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Instance flay02h
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ⓘ | 37.94646500 (ALPHAECP) 37.94733006 (ANTIGONE) 37.94733183 (BARON) 37.94733192 (BONMIN) 37.94733192 (COUENNE) 37.94733192 (LINDO) 37.94733024 (SCIP) 37.94733094 (SHOT) |
Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
Sourceⓘ | FLay02H.gms from CMU-IBM MINLP solver project page |
Applicationⓘ | Layout |
Added to libraryⓘ | 28 Sep 2013 |
Problem typeⓘ | MBNLP |
#Variablesⓘ | 46 |
#Binary Variablesⓘ | 4 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 2 |
#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ⓘ | 51 |
#Linear Constraintsⓘ | 49 |
#Quadratic Constraintsⓘ | 0 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 2 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | convex |
#Nonzeros in Jacobianⓘ | 136 |
#Nonlinear Nonzeros in Jacobianⓘ | 2 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 2 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 2 |
#Blocks in Hessian of Lagrangianⓘ | 2 |
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ⓘ | 5.0000e+01 |
Infeasibility of initial pointⓘ | 49 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 52 10 4 38 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 47 43 4 0 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 139 137 2 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,b43,b44,b45,b46,objvar; Positive Variables x1,x2,x3,x4,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; Binary Variables b43,b44,b45,b46; 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; e1.. - 2*x9 - 2*x10 + objvar =E= 0; e2.. - x1 - x5 + x9 =G= 0; e3.. - x2 - x6 + x9 =G= 0; e4.. - x3 - x7 + x10 =G= 0; e5.. - x4 - x8 + x10 =G= 0; e6.. 40/x7 - x5 =L= 0; e7.. 50/x8 - x6 =L= 0; e8.. x1 - x11 - x12 - x13 - x14 =E= 0; e9.. x2 - x15 - x16 - x17 - x18 =E= 0; e10.. x3 - x19 - x20 - x21 - x22 =E= 0; e11.. x4 - x23 - x24 - x25 - x26 =E= 0; e12.. x5 - x27 - x28 - x29 - x30 =E= 0; e13.. x6 - x31 - x32 - x33 - x34 =E= 0; e14.. x7 - x35 - x36 - x37 - x38 =E= 0; e15.. x8 - x39 - x40 - x41 - x42 =E= 0; e16.. x11 - 29*b43 =L= 0; e17.. x12 - 29*b44 =L= 0; e18.. x13 - 29*b45 =L= 0; e19.. x14 - 29*b46 =L= 0; e20.. x15 - 29*b43 =L= 0; e21.. x16 - 29*b44 =L= 0; e22.. x17 - 29*b45 =L= 0; e23.. x18 - 29*b46 =L= 0; e24.. x19 - 29*b43 =L= 0; e25.. x20 - 29*b44 =L= 0; e26.. x21 - 29*b45 =L= 0; e27.. x22 - 29*b46 =L= 0; e28.. x23 - 29*b43 =L= 0; e29.. x24 - 29*b44 =L= 0; e30.. x25 - 29*b45 =L= 0; e31.. x26 - 29*b46 =L= 0; e32.. x27 - 40*b43 =L= 0; e33.. x28 - 40*b44 =L= 0; e34.. x29 - 40*b45 =L= 0; e35.. x30 - 40*b46 =L= 0; e36.. x31 - 40*b43 =L= 0; e37.. x32 - 40*b44 =L= 0; e38.. x33 - 40*b45 =L= 0; e39.. x34 - 40*b46 =L= 0; e40.. x35 - 40*b43 =L= 0; e41.. x36 - 40*b44 =L= 0; e42.. x37 - 40*b45 =L= 0; e43.. x38 - 40*b46 =L= 0; e44.. x39 - 40*b43 =L= 0; e45.. x40 - 40*b44 =L= 0; e46.. x41 - 40*b45 =L= 0; e47.. x42 - 40*b46 =L= 0; e48.. x11 - x15 + x27 =L= 0; e49.. - x12 + x16 + x32 =L= 0; e50.. x21 - x25 + x37 =L= 0; e51.. - x22 + x26 + x42 =L= 0; e52.. b43 + b44 + b45 + b46 =E= 1; * set non-default bounds x1.up = 29; x2.up = 29; x3.up = 29; x4.up = 29; x5.lo = 1; x5.up = 40; x6.lo = 1; x6.up = 50; x7.lo = 1; x7.up = 40; x8.lo = 1; x8.up = 50; x9.up = 30; x10.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: 2024-12-17 Git hash: 8eaceb91