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Instance slay06m
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ⓘ | 29761.12900000 (ALPHAECP) 32757.01956000 (ANTIGONE) 32757.02015000 (BARON) 32757.02000000 (BONMIN) 32757.02000000 (COUENNE) 32757.02018000 (CPLEX) 32757.02018000 (GUROBI) 32757.02018000 (LINDO) 32757.02018000 (SCIP) 32757.02018000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay06M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 102 |
| #Binary Variablesⓘ | 60 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 12 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 42 |
| #Nonlinear Nonzeros in Objectiveⓘ | 12 |
| #Constraintsⓘ | 135 |
| #Linear Constraintsⓘ | 135 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 420 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #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ⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 3.9000e+02 |
| Infeasibility of initial pointⓘ | 2.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 136 16 60 60 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 103 43 60 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 463 451 12 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,b13,b14,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,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
,objvar;
Positive Variables 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;
Binary Variables b13,b14,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;
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;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x7)) + 390*(sqr((-10) + x2) + sqr((-15
) + x8)) + 240*(sqr((-7) + x3) + sqr((-9) + x9)) + 70*(sqr((-3) + x4) +
sqr((-3) + x10)) + 165*(sqr((-20) + x5) + sqr((-17) + x11)) + 100*(sqr((-
18) + x6) + sqr((-8) + x12))) - 300*x73 - 240*x74 - 210*x75 - 140*x76
- 300*x77 - 100*x78 - 150*x79 - 220*x80 - 200*x81 - 120*x82 - 300*x83
- 150*x84 - 100*x85 - 120*x86 - 130*x87 - 300*x88 - 240*x89 - 210*x90
- 140*x91 - 300*x92 - 100*x93 - 150*x94 - 220*x95 - 200*x96 - 120*x97
- 300*x98 - 150*x99 - 100*x100 - 120*x101 - 130*x102 + objvar =E= 0;
e2.. - x1 + x2 + x73 =G= 0;
e3.. - x1 + x3 + x74 =G= 0;
e4.. - x1 + x4 + x75 =G= 0;
e5.. - x1 + x5 + x76 =G= 0;
e6.. - x1 + x6 + x77 =G= 0;
e7.. - x2 + x3 + x78 =G= 0;
e8.. - x2 + x4 + x79 =G= 0;
e9.. - x2 + x5 + x80 =G= 0;
e10.. - x2 + x6 + x81 =G= 0;
e11.. - x3 + x4 + x82 =G= 0;
e12.. - x3 + x5 + x83 =G= 0;
e13.. - x3 + x6 + x84 =G= 0;
e14.. - x4 + x5 + x85 =G= 0;
e15.. - x4 + x6 + x86 =G= 0;
e16.. - x5 + x6 + x87 =G= 0;
e17.. x1 - x2 + x73 =G= 0;
e18.. x1 - x3 + x74 =G= 0;
e19.. x1 - x4 + x75 =G= 0;
e20.. x1 - x5 + x76 =G= 0;
e21.. x1 - x6 + x77 =G= 0;
e22.. x2 - x3 + x78 =G= 0;
e23.. x2 - x4 + x79 =G= 0;
e24.. x2 - x5 + x80 =G= 0;
e25.. x2 - x6 + x81 =G= 0;
e26.. x3 - x4 + x82 =G= 0;
e27.. x3 - x5 + x83 =G= 0;
e28.. x3 - x6 + x84 =G= 0;
e29.. x4 - x5 + x85 =G= 0;
e30.. x4 - x6 + x86 =G= 0;
e31.. x5 - x6 + x87 =G= 0;
e32.. - x7 + x8 + x88 =G= 0;
e33.. - x7 + x9 + x89 =G= 0;
e34.. - x7 + x10 + x90 =G= 0;
e35.. - x7 + x11 + x91 =G= 0;
e36.. - x7 + x12 + x92 =G= 0;
e37.. - x8 + x9 + x93 =G= 0;
e38.. - x8 + x10 + x94 =G= 0;
e39.. - x8 + x11 + x95 =G= 0;
e40.. - x8 + x12 + x96 =G= 0;
e41.. - x9 + x10 + x97 =G= 0;
e42.. - x9 + x11 + x98 =G= 0;
e43.. - x9 + x12 + x99 =G= 0;
e44.. - x10 + x11 + x100 =G= 0;
e45.. - x10 + x12 + x101 =G= 0;
e46.. - x11 + x12 + x102 =G= 0;
e47.. x7 - x8 + x88 =G= 0;
e48.. x7 - x9 + x89 =G= 0;
e49.. x7 - x10 + x90 =G= 0;
e50.. x7 - x11 + x91 =G= 0;
e51.. x7 - x12 + x92 =G= 0;
e52.. x8 - x9 + x93 =G= 0;
e53.. x8 - x10 + x94 =G= 0;
e54.. x8 - x11 + x95 =G= 0;
e55.. x8 - x12 + x96 =G= 0;
e56.. x9 - x10 + x97 =G= 0;
e57.. x9 - x11 + x98 =G= 0;
e58.. x9 - x12 + x99 =G= 0;
e59.. x10 - x11 + x100 =G= 0;
e60.. x10 - x12 + x101 =G= 0;
e61.. x11 - x12 + x102 =G= 0;
e62.. x1 - x2 + 30*b13 =L= 24;
e63.. x1 - x3 + 30*b14 =L= 26;
e64.. x1 - x4 + 30*b15 =L= 26.5;
e65.. x1 - x5 + 30*b16 =L= 25.5;
e66.. x1 - x6 + 30*b17 =L= 25;
e67.. x2 - x3 + 30*b18 =L= 25;
e68.. x2 - x4 + 30*b19 =L= 25.5;
e69.. x2 - x5 + 30*b20 =L= 24.5;
e70.. x2 - x6 + 30*b21 =L= 24;
e71.. x3 - x4 + 30*b22 =L= 27.5;
e72.. x3 - x5 + 30*b23 =L= 26.5;
e73.. x3 - x6 + 30*b24 =L= 26;
e74.. x4 - x5 + 30*b25 =L= 27;
e75.. x4 - x6 + 30*b26 =L= 26.5;
e76.. x5 - x6 + 30*b27 =L= 25.5;
e77.. - x1 + x2 + 30*b28 =L= 24;
e78.. - x1 + x3 + 30*b29 =L= 26;
e79.. - x1 + x4 + 30*b30 =L= 26.5;
e80.. - x1 + x5 + 30*b31 =L= 25.5;
e81.. - x1 + x6 + 30*b32 =L= 25;
e82.. - x2 + x3 + 30*b33 =L= 25;
e83.. - x2 + x4 + 30*b34 =L= 25.5;
e84.. - x2 + x5 + 30*b35 =L= 24.5;
e85.. - x2 + x6 + 30*b36 =L= 24;
e86.. - x3 + x4 + 30*b37 =L= 27.5;
e87.. - x3 + x5 + 30*b38 =L= 26.5;
e88.. - x3 + x6 + 30*b39 =L= 26;
e89.. - x4 + x5 + 30*b40 =L= 27;
e90.. - x4 + x6 + 30*b41 =L= 26.5;
e91.. - x5 + x6 + 30*b42 =L= 25.5;
e92.. x7 - x8 + 30*b43 =L= 24.5;
e93.. x7 - x9 + 30*b44 =L= 25.5;
e94.. x7 - x10 + 30*b45 =L= 25.5;
e95.. x7 - x11 + 30*b46 =L= 25;
e96.. x7 - x12 + 30*b47 =L= 26;
e97.. x8 - x9 + 30*b48 =L= 26;
e98.. x8 - x10 + 30*b49 =L= 26;
e99.. x8 - x11 + 30*b50 =L= 25.5;
e100.. x8 - x12 + 30*b51 =L= 26.5;
e101.. x9 - x10 + 30*b52 =L= 27;
e102.. x9 - x11 + 30*b53 =L= 26.5;
e103.. x9 - x12 + 30*b54 =L= 27.5;
e104.. x10 - x11 + 30*b55 =L= 26.5;
e105.. x10 - x12 + 30*b56 =L= 27.5;
e106.. x11 - x12 + 30*b57 =L= 27;
e107.. - x7 + x8 + 30*b58 =L= 24.5;
e108.. - x7 + x9 + 30*b59 =L= 25.5;
e109.. - x7 + x10 + 30*b60 =L= 25.5;
e110.. - x7 + x11 + 30*b61 =L= 25;
e111.. - x7 + x12 + 30*b62 =L= 26;
e112.. - x8 + x9 + 30*b63 =L= 26;
e113.. - x8 + x10 + 30*b64 =L= 26;
e114.. - x8 + x11 + 30*b65 =L= 25.5;
e115.. - x8 + x12 + 30*b66 =L= 26.5;
e116.. - x9 + x10 + 30*b67 =L= 27;
e117.. - x9 + x11 + 30*b68 =L= 26.5;
e118.. - x9 + x12 + 30*b69 =L= 27.5;
e119.. - x10 + x11 + 30*b70 =L= 26.5;
e120.. - x10 + x12 + 30*b71 =L= 27.5;
e121.. - x11 + x12 + 30*b72 =L= 27;
e122.. b13 + b28 + b43 + b58 =E= 1;
e123.. b14 + b29 + b44 + b59 =E= 1;
e124.. b15 + b30 + b45 + b60 =E= 1;
e125.. b16 + b31 + b46 + b61 =E= 1;
e126.. b17 + b32 + b47 + b62 =E= 1;
e127.. b18 + b33 + b48 + b63 =E= 1;
e128.. b19 + b34 + b49 + b64 =E= 1;
e129.. b20 + b35 + b50 + b65 =E= 1;
e130.. b21 + b36 + b51 + b66 =E= 1;
e131.. b22 + b37 + b52 + b67 =E= 1;
e132.. b23 + b38 + b53 + b68 =E= 1;
e133.. b24 + b39 + b54 + b69 =E= 1;
e134.. b25 + b40 + b55 + b70 =E= 1;
e135.. b26 + b41 + b56 + b71 =E= 1;
e136.. b27 + b42 + b57 + b72 =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 = 2; x5.up = 28;
x6.lo = 2.5; x6.up = 27.5;
x7.lo = 3; x7.up = 27;
x8.lo = 2.5; x8.up = 27.5;
x9.lo = 1.5; x9.up = 28.5;
x10.lo = 1.5; x10.up = 28.5;
x11.lo = 2; x11.up = 28;
x12.lo = 1; x12.up = 29;
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