MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance tls5
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 5.90000000 (ALPHAECP) 8.37000184 (ANTIGONE) 7.60000000 (BARON) 5.58604248 (BONMIN) 1.19372783 (COUENNE) 10.30000000 (GUROBI) 6.43333333 (LINDO) 7.40000000 (SCIP) 7.70735569 (SHOT) |
| Referencesⓘ | 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ⓘ | MacMINLP model trimlon.mod with trimloss2.dat |
| Applicationⓘ | Trim loss minimization problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 161 |
| #Binary Variablesⓘ | 131 |
| #Integer Variablesⓘ | 5 |
| #Nonlinear Variablesⓘ | 30 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 5 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 31 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 90 |
| #Linear Constraintsⓘ | 85 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 5 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 924 |
| #Nonlinear Nonzeros in Jacobianⓘ | 50 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 80 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 30 |
| #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ⓘ | 1.8500e+03 |
| Infeasibility of initial pointⓘ | 1800 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 91 31 0 60 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 162 26 131 5 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 956 906 50 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,i6,i7,i8,i9,i10,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,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,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,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,objvar;
Binary Variables b1,b2,b3,b4,b5,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,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
,b151,b152,b153,b154,b155,b156,b157,b158,b159,b160,b161;
Integer Variables i6,i7,i8,i9,i10;
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;
e1.. - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - b36 - 2*b37 - 3*b38
- 4*b39 - 5*b40 - 6*b41 - 7*b42 - 8*b43 - 9*b44 - b45 - 2*b46 - 3*b47
- 4*b48 - 5*b49 - 6*b50 - b51 - 2*b52 - 3*b53 - 4*b54 - 5*b55 - 6*b56
- b57 - 2*b58 - 3*b59 - b60 - 2*b61 + objvar =E= 0;
e2.. 330*b62 + 660*b63 + 990*b64 + 360*b77 + 720*b78 + 1080*b79 + 1440*b80
+ 1800*b81 + 370*b102 + 740*b103 + 1110*b104 + 1480*b105 + 1850*b106
+ 415*b127 + 830*b128 + 1245*b129 + 1660*b130 + 435*b147 + 870*b148
+ 1305*b149 =L= 2000;
e3.. 330*b65 + 660*b66 + 990*b67 + 360*b82 + 720*b83 + 1080*b84 + 1440*b85
+ 1800*b86 + 370*b107 + 740*b108 + 1110*b109 + 1480*b110 + 1850*b111
+ 415*b131 + 830*b132 + 1245*b133 + 1660*b134 + 435*b150 + 870*b151
+ 1305*b152 =L= 2000;
e4.. 330*b68 + 660*b69 + 990*b70 + 360*b87 + 720*b88 + 1080*b89 + 1440*b90
+ 1800*b91 + 370*b112 + 740*b113 + 1110*b114 + 1480*b115 + 1850*b116
+ 415*b135 + 830*b136 + 1245*b137 + 1660*b138 + 435*b153 + 870*b154
+ 1305*b155 =L= 2000;
e5.. 330*b71 + 660*b72 + 990*b73 + 360*b92 + 720*b93 + 1080*b94 + 1440*b95
+ 1800*b96 + 370*b117 + 740*b118 + 1110*b119 + 1480*b120 + 1850*b121
+ 415*b139 + 830*b140 + 1245*b141 + 1660*b142 + 435*b156 + 870*b157
+ 1305*b158 =L= 2000;
e6.. 330*b74 + 660*b75 + 990*b76 + 360*b97 + 720*b98 + 1080*b99 + 1440*b100
+ 1800*b101 + 370*b122 + 740*b123 + 1110*b124 + 1480*b125 + 1850*b126
+ 415*b143 + 830*b144 + 1245*b145 + 1660*b146 + 435*b159 + 870*b160
+ 1305*b161 =L= 2000;
e7.. - 330*b62 - 660*b63 - 990*b64 - 360*b77 - 720*b78 - 1080*b79 - 1440*b80
- 1800*b81 - 370*b102 - 740*b103 - 1110*b104 - 1480*b105 - 1850*b106
- 415*b127 - 830*b128 - 1245*b129 - 1660*b130 - 435*b147 - 870*b148
- 1305*b149 =L= -1800;
e8.. - 330*b65 - 660*b66 - 990*b67 - 360*b82 - 720*b83 - 1080*b84 - 1440*b85
- 1800*b86 - 370*b107 - 740*b108 - 1110*b109 - 1480*b110 - 1850*b111
- 415*b131 - 830*b132 - 1245*b133 - 1660*b134 - 435*b150 - 870*b151
- 1305*b152 =L= -1800;
e9.. - 330*b68 - 660*b69 - 990*b70 - 360*b87 - 720*b88 - 1080*b89 - 1440*b90
- 1800*b91 - 370*b112 - 740*b113 - 1110*b114 - 1480*b115 - 1850*b116
- 415*b135 - 830*b136 - 1245*b137 - 1660*b138 - 435*b153 - 870*b154
- 1305*b155 =L= -1800;
e10.. - 330*b71 - 660*b72 - 990*b73 - 360*b92 - 720*b93 - 1080*b94 - 1440*b95
- 1800*b96 - 370*b117 - 740*b118 - 1110*b119 - 1480*b120 - 1850*b121
- 415*b139 - 830*b140 - 1245*b141 - 1660*b142 - 435*b156 - 870*b157
- 1305*b158 =L= -1800;
e11.. - 330*b74 - 660*b75 - 990*b76 - 360*b97 - 720*b98 - 1080*b99 - 1440*b100
- 1800*b101 - 370*b122 - 740*b123 - 1110*b124 - 1480*b125 - 1850*b126
- 415*b143 - 830*b144 - 1245*b145 - 1660*b146 - 435*b159 - 870*b160
- 1305*b161 =L= -1800;
e12.. b62 + 2*b63 + 3*b64 + b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81 + b102
+ 2*b103 + 3*b104 + 4*b105 + 5*b106 + b127 + 2*b128 + 3*b129 + 4*b130
+ b147 + 2*b148 + 3*b149 =L= 5;
e13.. b65 + 2*b66 + 3*b67 + b82 + 2*b83 + 3*b84 + 4*b85 + 5*b86 + b107
+ 2*b108 + 3*b109 + 4*b110 + 5*b111 + b131 + 2*b132 + 3*b133 + 4*b134
+ b150 + 2*b151 + 3*b152 =L= 5;
e14.. b68 + 2*b69 + 3*b70 + b87 + 2*b88 + 3*b89 + 4*b90 + 5*b91 + b112
+ 2*b113 + 3*b114 + 4*b115 + 5*b116 + b135 + 2*b136 + 3*b137 + 4*b138
+ b153 + 2*b154 + 3*b155 =L= 5;
e15.. b71 + 2*b72 + 3*b73 + b92 + 2*b93 + 3*b94 + 4*b95 + 5*b96 + b117
+ 2*b118 + 3*b119 + 4*b120 + 5*b121 + b139 + 2*b140 + 3*b141 + 4*b142
+ b156 + 2*b157 + 3*b158 =L= 5;
e16.. b74 + 2*b75 + 3*b76 + b97 + 2*b98 + 3*b99 + 4*b100 + 5*b101 + b122
+ 2*b123 + 3*b124 + 4*b125 + 5*b126 + b143 + 2*b144 + 3*b145 + 4*b146
+ b159 + 2*b160 + 3*b161 =L= 5;
e17.. b1 - b36 - 2*b37 - 3*b38 - 4*b39 - 5*b40 - 6*b41 - 7*b42 - 8*b43
- 9*b44 =L= 0;
e18.. b2 - b45 - 2*b46 - 3*b47 - 4*b48 - 5*b49 - 6*b50 =L= 0;
e19.. b3 - b51 - 2*b52 - 3*b53 - 4*b54 - 5*b55 - 6*b56 =L= 0;
e20.. b4 - b57 - 2*b58 - 3*b59 =L= 0;
e21.. b5 - b60 - 2*b61 =L= 0;
e22.. - 9*b1 + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 =L= 0;
e23.. - 6*b2 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 =L= 0;
e24.. - 6*b3 + b51 + 2*b52 + 3*b53 + 4*b54 + 5*b55 + 6*b56 =L= 0;
e25.. - 3*b4 + b57 + 2*b58 + 3*b59 =L= 0;
e26.. - 2*b5 + b60 + 2*b61 =L= 0;
e27.. i6 - 3*b36 - 8*b37 - 15*b38 - 24*b39 - 35*b40 - 48*b41 - 63*b42
- 80*b43 - 99*b44 =E= 1;
e28.. i7 - 3*b45 - 8*b46 - 15*b47 - 24*b48 - 35*b49 - 48*b50 =E= 1;
e29.. i8 - 3*b51 - 8*b52 - 15*b53 - 24*b54 - 35*b55 - 48*b56 =E= 1;
e30.. i9 - 3*b57 - 8*b58 - 15*b59 =E= 1;
e31.. i10 - 3*b60 - 8*b61 =E= 1;
e32.. b36 + b37 + b38 + b39 + b40 + b41 + b42 + b43 + b44 =L= 1;
e33.. b45 + b46 + b47 + b48 + b49 + b50 =L= 1;
e34.. b51 + b52 + b53 + b54 + b55 + b56 =L= 1;
e35.. b57 + b58 + b59 =L= 1;
e36.. b60 + b61 =L= 1;
e37.. x11 - 3*b62 - 8*b63 - 15*b64 =E= 1;
e38.. x12 - 3*b65 - 8*b66 - 15*b67 =E= 1;
e39.. x13 - 3*b68 - 8*b69 - 15*b70 =E= 1;
e40.. x14 - 3*b71 - 8*b72 - 15*b73 =E= 1;
e41.. x15 - 3*b74 - 8*b75 - 15*b76 =E= 1;
e42.. x16 - 3*b77 - 8*b78 - 15*b79 - 24*b80 - 35*b81 =E= 1;
e43.. x17 - 3*b82 - 8*b83 - 15*b84 - 24*b85 - 35*b86 =E= 1;
e44.. x18 - 3*b87 - 8*b88 - 15*b89 - 24*b90 - 35*b91 =E= 1;
e45.. x19 - 3*b92 - 8*b93 - 15*b94 - 24*b95 - 35*b96 =E= 1;
e46.. x20 - 3*b97 - 8*b98 - 15*b99 - 24*b100 - 35*b101 =E= 1;
e47.. x21 - 3*b102 - 8*b103 - 15*b104 - 24*b105 - 35*b106 =E= 1;
e48.. x22 - 3*b107 - 8*b108 - 15*b109 - 24*b110 - 35*b111 =E= 1;
e49.. x23 - 3*b112 - 8*b113 - 15*b114 - 24*b115 - 35*b116 =E= 1;
e50.. x24 - 3*b117 - 8*b118 - 15*b119 - 24*b120 - 35*b121 =E= 1;
e51.. x25 - 3*b122 - 8*b123 - 15*b124 - 24*b125 - 35*b126 =E= 1;
e52.. x26 - 3*b127 - 8*b128 - 15*b129 - 24*b130 =E= 1;
e53.. x27 - 3*b131 - 8*b132 - 15*b133 - 24*b134 =E= 1;
e54.. x28 - 3*b135 - 8*b136 - 15*b137 - 24*b138 =E= 1;
e55.. x29 - 3*b139 - 8*b140 - 15*b141 - 24*b142 =E= 1;
e56.. x30 - 3*b143 - 8*b144 - 15*b145 - 24*b146 =E= 1;
e57.. x31 - 3*b147 - 8*b148 - 15*b149 =E= 1;
e58.. x32 - 3*b150 - 8*b151 - 15*b152 =E= 1;
e59.. x33 - 3*b153 - 8*b154 - 15*b155 =E= 1;
e60.. x34 - 3*b156 - 8*b157 - 15*b158 =E= 1;
e61.. x35 - 3*b159 - 8*b160 - 15*b161 =E= 1;
e62.. b62 + b63 + b64 =L= 1;
e63.. b65 + b66 + b67 =L= 1;
e64.. b68 + b69 + b70 =L= 1;
e65.. b71 + b72 + b73 =L= 1;
e66.. b74 + b75 + b76 =L= 1;
e67.. b77 + b78 + b79 + b80 + b81 =L= 1;
e68.. b82 + b83 + b84 + b85 + b86 =L= 1;
e69.. b87 + b88 + b89 + b90 + b91 =L= 1;
e70.. b92 + b93 + b94 + b95 + b96 =L= 1;
e71.. b97 + b98 + b99 + b100 + b101 =L= 1;
e72.. b102 + b103 + b104 + b105 + b106 =L= 1;
e73.. b107 + b108 + b109 + b110 + b111 =L= 1;
e74.. b112 + b113 + b114 + b115 + b116 =L= 1;
e75.. b117 + b118 + b119 + b120 + b121 =L= 1;
e76.. b122 + b123 + b124 + b125 + b126 =L= 1;
e77.. b127 + b128 + b129 + b130 =L= 1;
e78.. b131 + b132 + b133 + b134 =L= 1;
e79.. b135 + b136 + b137 + b138 =L= 1;
e80.. b139 + b140 + b141 + b142 =L= 1;
e81.. b143 + b144 + b145 + b146 =L= 1;
e82.. b147 + b148 + b149 =L= 1;
e83.. b150 + b151 + b152 =L= 1;
e84.. b153 + b154 + b155 =L= 1;
e85.. b156 + b157 + b158 =L= 1;
e86.. b159 + b160 + b161 =L= 1;
e87.. -(sqrt(i6*x11) + sqrt(i7*x12) + sqrt(i8*x13) + sqrt(i9*x14) + sqrt(i10*
x15)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
+ 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
+ b62 + 2*b63 + 3*b64 + b65 + 2*b66 + 3*b67 + b68 + 2*b69 + 3*b70 + b71
+ 2*b72 + 3*b73 + b74 + 2*b75 + 3*b76 =L= -17;
e88.. -(sqrt(i6*x16) + sqrt(i7*x17) + sqrt(i8*x18) + sqrt(i9*x19) + sqrt(i10*
x20)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
+ 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
+ b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81 + b82 + 2*b83 + 3*b84 + 4*b85
+ 5*b86 + b87 + 2*b88 + 3*b89 + 4*b90 + 5*b91 + b92 + 2*b93 + 3*b94
+ 4*b95 + 5*b96 + b97 + 2*b98 + 3*b99 + 4*b100 + 5*b101 =L= -11;
e89.. -(sqrt(i6*x21) + sqrt(i7*x22) + sqrt(i8*x23) + sqrt(i9*x24) + sqrt(i10*
x25)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
+ 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
+ b102 + 2*b103 + 3*b104 + 4*b105 + 5*b106 + b107 + 2*b108 + 3*b109
+ 4*b110 + 5*b111 + b112 + 2*b113 + 3*b114 + 4*b115 + 5*b116 + b117
+ 2*b118 + 3*b119 + 4*b120 + 5*b121 + b122 + 2*b123 + 3*b124 + 4*b125
+ 5*b126 =L= -20;
e90.. -(sqrt(i6*x26) + sqrt(i7*x27) + sqrt(i8*x28) + sqrt(i9*x29) + sqrt(i10*
x30)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
+ 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
+ b127 + 2*b128 + 3*b129 + 4*b130 + b131 + 2*b132 + 3*b133 + 4*b134
+ b135 + 2*b136 + 3*b137 + 4*b138 + b139 + 2*b140 + 3*b141 + 4*b142
+ b143 + 2*b144 + 3*b145 + 4*b146 =L= -11;
e91.. -(sqrt(i6*x31) + sqrt(i7*x32) + sqrt(i8*x33) + sqrt(i9*x34) + sqrt(i10*
x35)) + b36 + 2*b37 + 3*b38 + 4*b39 + 5*b40 + 6*b41 + 7*b42 + 8*b43
+ 9*b44 + b45 + 2*b46 + 3*b47 + 4*b48 + 5*b49 + 6*b50 + b51 + 2*b52
+ 3*b53 + 4*b54 + 5*b55 + 6*b56 + b57 + 2*b58 + 3*b59 + b60 + 2*b61
+ b147 + 2*b148 + 3*b149 + b150 + 2*b151 + 3*b152 + b153 + 2*b154
+ 3*b155 + b156 + 2*b157 + 3*b158 + b159 + 2*b160 + 3*b161 =L= -14;
* set non-default bounds
i6.lo = 1; i6.up = 100;
i7.lo = 1; i7.up = 100;
i8.lo = 1; i8.up = 100;
i9.lo = 1; i9.up = 100;
i10.lo = 1; i10.up = 100;
x11.lo = 1;
x12.lo = 1;
x13.lo = 1;
x14.lo = 1;
x15.lo = 1;
x16.lo = 1;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 1;
x21.lo = 1;
x22.lo = 1;
x23.lo = 1;
x24.lo = 1;
x25.lo = 1;
x26.lo = 1;
x27.lo = 1;
x28.lo = 1;
x29.lo = 1;
x30.lo = 1;
x31.lo = 1;
x32.lo = 1;
x33.lo = 1;
x34.lo = 1;
x35.lo = 1;
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: 2024-08-26 Git hash: 6cc1607f