MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1265
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 10.30000000 (ANTIGONE) 10.30000000 (BARON) 10.30000000 (COUENNE) 10.30000000 (GUROBI) 10.30000000 (LINDO) 10.30000000 (SCIP) 10.10000000 (SHOT) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Harjunkoski, Iiro, Westerlund, Tapio, Pörn, Ray, and Skrifvars, Hans, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP, European Journal of Operational Research, 105:3, 1998, 594-603. |
| Sourceⓘ | Test Problem ex12.6.5 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Trim loss minimization problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 130 |
| #Binary Variablesⓘ | 100 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 30 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 10 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 74 |
| #Linear Constraintsⓘ | 69 |
| #Quadratic Constraintsⓘ | 5 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 336 |
| #Nonlinear Nonzeros in Jacobianⓘ | 50 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 50 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 5 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 6 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 6 |
| Average blocksize in Hessian of Lagrangianⓘ | 6.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 2.0000e+03 |
| Infeasibility of initial pointⓘ | 15 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 75 31 6 38 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 131 31 100 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 347 297 50 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,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,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,x106,x107,x108,x109,x110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,objvar;
Positive 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,x106,x107,x108,x109,x110;
Binary Variables 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,b73,b74
,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87,b88,b89,b90,b91
,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103,b104,b105,b111
,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124
,b125,b126,b127,b128,b129,b130;
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;
e1.. - 0.1*b101 - 0.2*b102 - 0.3*b103 - 0.4*b104 - 0.5*b105 - x106 - x107
- x108 - x109 - x110 + objvar =E= 0;
e2.. x106*x1 + x107*x2 + x108*x3 + x109*x4 + x110*x5 =G= 12;
e3.. x106*x6 + x107*x7 + x108*x8 + x109*x9 + x110*x10 =G= 6;
e4.. x106*x11 + x107*x12 + x108*x13 + x109*x14 + x110*x15 =G= 15;
e5.. x106*x16 + x107*x17 + x108*x18 + x109*x19 + x110*x20 =G= 6;
e6.. x106*x21 + x107*x22 + x108*x23 + x109*x24 + x110*x25 =G= 9;
e7.. - 330*x1 - 360*x6 - 370*x11 - 415*x16 - 435*x21 + 1800*b101 =L= 0;
e8.. - 330*x2 - 360*x7 - 370*x12 - 415*x17 - 435*x22 + 1800*b102 =L= 0;
e9.. - 330*x3 - 360*x8 - 370*x13 - 415*x18 - 435*x23 + 1800*b103 =L= 0;
e10.. - 330*x4 - 360*x9 - 370*x14 - 415*x19 - 435*x24 + 1800*b104 =L= 0;
e11.. - 330*x5 - 360*x10 - 370*x15 - 415*x20 - 435*x25 + 1800*b105 =L= 0;
e12.. 330*x1 + 360*x6 + 370*x11 + 415*x16 + 435*x21 - 2000*b101 =L= 0;
e13.. 330*x2 + 360*x7 + 370*x12 + 415*x17 + 435*x22 - 2000*b102 =L= 0;
e14.. 330*x3 + 360*x8 + 370*x13 + 415*x18 + 435*x23 - 2000*b103 =L= 0;
e15.. 330*x4 + 360*x9 + 370*x14 + 415*x19 + 435*x24 - 2000*b104 =L= 0;
e16.. 330*x5 + 360*x10 + 370*x15 + 415*x20 + 435*x25 - 2000*b105 =L= 0;
e17.. - x1 - x6 - x11 - x16 - x21 + b101 =L= 0;
e18.. - x2 - x7 - x12 - x17 - x22 + b102 =L= 0;
e19.. - x3 - x8 - x13 - x18 - x23 + b103 =L= 0;
e20.. - x4 - x9 - x14 - x19 - x24 + b104 =L= 0;
e21.. - x5 - x10 - x15 - x20 - x25 + b105 =L= 0;
e22.. x1 + x6 + x11 + x16 + x21 - 5*b101 =L= 0;
e23.. x2 + x7 + x12 + x17 + x22 - 5*b102 =L= 0;
e24.. x3 + x8 + x13 + x18 + x23 - 5*b103 =L= 0;
e25.. x4 + x9 + x14 + x19 + x24 - 5*b104 =L= 0;
e26.. x5 + x10 + x15 + x20 + x25 - 5*b105 =L= 0;
e27.. b101 - x106 =L= 0;
e28.. b102 - x107 =L= 0;
e29.. b103 - x108 =L= 0;
e30.. b104 - x109 =L= 0;
e31.. b105 - x110 =L= 0;
e32.. - 15*b101 + x106 =L= 0;
e33.. - 12*b102 + x107 =L= 0;
e34.. - 9*b103 + x108 =L= 0;
e35.. - 6*b104 + x109 =L= 0;
e36.. - 6*b105 + x110 =L= 0;
e37.. x106 + x107 + x108 + x109 + x110 =G= 10;
e38.. - b101 + b102 =L= 0;
e39.. - b102 + b103 =L= 0;
e40.. - b103 + b104 =L= 0;
e41.. - b104 + b105 =L= 0;
e42.. - x106 + x107 =L= 0;
e43.. - x107 + x108 =L= 0;
e44.. - x108 + x109 =L= 0;
e45.. - x109 + x110 =L= 0;
e46.. x1 - b26 - 2*b27 - 4*b28 =E= 0;
e47.. x2 - b29 - 2*b30 - 4*b31 =E= 0;
e48.. x3 - b32 - 2*b33 - 4*b34 =E= 0;
e49.. x4 - b35 - 2*b36 - 4*b37 =E= 0;
e50.. x5 - b38 - 2*b39 - 4*b40 =E= 0;
e51.. x6 - b41 - 2*b42 - 4*b43 =E= 0;
e52.. x7 - b44 - 2*b45 - 4*b46 =E= 0;
e53.. x8 - b47 - 2*b48 - 4*b49 =E= 0;
e54.. x9 - b50 - 2*b51 - 4*b52 =E= 0;
e55.. x10 - b53 - 2*b54 - 4*b55 =E= 0;
e56.. x11 - b56 - 2*b57 - 4*b58 =E= 0;
e57.. x12 - b59 - 2*b60 - 4*b61 =E= 0;
e58.. x13 - b62 - 2*b63 - 4*b64 =E= 0;
e59.. x14 - b65 - 2*b66 - 4*b67 =E= 0;
e60.. x15 - b68 - 2*b69 - 4*b70 =E= 0;
e61.. x16 - b71 - 2*b72 - 4*b73 =E= 0;
e62.. x17 - b74 - 2*b75 - 4*b76 =E= 0;
e63.. x18 - b77 - 2*b78 - 4*b79 =E= 0;
e64.. x19 - b80 - 2*b81 - 4*b82 =E= 0;
e65.. x20 - b83 - 2*b84 - 4*b85 =E= 0;
e66.. x21 - b86 - 2*b87 - 4*b88 =E= 0;
e67.. x22 - b89 - 2*b90 - 4*b91 =E= 0;
e68.. x23 - b92 - 2*b93 - 4*b94 =E= 0;
e69.. x24 - b95 - 2*b96 - 4*b97 =E= 0;
e70.. x25 - b98 - 2*b99 - 4*b100 =E= 0;
e71.. x106 - b111 - 2*b112 - 4*b113 - 8*b114 =E= 0;
e72.. x107 - b115 - 2*b116 - 4*b117 - 8*b118 =E= 0;
e73.. x108 - b119 - 2*b120 - 4*b121 - 8*b122 =E= 0;
e74.. x109 - b123 - 2*b124 - 4*b125 - 8*b126 =E= 0;
e75.. x110 - b127 - 2*b128 - 4*b129 - 8*b130 =E= 0;
* set non-default bounds
x1.up = 5;
x2.up = 5;
x3.up = 5;
x4.up = 5;
x5.up = 5;
x6.up = 5;
x7.up = 5;
x8.up = 5;
x9.up = 5;
x10.up = 5;
x11.up = 5;
x12.up = 5;
x13.up = 5;
x14.up = 5;
x15.up = 5;
x16.up = 5;
x17.up = 5;
x18.up = 5;
x19.up = 5;
x20.up = 5;
x21.up = 5;
x22.up = 5;
x23.up = 5;
x24.up = 5;
x25.up = 5;
x106.up = 15;
x107.up = 12;
x108.up = 9;
x109.up = 6;
x110.up = 6;
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: 2024-04-02 Git hash: 1dd5fb9b