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Instance flay05m
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ⓘ | 59.99467900 (ALPHAECP) 64.49805097 (ANTIGONE) 64.49805581 (BARON) 64.49806199 (BONMIN) 64.49803085 (COUENNE) 64.49806062 (LINDO) 64.49805558 (SCIP) 64.49804161 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | FLay05M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 62 |
| #Binary Variablesⓘ | 40 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 5 |
| #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ⓘ | 65 |
| #Linear Constraintsⓘ | 60 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 5 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 240 |
| #Nonlinear Nonzeros in Jacobianⓘ | 5 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 5 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 5 |
| #Blocks in Hessian of Lagrangianⓘ | 5 |
| 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ⓘ | 1.0400e+02 |
| Infeasibility of initial pointⓘ | 74 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 66 11 10 45 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 63 23 40 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 243 238 5 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,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,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x21,x22;
Binary Variables 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;
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;
e1.. - 2*x21 - 2*x22 + objvar =E= 0;
e2.. - x1 - x11 + x21 =G= 0;
e3.. - x2 - x12 + x21 =G= 0;
e4.. - x3 - x13 + x21 =G= 0;
e5.. - x4 - x14 + x21 =G= 0;
e6.. - x5 - x15 + x21 =G= 0;
e7.. - x6 - x16 + x22 =G= 0;
e8.. - x7 - x17 + x22 =G= 0;
e9.. - x8 - x18 + x22 =G= 0;
e10.. - x9 - x19 + x22 =G= 0;
e11.. - x10 - x20 + x22 =G= 0;
e12.. 40/x16 - x11 =L= 0;
e13.. 50/x17 - x12 =L= 0;
e14.. 60/x18 - x13 =L= 0;
e15.. 35/x19 - x14 =L= 0;
e16.. 75/x20 - x15 =L= 0;
e17.. x1 - x2 + x11 + 69*b23 =L= 69;
e18.. x1 - x3 + x11 + 69*b24 =L= 69;
e19.. x1 - x4 + x11 + 69*b25 =L= 69;
e20.. x1 - x5 + x11 + 69*b26 =L= 69;
e21.. x2 - x3 + x12 + 79*b27 =L= 79;
e22.. x2 - x4 + x12 + 79*b28 =L= 79;
e23.. x2 - x5 + x12 + 79*b29 =L= 79;
e24.. x3 - x4 + x13 + 89*b30 =L= 89;
e25.. x3 - x5 + x13 + 89*b31 =L= 89;
e26.. x4 - x5 + x14 + 64*b32 =L= 64;
e27.. - x1 + x2 + x12 + 79*b33 =L= 79;
e28.. - x1 + x3 + x13 + 89*b34 =L= 89;
e29.. - x1 + x4 + x14 + 64*b35 =L= 64;
e30.. - x1 + x5 + x15 + 104*b36 =L= 104;
e31.. - x2 + x3 + x13 + 89*b37 =L= 89;
e32.. - x2 + x4 + x14 + 64*b38 =L= 64;
e33.. - x2 + x5 + x15 + 104*b39 =L= 104;
e34.. - x3 + x4 + x14 + 64*b40 =L= 64;
e35.. - x3 + x5 + x15 + 104*b41 =L= 104;
e36.. - x4 + x5 + x15 + 104*b42 =L= 104;
e37.. x6 - x7 + x16 + 69*b43 =L= 69;
e38.. x6 - x8 + x16 + 69*b44 =L= 69;
e39.. x6 - x9 + x16 + 69*b45 =L= 69;
e40.. x6 - x10 + x16 + 69*b46 =L= 69;
e41.. x7 - x8 + x17 + 79*b47 =L= 79;
e42.. x7 - x9 + x17 + 79*b48 =L= 79;
e43.. x7 - x10 + x17 + 79*b49 =L= 79;
e44.. x8 - x9 + x18 + 89*b50 =L= 89;
e45.. x8 - x10 + x18 + 89*b51 =L= 89;
e46.. x9 - x10 + x19 + 64*b52 =L= 64;
e47.. - x6 + x7 + x17 + 79*b53 =L= 79;
e48.. - x6 + x8 + x18 + 89*b54 =L= 89;
e49.. - x6 + x9 + x19 + 64*b55 =L= 64;
e50.. - x6 + x10 + x20 + 104*b56 =L= 104;
e51.. - x7 + x8 + x18 + 89*b57 =L= 89;
e52.. - x7 + x9 + x19 + 64*b58 =L= 64;
e53.. - x7 + x10 + x20 + 104*b59 =L= 104;
e54.. - x8 + x9 + x19 + 64*b60 =L= 64;
e55.. - x8 + x10 + x20 + 104*b61 =L= 104;
e56.. - x9 + x10 + x20 + 104*b62 =L= 104;
e57.. b23 + b33 + b43 + b53 =E= 1;
e58.. b24 + b34 + b44 + b54 =E= 1;
e59.. b25 + b35 + b45 + b55 =E= 1;
e60.. b26 + b36 + b46 + b56 =E= 1;
e61.. b27 + b37 + b47 + b57 =E= 1;
e62.. b28 + b38 + b48 + b58 =E= 1;
e63.. b29 + b39 + b49 + b59 =E= 1;
e64.. b30 + b40 + b50 + b60 =E= 1;
e65.. b31 + b41 + b51 + b61 =E= 1;
e66.. b32 + b42 + b52 + b62 =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.up = 29;
x8.up = 29;
x9.up = 29;
x10.up = 29;
x11.lo = 1; x11.up = 40;
x12.lo = 1; x12.up = 50;
x13.lo = 1; x13.up = 60;
x14.lo = 1; x14.up = 35;
x15.lo = 1; x15.up = 75;
x16.lo = 1; x16.up = 40;
x17.lo = 1; x17.up = 50;
x18.lo = 1; x18.up = 60;
x19.lo = 1; x19.up = 35;
x20.lo = 1; x20.up = 75;
x21.up = 30;
x22.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