MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance lip
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 5685067.88300000 (ANTIGONE) 5685067.88300000 (BARON) 5685067.87700000 (COUENNE) 5685067.87700000 (LINDO) 5685067.88100000 (SCIP) 26765000.00000000 (SHOT) |
| Sourceⓘ | AIMMS clients |
| Applicationⓘ | Location Item Planning |
| Added to libraryⓘ | 07 Mar 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 60 |
| #Binary Variablesⓘ | 52 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 48 |
| #Nonlinear Binary Variablesⓘ | 48 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 60 |
| #Nonlinear Nonzeros in Objectiveⓘ | 48 |
| #Constraintsⓘ | 83 |
| #Linear Constraintsⓘ | 83 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | vcpower |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 280 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 576 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 48 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 12 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 12 |
| Average blocksize in Hessian of Lagrangianⓘ | 12.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 8.0000e+05 |
| Infeasibility of initial pointⓘ | 6000 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 84 15 17 52 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 61 9 52 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 341 293 48 0
*
* Solve m using MINLP maximizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,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,b51,b52,x53
,x54,x55,x56,x57,x58,x59,x60,objvar;
Positive Variables x53,x54,x55,x56,x57,x58,x59,x60;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,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,b51
,b52;
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;
e1.. b49 + b50 + b51 + b52 =G= 1;
e2.. b1 + b3 + b5 + b7 =E= 1;
e3.. b2 + b4 + b6 + b8 =E= 1;
e4.. b9 + b11 + b13 + b15 =E= 1;
e5.. b10 + b12 + b14 + b16 =E= 1;
e6.. b17 + b19 + b21 + b23 =E= 1;
e7.. b18 + b20 + b22 + b24 =E= 1;
e8.. b25 + b27 + b29 + b31 =E= 1;
e9.. b26 + b28 + b30 + b32 =E= 1;
e10.. b33 + b35 + b37 + b39 =E= 1;
e11.. b34 + b36 + b38 + b40 =E= 1;
e12.. b41 + b43 + b45 + b47 =E= 1;
e13.. b42 + b44 + b46 + b48 =E= 1;
e14.. b1 - b49 =L= 0;
e15.. b2 - b49 =L= 0;
e16.. b3 - b50 =L= 0;
e17.. b4 - b50 =L= 0;
e18.. b5 - b51 =L= 0;
e19.. b6 - b51 =L= 0;
e20.. b7 - b52 =L= 0;
e21.. b8 - b52 =L= 0;
e22.. b9 - b49 =L= 0;
e23.. b10 - b49 =L= 0;
e24.. b11 - b50 =L= 0;
e25.. b12 - b50 =L= 0;
e26.. b13 - b51 =L= 0;
e27.. b14 - b51 =L= 0;
e28.. b15 - b52 =L= 0;
e29.. b16 - b52 =L= 0;
e30.. b17 - b49 =L= 0;
e31.. b18 - b49 =L= 0;
e32.. b19 - b50 =L= 0;
e33.. b20 - b50 =L= 0;
e34.. b21 - b51 =L= 0;
e35.. b22 - b51 =L= 0;
e36.. b23 - b52 =L= 0;
e37.. b24 - b52 =L= 0;
e38.. b25 - b49 =L= 0;
e39.. b26 - b49 =L= 0;
e40.. b27 - b50 =L= 0;
e41.. b28 - b50 =L= 0;
e42.. b29 - b51 =L= 0;
e43.. b30 - b51 =L= 0;
e44.. b31 - b52 =L= 0;
e45.. b32 - b52 =L= 0;
e46.. b33 - b49 =L= 0;
e47.. b34 - b49 =L= 0;
e48.. b35 - b50 =L= 0;
e49.. b36 - b50 =L= 0;
e50.. b37 - b51 =L= 0;
e51.. b38 - b51 =L= 0;
e52.. b39 - b52 =L= 0;
e53.. b40 - b52 =L= 0;
e54.. b41 - b49 =L= 0;
e55.. b42 - b49 =L= 0;
e56.. b43 - b50 =L= 0;
e57.. b44 - b50 =L= 0;
e58.. b45 - b51 =L= 0;
e59.. b46 - b51 =L= 0;
e60.. b47 - b52 =L= 0;
e61.. b48 - b52 =L= 0;
e62.. b1 + b9 + b17 + b25 + b33 + b41 - b49 =G= 0;
e63.. b2 + b10 + b18 + b26 + b34 + b42 - b49 =G= 0;
e64.. b3 + b11 + b19 + b27 + b35 + b43 - b50 =G= 0;
e65.. b4 + b12 + b20 + b28 + b36 + b44 - b50 =G= 0;
e66.. b5 + b13 + b21 + b29 + b37 + b45 - b51 =G= 0;
e67.. b6 + b14 + b22 + b30 + b38 + b46 - b51 =G= 0;
e68.. b7 + b15 + b23 + b31 + b39 + b47 - b52 =G= 0;
e69.. b8 + b16 + b24 + b32 + b40 + b48 - b52 =G= 0;
e70.. - 5000*b49 + x53 + x54 =L= 0;
e71.. - 3000*b50 + x55 + x56 =L= 0;
e72.. - 3000*b51 + x57 + x58 =L= 0;
e73.. - 2000*b52 + x59 + x60 =L= 0;
e74.. x53 + x55 + x57 + x59 =E= 6000;
e75.. x54 + x56 + x58 + x60 =E= 4800;
e76.. - 1000*b1 - 1000*b9 - 1000*b17 - 1000*b25 - 1000*b33 - 1000*b41 + x53
=G= 0;
e77.. - 800*b2 - 800*b10 - 800*b18 - 800*b26 - 800*b34 - 800*b42 + x54 =G= 0;
e78.. - 1000*b3 - 1000*b11 - 1000*b19 - 1000*b27 - 1000*b35 - 1000*b43 + x55
=G= 0;
e79.. - 800*b4 - 800*b12 - 800*b20 - 800*b28 - 800*b36 - 800*b44 + x56 =G= 0;
e80.. - 1000*b5 - 1000*b13 - 1000*b21 - 1000*b29 - 1000*b37 - 1000*b45 + x57
=G= 0;
e81.. - 800*b6 - 800*b14 - 800*b22 - 800*b30 - 800*b38 - 800*b46 + x58 =G= 0;
e82.. - 1000*b7 - 1000*b15 - 1000*b23 - 1000*b31 - 1000*b39 - 1000*b47 + x59
=G= 0;
e83.. - 800*b8 - 800*b16 - 800*b24 - 800*b32 - 800*b40 - 800*b48 + x60 =G= 0;
e84.. 39.2*((25*b1 + 25*b2 + 25*b9 + 25*b10 + 25*b17 + 25*b18 + 25*b25 + 25*b26
+ 25*b33 + 25*b34 + 25*b41 + 25*b42)**0.5 + (25*b3 + 25*b4 + 25*b11 + 25
*b12 + 25*b19 + 25*b20 + 25*b27 + 25*b28 + 25*b35 + 25*b36 + 25*b43 + 25*
b44)**0.5 + (25*b5 + 25*b6 + 25*b13 + 25*b14 + 25*b21 + 25*b22 + 25*b29
+ 25*b30 + 25*b37 + 25*b38 + 25*b45 + 25*b46)**0.5 + (25*b7 + 25*b8 + 25
*b15 + 25*b16 + 25*b23 + 25*b24 + 25*b31 + 25*b32 + 25*b39 + 25*b40 + 25*
b47 + 25*b48)**0.5) - 300000*b1 - 800000*b2 - 300000*b3 - 800000*b4 -
300000*b5 - 800000*b6 - 300000*b7 - 800000*b8 - 300000*b9 - 800000*b10 -
300000*b11 - 800000*b12 - 300000*b13 - 800000*b14 - 300000*b15 - 800000*
b16 - 300000*b17 - 800000*b18 - 300000*b19 - 800000*b20 - 300000*b21 -
800000*b22 - 300000*b23 - 800000*b24 - 300000*b25 - 800000*b26 - 300000*
b27 - 800000*b28 - 300000*b29 - 800000*b30 - 300000*b31 - 800000*b32 -
300000*b33 - 800000*b34 - 300000*b35 - 800000*b36 - 300000*b37 - 800000*
b38 - 300000*b39 - 800000*b40 - 300000*b41 - 800000*b42 - 300000*b43 -
800000*b44 - 300000*b45 - 800000*b46 - 300000*b47 - 800000*b48 + 100000*
b1 + 100000*b9 + 100000*b17 + 100000*b25 + 100000*b33 + 100000*b41 +
400000*b2 + 400000*b10 + 400000*b18 + 400000*b26 + 400000*b34 + 400000*
b42 + 100000*b3 + 100000*b11 + 100000*b19 + 100000*b27 + 100000*b35 +
100000*b43 + 400000*b4 + 400000*b12 + 400000*b20 + 400000*b28 + 400000*
b36 + 400000*b44 + 100000*b5 + 100000*b13 + 100000*b21 + 100000*b29 +
100000*b37 + 100000*b45 + 400000*b6 + 400000*b14 + 400000*b22 + 400000*
b30 + 400000*b38 + 400000*b46 + 100000*b7 + 100000*b15 + 100000*b23 +
100000*b31 + 100000*b39 + 100000*b47 + 400000*b8 + 400000*b16 + 400000*
b24 + 400000*b32 + 400000*b40 + 400000*b48 + 4000*b1 + 3200*b2 + 8000*b9
+ 6400*b10 + 8000*b17 + 6400*b18 + 16000*b25 + 12800*b26 + 16000*b33 +
12800*b34 + 32000*b41 + 25600*b42 + 8000*b3 + 6400*b4 + 4000*b11 + 3200*
b12 + 16000*b19 + 12800*b20 + 24000*b27 + 19200*b28 + 8000*b35 + 6400*b36
+ 24000*b43 + 19200*b44 + 16000*b5 + 12800*b6 + 24000*b13 + 19200*b14 +
4000*b21 + 3200*b22 + 4000*b29 + 3200*b30 + 16000*b37 + 12800*b38 + 16000
*b45 + 12800*b46 + 200000*b7 + 160000*b8 + 200000*b15 + 160000*b16 +
150000*b23 + 120000*b24 + 50000*b31 + 40000*b32 + 100000*b39 + 80000*b40
+ 25000*b47 + 20000*b48 + 80000*b49 + 80000*b50 + 80000*b51 + 80000*b52
- 55*x53 - 455*x54 - 50*x55 - 450*x56 - 55*x57 - 455*x58 - 55*x59
- 455*x60 + objvar =E= 0;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc