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Instance slay05m
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ⓘ | 22664.67800000 (ALPHAECP) 22664.67846000 (ANTIGONE) 22664.67865000 (BARON) 22664.67865000 (BONMIN) 22664.67843000 (COUENNE) 22664.67865000 (CPLEX) 22664.67865000 (GUROBI) 22664.67865000 (LINDO) 22664.67865000 (SCIP) 22664.67865000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay05M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 70 |
| #Binary Variablesⓘ | 40 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 10 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 30 |
| #Nonlinear Nonzeros in Objectiveⓘ | 10 |
| #Constraintsⓘ | 90 |
| #Linear Constraintsⓘ | 90 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 280 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 10 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 10 |
| #Blocks in Hessian of Lagrangianⓘ | 10 |
| 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
* 91 11 40 40 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 71 31 40 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 311 301 10 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,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,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,objvar;
Positive Variables x51,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64
,x65,x66,x67,x68,x69,x70;
Binary Variables b11,b12,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;
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;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x6)) + 390*(sqr((-10) + x2) + sqr((-15
) + x7)) + 240*(sqr((-7) + x3) + sqr((-9) + x8)) + 70*(sqr((-3) + x4) +
sqr((-3) + x9)) + 165*(sqr((-20) + x5) + sqr((-17) + x10))) - 300*x51
- 240*x52 - 210*x53 - 140*x54 - 100*x55 - 150*x56 - 220*x57 - 120*x58
- 300*x59 - 100*x60 - 300*x61 - 240*x62 - 210*x63 - 140*x64 - 100*x65
- 150*x66 - 220*x67 - 120*x68 - 300*x69 - 100*x70 + objvar =E= 0;
e2.. - x1 + x2 + x51 =G= 0;
e3.. - x1 + x3 + x52 =G= 0;
e4.. - x1 + x4 + x53 =G= 0;
e5.. - x1 + x5 + x54 =G= 0;
e6.. - x2 + x3 + x55 =G= 0;
e7.. - x2 + x4 + x56 =G= 0;
e8.. - x2 + x5 + x57 =G= 0;
e9.. - x3 + x4 + x58 =G= 0;
e10.. - x3 + x5 + x59 =G= 0;
e11.. - x4 + x5 + x60 =G= 0;
e12.. x1 - x2 + x51 =G= 0;
e13.. x1 - x3 + x52 =G= 0;
e14.. x1 - x4 + x53 =G= 0;
e15.. x1 - x5 + x54 =G= 0;
e16.. x2 - x3 + x55 =G= 0;
e17.. x2 - x4 + x56 =G= 0;
e18.. x2 - x5 + x57 =G= 0;
e19.. x3 - x4 + x58 =G= 0;
e20.. x3 - x5 + x59 =G= 0;
e21.. x4 - x5 + x60 =G= 0;
e22.. - x6 + x7 + x61 =G= 0;
e23.. - x6 + x8 + x62 =G= 0;
e24.. - x6 + x9 + x63 =G= 0;
e25.. - x6 + x10 + x64 =G= 0;
e26.. - x7 + x8 + x65 =G= 0;
e27.. - x7 + x9 + x66 =G= 0;
e28.. - x7 + x10 + x67 =G= 0;
e29.. - x8 + x9 + x68 =G= 0;
e30.. - x8 + x10 + x69 =G= 0;
e31.. - x9 + x10 + x70 =G= 0;
e32.. x6 - x7 + x61 =G= 0;
e33.. x6 - x8 + x62 =G= 0;
e34.. x6 - x9 + x63 =G= 0;
e35.. x6 - x10 + x64 =G= 0;
e36.. x7 - x8 + x65 =G= 0;
e37.. x7 - x9 + x66 =G= 0;
e38.. x7 - x10 + x67 =G= 0;
e39.. x8 - x9 + x68 =G= 0;
e40.. x8 - x10 + x69 =G= 0;
e41.. x9 - x10 + x70 =G= 0;
e42.. x1 - x2 + 30*b11 =L= 24;
e43.. x1 - x3 + 30*b12 =L= 26;
e44.. x1 - x4 + 30*b13 =L= 26.5;
e45.. x1 - x5 + 30*b14 =L= 25.5;
e46.. x2 - x3 + 30*b15 =L= 25;
e47.. x2 - x4 + 30*b16 =L= 25.5;
e48.. x2 - x5 + 30*b17 =L= 24.5;
e49.. x3 - x4 + 30*b18 =L= 27.5;
e50.. x3 - x5 + 30*b19 =L= 26.5;
e51.. x4 - x5 + 30*b20 =L= 27;
e52.. - x1 + x2 + 30*b21 =L= 24;
e53.. - x1 + x3 + 30*b22 =L= 26;
e54.. - x1 + x4 + 30*b23 =L= 26.5;
e55.. - x1 + x5 + 30*b24 =L= 25.5;
e56.. - x2 + x3 + 30*b25 =L= 25;
e57.. - x2 + x4 + 30*b26 =L= 25.5;
e58.. - x2 + x5 + 30*b27 =L= 24.5;
e59.. - x3 + x4 + 30*b28 =L= 27.5;
e60.. - x3 + x5 + 30*b29 =L= 26.5;
e61.. - x4 + x5 + 30*b30 =L= 27;
e62.. x6 - x7 + 30*b31 =L= 24.5;
e63.. x6 - x8 + 30*b32 =L= 25.5;
e64.. x6 - x9 + 30*b33 =L= 25.5;
e65.. x6 - x10 + 30*b34 =L= 25;
e66.. x7 - x8 + 30*b35 =L= 26;
e67.. x7 - x9 + 30*b36 =L= 26;
e68.. x7 - x10 + 30*b37 =L= 25.5;
e69.. x8 - x9 + 30*b38 =L= 27;
e70.. x8 - x10 + 30*b39 =L= 26.5;
e71.. x9 - x10 + 30*b40 =L= 26.5;
e72.. - x6 + x7 + 30*b41 =L= 24.5;
e73.. - x6 + x8 + 30*b42 =L= 25.5;
e74.. - x6 + x9 + 30*b43 =L= 25.5;
e75.. - x6 + x10 + 30*b44 =L= 25;
e76.. - x7 + x8 + 30*b45 =L= 26;
e77.. - x7 + x9 + 30*b46 =L= 26;
e78.. - x7 + x10 + 30*b47 =L= 25.5;
e79.. - x8 + x9 + 30*b48 =L= 27;
e80.. - x8 + x10 + 30*b49 =L= 26.5;
e81.. - x9 + x10 + 30*b50 =L= 26.5;
e82.. b11 + b21 + b31 + b41 =E= 1;
e83.. b12 + b22 + b32 + b42 =E= 1;
e84.. b13 + b23 + b33 + b43 =E= 1;
e85.. b14 + b24 + b34 + b44 =E= 1;
e86.. b15 + b25 + b35 + b45 =E= 1;
e87.. b16 + b26 + b36 + b46 =E= 1;
e88.. b17 + b27 + b37 + b47 =E= 1;
e89.. b18 + b28 + b38 + b48 =E= 1;
e90.. b19 + b29 + b39 + b49 =E= 1;
e91.. b20 + b30 + b40 + b50 =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 = 3; x6.up = 27;
x7.lo = 2.5; x7.up = 27.5;
x8.lo = 1.5; x8.up = 28.5;
x9.lo = 1.5; x9.up = 28.5;
x10.lo = 2; x10.up = 28;
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