= 36;
e170.. b15 + b36 + b57 + b78 =E= 1;
e171.. b16 + b37 + b58 + b79 =E= 1;
e172.. b17 + b38 + b59 + b80 =E= 1;
e173.. b18 + b39 + b60 + b81 =E= 1;
e174.. b19 + b40 + b61 + b82 =E= 1;
e175.. b20 + b41 + b62 + b83 =E= 1;
e176.. b21 + b42 + b63 + b84 =E= 1;
e177.. b22 + b43 + b64 + b85 =E= 1;
e178.. b23 + b44 + b65 + b86 =E= 1;
e179.. b24 + b45 + b66 + b87 =E= 1;
e180.. b25 + b46 + b67 + b88 =E= 1;
e181.. b26 + b47 + b68 + b89 =E= 1;
e182.. b27 + b48 + b69 + b90 =E= 1;
e183.. b28 + b49 + b70 + b91 =E= 1;
e184.. b29 + b50 + b71 + b92 =E= 1;
e185.. b30 + b51 + b72 + b93 =E= 1;
e186.. b31 + b52 + b73 + b94 =E= 1;
e187.. b32 + b53 + b74 + b95 =E= 1;
e188.. b33 + b54 + b75 + b96 =E= 1;
e189.. b34 + b55 + b76 + b97 =E= 1;
e190.. b35 + b56 + b77 + b98 =E= 1;
* set non-default bounds
x1.lo = 2.5; x1.up = 37.5;
x2.lo = 3.5; x2.up = 36.5;
x3.lo = 1.5; x3.up = 38.5;
x4.lo = 1; x4.up = 39;
x5.lo = 2; x5.up = 38;
x6.lo = 2.5; x6.up = 37.5;
x7.lo = 4; x7.up = 36;
x8.lo = 3; x8.up = 37;
x9.lo = 2.5; x9.up = 37.5;
x10.lo = 1.5; x10.up = 38.5;
x11.lo = 1.5; x11.up = 38.5;
x12.lo = 2; x12.up = 38;
x13.lo = 1; x13.up = 39;
x14.lo = 3; x14.up = 37;
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