MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1266
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 16.30000000 (ANTIGONE) 16.30000000 (BARON) 16.30000000 (COUENNE) 16.30000000 (GUROBI) 16.30000000 (LINDO) 16.30000000 (SCIP) 16.30000000 (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 ex12.6.6 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Trim loss minimization problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 180 |
| #Binary Variablesⓘ | 138 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 42 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 11 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 95 |
| #Linear Constraintsⓘ | 89 |
| #Quadratic Constraintsⓘ | 6 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 464 |
| #Nonlinear Nonzeros in Jacobianⓘ | 72 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 72 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 7 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 2.2000e+03 |
| Infeasibility of initial pointⓘ | 2170 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 96 43 7 46 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 181 43 138 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 476 404 72 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
,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,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,x151,x152,x153,x154,x155
,x156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,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,x26,x27,x28,x29,x30,x31,x32,x33,x34
,x35,x36,x151,x152,x153,x154,x155,x156;
Binary Variables 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,b106,b107,b108,b109,b110,b111,b112,b113,b114
,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127
,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b157,b158,b159
,b160,b161,b162,b163,b164,b165,b166,b167,b168,b169,b170,b171,b172
,b173,b174,b175,b176,b177,b178,b179,b180;
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,e92,e93,e94,e95,e96;
e1.. - 0.1*b145 - 0.2*b146 - 0.3*b147 - 0.4*b148 - 0.5*b149 - x151 - x152
- x153 - x154 - x155 - x156 + objvar =E= 0;
e2.. x151*x1 + x152*x2 + x153*x3 + x154*x4 + x155*x5 + x156*x6 =G= 8;
e3.. x151*x7 + x152*x8 + x153*x9 + x154*x10 + x155*x11 + x156*x12 =G= 16;
e4.. x151*x13 + x152*x14 + x153*x15 + x154*x16 + x155*x17 + x156*x18 =G= 12;
e5.. x151*x19 + x152*x20 + x153*x21 + x154*x22 + x155*x23 + x156*x24 =G= 7;
e6.. x151*x25 + x152*x26 + x153*x27 + x154*x28 + x155*x29 + x156*x30 =G= 14;
e7.. x151*x31 + x152*x32 + x153*x33 + x154*x34 + x155*x35 + x156*x36 =G= 16;
e8.. - 330*x1 - 360*x7 - 380*x13 - 430*x19 - 490*x25 - 530*x31 + 2100*b145
=L= 0;
e9.. - 330*x2 - 360*x8 - 380*x14 - 430*x20 - 490*x26 - 530*x32 + 2100*b146
=L= 0;
e10.. - 330*x3 - 360*x9 - 380*x15 - 430*x21 - 490*x27 - 530*x33 + 2100*b147
=L= 0;
e11.. - 330*x4 - 360*x10 - 380*x16 - 430*x22 - 490*x28 - 530*x34 + 2100*b148
=L= 0;
e12.. - 330*x5 - 360*x11 - 380*x17 - 430*x23 - 490*x29 - 530*x35 + 2100*b149
=L= 0;
e13.. - 330*x6 - 360*x12 - 380*x18 - 430*x24 - 490*x30 - 530*x36 + 2100*b150
=L= 0;
e14.. 330*x1 + 360*x7 + 380*x13 + 430*x19 + 490*x25 + 530*x31 - 2200*b145
=L= 0;
e15.. 330*x2 + 360*x8 + 380*x14 + 430*x20 + 490*x26 + 530*x32 - 2200*b146
=L= 0;
e16.. 330*x3 + 360*x9 + 380*x15 + 430*x21 + 490*x27 + 530*x33 - 2200*b147
=L= 0;
e17.. 330*x4 + 360*x10 + 380*x16 + 430*x22 + 490*x28 + 530*x34 - 2200*b148
=L= 0;
e18.. 330*x5 + 360*x11 + 380*x17 + 430*x23 + 490*x29 + 530*x35 - 2200*b149
=L= 0;
e19.. 330*x6 + 360*x12 + 380*x18 + 430*x24 + 490*x30 + 530*x36 - 2200*b150
=L= 0;
e20.. - x1 - x7 - x13 - x19 - x25 - x31 + b145 =L= 0;
e21.. - x2 - x8 - x14 - x20 - x26 - x32 + b146 =L= 0;
e22.. - x3 - x9 - x15 - x21 - x27 - x33 + b147 =L= 0;
e23.. - x4 - x10 - x16 - x22 - x28 - x34 + b148 =L= 0;
e24.. - x5 - x11 - x17 - x23 - x29 - x35 + b149 =L= 0;
e25.. - x6 - x12 - x18 - x24 - x30 - x36 + b150 =L= 0;
e26.. x1 + x7 + x13 + x19 + x25 + x31 - 5*b145 =L= 0;
e27.. x2 + x8 + x14 + x20 + x26 + x32 - 5*b146 =L= 0;
e28.. x3 + x9 + x15 + x21 + x27 + x33 - 5*b147 =L= 0;
e29.. x4 + x10 + x16 + x22 + x28 + x34 - 5*b148 =L= 0;
e30.. x5 + x11 + x17 + x23 + x29 + x35 - 5*b149 =L= 0;
e31.. x6 + x12 + x18 + x24 + x30 + x36 - 5*b150 =L= 0;
e32.. b145 - x151 =L= 0;
e33.. b146 - x152 =L= 0;
e34.. b147 - x153 =L= 0;
e35.. b148 - x154 =L= 0;
e36.. b149 - x155 =L= 0;
e37.. b150 - x156 =L= 0;
e38.. - 15*b145 + x151 =L= 0;
e39.. - 12*b146 + x152 =L= 0;
e40.. - 8*b147 + x153 =L= 0;
e41.. - 7*b148 + x154 =L= 0;
e42.. - 4*b149 + x155 =L= 0;
e43.. - 2*b150 + x156 =L= 0;
e44.. x151 + x152 + x153 + x154 + x155 + x156 =G= 16;
e45.. - b145 + b146 =L= 0;
e46.. - b146 + b147 =L= 0;
e47.. - b147 + b148 =L= 0;
e48.. - b148 + b149 =L= 0;
e49.. - b149 + b150 =L= 0;
e50.. - x151 + x152 =L= 0;
e51.. - x152 + x153 =L= 0;
e52.. - x153 + x154 =L= 0;
e53.. - x154 + x155 =L= 0;
e54.. - x155 + x156 =L= 0;
e55.. x1 - b37 - 2*b38 - 4*b39 =E= 0;
e56.. x2 - b40 - 2*b41 - 4*b42 =E= 0;
e57.. x3 - b43 - 2*b44 - 4*b45 =E= 0;
e58.. x4 - b46 - 2*b47 - 4*b48 =E= 0;
e59.. x5 - b49 - 2*b50 - 4*b51 =E= 0;
e60.. x6 - b52 - 2*b53 - 4*b54 =E= 0;
e61.. x7 - b55 - 2*b56 - 4*b57 =E= 0;
e62.. x8 - b58 - 2*b59 - 4*b60 =E= 0;
e63.. x9 - b61 - 2*b62 - 4*b63 =E= 0;
e64.. x10 - b64 - 2*b65 - 4*b66 =E= 0;
e65.. x11 - b67 - 2*b68 - 4*b69 =E= 0;
e66.. x12 - b70 - 2*b71 - 4*b72 =E= 0;
e67.. x13 - b73 - 2*b74 - 4*b75 =E= 0;
e68.. x14 - b76 - 2*b77 - 4*b78 =E= 0;
e69.. x15 - b79 - 2*b80 - 4*b81 =E= 0;
e70.. x16 - b82 - 2*b83 - 4*b84 =E= 0;
e71.. x17 - b85 - 2*b86 - 4*b87 =E= 0;
e72.. x18 - b88 - 2*b89 - 4*b90 =E= 0;
e73.. x19 - b91 - 2*b92 - 4*b93 =E= 0;
e74.. x20 - b94 - 2*b95 - 4*b96 =E= 0;
e75.. x21 - b97 - 2*b98 - 4*b99 =E= 0;
e76.. x22 - b100 - 2*b101 - 4*b102 =E= 0;
e77.. x23 - b103 - 2*b104 - 4*b105 =E= 0;
e78.. x24 - b106 - 2*b107 - 4*b108 =E= 0;
e79.. x25 - b109 - 2*b110 - 4*b111 =E= 0;
e80.. x26 - b112 - 2*b113 - 4*b114 =E= 0;
e81.. x27 - b115 - 2*b116 - 4*b117 =E= 0;
e82.. x28 - b118 - 2*b119 - 4*b120 =E= 0;
e83.. x29 - b121 - 2*b122 - 4*b123 =E= 0;
e84.. x30 - b124 - 2*b125 - 4*b126 =E= 0;
e85.. x31 - b127 - 2*b128 - 4*b129 =E= 0;
e86.. x32 - b130 - 2*b131 - 4*b132 =E= 0;
e87.. x33 - b133 - 2*b134 - 4*b135 =E= 0;
e88.. x34 - b136 - 2*b137 - 4*b138 =E= 0;
e89.. x35 - b139 - 2*b140 - 4*b141 =E= 0;
e90.. x36 - b142 - 2*b143 - 4*b144 =E= 0;
e91.. x151 - b157 - 2*b158 - 4*b159 - 8*b160 =E= 0;
e92.. x152 - b161 - 2*b162 - 4*b163 - 8*b164 =E= 0;
e93.. x153 - b165 - 2*b166 - 4*b167 - 8*b168 =E= 0;
e94.. x154 - b169 - 2*b170 - 4*b171 - 8*b172 =E= 0;
e95.. x155 - b173 - 2*b174 - 4*b175 - 8*b176 =E= 0;
e96.. x156 - b177 - 2*b178 - 4*b179 - 8*b180 =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;
x26.up = 5;
x27.up = 5;
x28.up = 5;
x29.up = 5;
x30.up = 5;
x31.up = 5;
x32.up = 5;
x33.up = 5;
x34.up = 5;
x35.up = 5;
x36.up = 5;
x151.up = 15;
x152.up = 12;
x153.up = 8;
x154.up = 7;
x155.up = 4;
x156.up = 2;
* set non-default levels
x1.l = 1;
x7.l = 2;
x14.l = 2;
x20.l = 1;
x26.l = 2;
x31.l = 1;
x151.l = 8;
x152.l = 7;
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