MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance feedtray2
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -0.00000000 (ANTIGONE) -0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (GUROBI) 0.00000000 (LINDO) 0.00000000 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Viswanathan, J and Grossmann, I E, A Combined Penalty Function and Outer Approximation Method for MINLP Optimization, Computers and Chemical Engineering, 14:7, 1990, 769-782. |
| Sourceⓘ | MacMINLP model feedloc.mod |
| Applicationⓘ | Feed Plate Location |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 88 |
| #Binary Variablesⓘ | 36 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 63 |
| #Nonlinear Binary Variablesⓘ | 11 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 284 |
| #Linear Constraintsⓘ | 137 |
| #Quadratic Constraintsⓘ | 147 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1627 |
| #Nonlinear Nonzeros in Jacobianⓘ | 942 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 496 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 63 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 63 |
| Average blocksize in Hessian of Lagrangianⓘ | 63.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+03 |
| Infeasibility of initial pointⓘ | 1000 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 284 7 114 163 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 88 52 36 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1627 685 942 0
*
* Solve m using MINLP minimizing 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
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,objvar;
Positive Variables x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50
,x51,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67
,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84
,x85,x86,x87;
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;
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,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284;
e1.. x87*x61 + 1000*b1 =L= 1000.024;
e2.. x87*x63 + 1000*b2 =L= 1000.024;
e3.. x87*x65 + 1000*b3 =L= 1000.024;
e4.. x87*x67 + 1000*b4 =L= 1000.024;
e5.. x87*x69 + 1000*b5 =L= 1000.024;
e6.. x87*x71 + 1000*b6 =L= 1000.024;
e7.. x87*x73 + 1000*b7 =L= 1000.024;
e8.. x87*x75 + 1000*b8 =L= 1000.024;
e9.. x87*x77 + 1000*b9 =L= 1000.024;
e10.. x87*x79 + 1000*b10 =L= 1000.024;
e11.. x87*x81 + 1000*b11 =L= 1000.024;
e12.. x87*x83 + 1000*b12 =L= 1000.024;
e13.. (100*b14 + 100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 +
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x39 + x86*x63 - (100*b15 +
100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100
*b23 + 100*b24 + x85)*x41 - x86*x61 - 80*b14 - 1000*b2 + 1000*b26
=L= 1000;
e14.. (100*b14 + 100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 +
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x40 + x86*x64 - (100*b15 +
100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100
*b23 + 100*b24 + x85)*x42 - x86*x62 - 20*b14 - 1000*b2 + 1000*b26
=L= 1000;
e15.. (100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x41 + x86*x65 - (100*b16 + 100*b17 +
100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85
)*x43 - x86*x63 - 80*b15 - 1000*b3 + 1000*b27 =L= 1000;
e16.. (100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x42 + x86*x66 - (100*b16 + 100*b17 +
100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85
)*x44 - x86*x64 - 20*b15 - 1000*b3 + 1000*b27 =L= 1000;
e17.. (100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 +
100*b23 + 100*b24 + x85)*x43 + x86*x67 - (100*b17 + 100*b18 + 100*b19 +
100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x45 - x86*x65 - 80
*b16 - 1000*b4 + 1000*b28 =L= 1000;
e18.. (100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 +
100*b23 + 100*b24 + x85)*x44 + x86*x68 - (100*b17 + 100*b18 + 100*b19 +
100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x46 - x86*x66 - 20
*b16 - 1000*b4 + 1000*b28 =L= 1000;
e19.. (100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x45 + x86*x69 - (100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x47 - x86*x67 - 80*b17 - 1000*b5
+ 1000*b29 =L= 1000;
e20.. (100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x46 + x86*x70 - (100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x48 - x86*x68 - 20*b17 - 1000*b5
+ 1000*b29 =L= 1000;
e21.. (100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 +
x85)*x47 + x86*x71 - (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x49 - x86*x69 - 80*b18 - 1000*b6 + 1000*b30 =L= 1000;
e22.. (100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 +
x85)*x48 + x86*x72 - (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x50 - x86*x70 - 20*b18 - 1000*b6 + 1000*b30 =L= 1000;
e23.. (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x49 +
x86*x73 - (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x51 -
x86*x71 - 80*b19 - 1000*b7 + 1000*b31 =L= 1000;
e24.. (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x50 +
x86*x74 - (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x52 -
x86*x72 - 20*b19 - 1000*b7 + 1000*b31 =L= 1000;
e25.. (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x51 + x86*x75 - (
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x53 - x86*x73 - 80*b20
- 1000*b8 + 1000*b32 =L= 1000;
e26.. (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x52 + x86*x76 - (
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x54 - x86*x74 - 20*b20
- 1000*b8 + 1000*b32 =L= 1000;
e27.. (100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x53 + x86*x77 - (100*b22 +
100*b23 + 100*b24 + x85)*x55 - x86*x75 - 80*b21 - 1000*b9 + 1000*b33
=L= 1000;
e28.. (100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x54 + x86*x78 - (100*b22 +
100*b23 + 100*b24 + x85)*x56 - x86*x76 - 20*b21 - 1000*b9 + 1000*b33
=L= 1000;
e29.. (100*b22 + 100*b23 + 100*b24 + x85)*x55 + x86*x79 - (100*b23 + 100*b24 +
x85)*x57 - x86*x77 - 80*b22 - 1000*b10 + 1000*b34 =L= 1000;
e30.. (100*b22 + 100*b23 + 100*b24 + x85)*x56 + x86*x80 - (100*b23 + 100*b24 +
x85)*x58 - x86*x78 - 20*b22 - 1000*b10 + 1000*b34 =L= 1000;
e31.. (100*b23 + 100*b24 + x85)*x57 + x86*x81 - (100*b24 + x85)*x59 - x86*x79
- 80*b23 - 1000*b11 + 1000*b35 =L= 1000;
e32.. (100*b23 + 100*b24 + x85)*x58 + x86*x82 - (100*b24 + x85)*x60 - x86*x80
- 20*b23 - 1000*b11 + 1000*b35 =L= 1000;
e33.. x86*x61 - (100 + x85)*x39 + 80*x37 =E= 0;
e34.. x86*x62 - (100 + x85)*x40 + 80*x38 =E= 0;
e35.. (100*b14 + 100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 +
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x39 + x86*x63 - (100*b15 +
100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100
*b23 + 100*b24 + x85)*x41 - x86*x61 - 80*b14 - 1000*b2 + 1000*b26
=G= 1000;
e36.. (100*b14 + 100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 +
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x40 + x86*x64 - (100*b15 +
100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100
*b23 + 100*b24 + x85)*x42 - x86*x62 - 20*b14 - 1000*b2 + 1000*b26
=G= 1000;
e37.. (100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x41 + x86*x65 - (100*b16 + 100*b17 +
100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85
)*x43 - x86*x63 - 80*b15 - 1000*b3 + 1000*b27 =G= 1000;
e38.. (100*b15 + 100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x42 + x86*x66 - (100*b16 + 100*b17 +
100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85
)*x44 - x86*x64 - 20*b15 - 1000*b3 + 1000*b27 =G= 1000;
e39.. (100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 +
100*b23 + 100*b24 + x85)*x43 + x86*x67 - (100*b17 + 100*b18 + 100*b19 +
100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x45 - x86*x65 - 80
*b16 - 1000*b4 + 1000*b28 =G= 1000;
e40.. (100*b16 + 100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 +
100*b23 + 100*b24 + x85)*x44 + x86*x68 - (100*b17 + 100*b18 + 100*b19 +
100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x46 - x86*x66 - 20
*b16 - 1000*b4 + 1000*b28 =G= 1000;
e41.. (100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x45 + x86*x69 - (100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x47 - x86*x67 - 80*b17 - 1000*b5
+ 1000*b29 =G= 1000;
e42.. (100*b17 + 100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x46 + x86*x70 - (100*b18 + 100*b19 + 100*b20 + 100*b21 +
100*b22 + 100*b23 + 100*b24 + x85)*x48 - x86*x68 - 20*b17 - 1000*b5
+ 1000*b29 =G= 1000;
e43.. (100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 +
x85)*x47 + x86*x71 - (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x49 - x86*x69 - 80*b18 - 1000*b6 + 1000*b30 =G= 1000;
e44.. (100*b18 + 100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 +
x85)*x48 + x86*x72 - (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 +
100*b24 + x85)*x50 - x86*x70 - 20*b18 - 1000*b6 + 1000*b30 =G= 1000;
e45.. (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x49 +
x86*x73 - (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x51 -
x86*x71 - 80*b19 - 1000*b7 + 1000*b31 =G= 1000;
e46.. (100*b19 + 100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x50 +
x86*x74 - (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x52 -
x86*x72 - 20*b19 - 1000*b7 + 1000*b31 =G= 1000;
e47.. (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x51 + x86*x75 - (
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x53 - x86*x73 - 80*b20
- 1000*b8 + 1000*b32 =G= 1000;
e48.. (100*b20 + 100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x52 + x86*x76 - (
100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x54 - x86*x74 - 20*b20
- 1000*b8 + 1000*b32 =G= 1000;
e49.. (100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x53 + x86*x77 - (100*b22 +
100*b23 + 100*b24 + x85)*x55 - x86*x75 - 80*b21 - 1000*b9 + 1000*b33
=G= 1000;
e50.. (100*b21 + 100*b22 + 100*b23 + 100*b24 + x85)*x54 + x86*x78 - (100*b22 +
100*b23 + 100*b24 + x85)*x56 - x86*x76 - 20*b21 - 1000*b9 + 1000*b33
=G= 1000;
e51.. (100*b22 + 100*b23 + 100*b24 + x85)*x55 + x86*x79 - (100*b23 + 100*b24 +
x85)*x57 - x86*x77 - 80*b22 - 1000*b10 + 1000*b34 =G= 1000;
e52.. (100*b22 + 100*b23 + 100*b24 + x85)*x56 + x86*x80 - (100*b23 + 100*b24 +
x85)*x58 - x86*x78 - 20*b22 - 1000*b10 + 1000*b34 =G= 1000;
e53.. (100*b23 + 100*b24 + x85)*x57 + x86*x81 - (100*b24 + x85)*x59 - x86*x79
- 80*b23 - 1000*b11 + 1000*b35 =G= 1000;
e54.. (100*b23 + 100*b24 + x85)*x58 + x86*x82 - (100*b24 + x85)*x60 - x86*x80
- 20*b23 - 1000*b11 + 1000*b35 =G= 1000;
e55.. x85*x39 + x87*x63 - x86*x61 + 1000*b2 =L= 1000;
e56.. x85*x40 + x87*x64 - x86*x62 + 1000*b2 =L= 1000;
e57.. x85*x41 + x87*x65 - x86*x63 + 1000*b3 =L= 1000;
e58.. x85*x42 + x87*x66 - x86*x64 + 1000*b3 =L= 1000;
e59.. x85*x43 + x87*x67 - x86*x65 + 1000*b4 =L= 1000;
e60.. x85*x44 + x87*x68 - x86*x66 + 1000*b4 =L= 1000;
e61.. x85*x45 + x87*x69 - x86*x67 + 1000*b5 =L= 1000;
e62.. x85*x46 + x87*x70 - x86*x68 + 1000*b5 =L= 1000;
e63.. x85*x47 + x87*x71 - x86*x69 + 1000*b6 =L= 1000;
e64.. x85*x48 + x87*x72 - x86*x70 + 1000*b6 =L= 1000;
e65.. x85*x49 + x87*x73 - x86*x71 + 1000*b7 =L= 1000;
e66.. x85*x50 + x87*x74 - x86*x72 + 1000*b7 =L= 1000;
e67.. x85*x51 + x87*x75 - x86*x73 + 1000*b8 =L= 1000;
e68.. x85*x52 + x87*x76 - x86*x74 + 1000*b8 =L= 1000;
e69.. x85*x53 + x87*x77 - x86*x75 + 1000*b9 =L= 1000;
e70.. x85*x54 + x87*x78 - x86*x76 + 1000*b9 =L= 1000;
e71.. x85*x55 + x87*x79 - x86*x77 + 1000*b10 =L= 1000;
e72.. x85*x56 + x87*x80 - x86*x78 + 1000*b10 =L= 1000;
e73.. x85*x57 + x87*x81 - x86*x79 + 1000*b11 =L= 1000;
e74.. x85*x58 + x87*x82 - x86*x80 + 1000*b11 =L= 1000;
e75.. x85*x59 + x87*x83 - x86*x81 + 1000*b12 =L= 1000;
e76.. x85*x60 + x87*x84 - x86*x82 + 1000*b12 =L= 1000;
e77.. x85*x39 + x87*x63 - x86*x61 - 1000*b2 =G= -1000;
e78.. x85*x40 + x87*x64 - x86*x62 - 1000*b2 =G= -1000;
e79.. x85*x41 + x87*x65 - x86*x63 - 1000*b3 =G= -1000;
e80.. x85*x42 + x87*x66 - x86*x64 - 1000*b3 =G= -1000;
e81.. x85*x43 + x87*x67 - x86*x65 - 1000*b4 =G= -1000;
e82.. x85*x44 + x87*x68 - x86*x66 - 1000*b4 =G= -1000;
e83.. x85*x45 + x87*x69 - x86*x67 - 1000*b5 =G= -1000;
e84.. x85*x46 + x87*x70 - x86*x68 - 1000*b5 =G= -1000;
e85.. x85*x47 + x87*x71 - x86*x69 - 1000*b6 =G= -1000;
e86.. x85*x48 + x87*x72 - x86*x70 - 1000*b6 =G= -1000;
e87.. x85*x49 + x87*x73 - x86*x71 - 1000*b7 =G= -1000;
e88.. x85*x50 + x87*x74 - x86*x72 - 1000*b7 =G= -1000;
e89.. x85*x51 + x87*x75 - x86*x73 - 1000*b8 =G= -1000;
e90.. x85*x52 + x87*x76 - x86*x74 - 1000*b8 =G= -1000;
e91.. x85*x53 + x87*x77 - x86*x75 - 1000*b9 =G= -1000;
e92.. x85*x54 + x87*x78 - x86*x76 - 1000*b9 =G= -1000;
e93.. x85*x55 + x87*x79 - x86*x77 - 1000*b10 =G= -1000;
e94.. x85*x56 + x87*x80 - x86*x78 - 1000*b10 =G= -1000;
e95.. x85*x57 + x87*x81 - x86*x79 - 1000*b11 =G= -1000;
e96.. x85*x58 + x87*x82 - x86*x80 - 1000*b11 =G= -1000;
e97.. x85*x59 + x87*x83 - x86*x81 - 1000*b12 =G= -1000;
e98.. x85*x60 + x87*x84 - x86*x82 - 1000*b12 =G= -1000;
e99.. -objvar*x87 + x85 =E= 0;
e100.. b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 + b21 + b22 + b23 + b24
=E= 1;
e101.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 =E= 1;
e102.. b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 + b33 + b34 + b35 + b36
=E= 12;
e103.. b1 + 2*b2 + 3*b3 + 4*b4 + 5*b5 + 6*b6 + 7*b7 + 8*b8 + 9*b9 + 10*b10
+ 11*b11 + 12*b12 =E= 12;
e104.. - b1 - 2*b2 - 3*b3 - 4*b4 - 5*b5 - 6*b6 - 7*b7 - 8*b8 - 9*b9 - 10*b10
- 11*b11 - 12*b12 + b13 + 2*b14 + 3*b15 + 4*b16 + 5*b17 + 6*b18 + 7*b19
+ 8*b20 + 9*b21 + 10*b22 + 11*b23 + 12*b24 =L= 0;
e105.. b1 - b25 =L= 0;
e106.. b2 - b26 =L= 0;
e107.. b3 - b27 =L= 0;
e108.. b4 - b28 =L= 0;
e109.. b5 - b29 =L= 0;
e110.. b6 - b30 =L= 0;
e111.. b7 - b31 =L= 0;
e112.. b8 - b32 =L= 0;
e113.. b9 - b33 =L= 0;
e114.. b10 - b34 =L= 0;
e115.. b11 - b35 =L= 0;
e116.. b12 - b36 =L= 0;
e117.. b13 - b25 =L= 0;
e118.. b14 - b26 =L= 0;
e119.. b15 - b27 =L= 0;
e120.. b16 - b28 =L= 0;
e121.. b17 - b29 =L= 0;
e122.. b18 - b30 =L= 0;
e123.. b19 - b31 =L= 0;
e124.. b20 - b32 =L= 0;
e125.. b21 - b33 =L= 0;
e126.. b22 - b34 =L= 0;
e127.. b23 - b35 =L= 0;
e128.. b24 - b36 =L= 0;
e129.. - b1 - b2 - b3 - b4 - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b25
=L= 0;
e130.. - b2 - b3 - b4 - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b26 =L= 0;
e131.. - b3 - b4 - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b27 =L= 0;
e132.. - b4 - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b28 =L= 0;
e133.. - b5 - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b29 =L= 0;
e134.. - b6 - b7 - b8 - b9 - b10 - b11 - b12 + b30 =L= 0;
e135.. - b7 - b8 - b9 - b10 - b11 - b12 + b31 =L= 0;
e136.. - b8 - b9 - b10 - b11 - b12 + b32 =L= 0;
e137.. - b9 - b10 - b11 - b12 + b33 =L= 0;
e138.. - b10 - b11 - b12 + b34 =L= 0;
e139.. - b11 - b12 + b35 =L= 0;
e140.. - b12 + b36 =L= 0;
e141.. - b25 - x61 - x62 =L= 0;
e142.. - b26 - x63 - x64 =L= 0;
e143.. - b27 - x65 - x66 =L= 0;
e144.. - b28 - x67 - x68 =L= 0;
e145.. - b29 - x69 - x70 =L= 0;
e146.. - b30 - x71 - x72 =L= 0;
e147.. - b31 - x73 - x74 =L= 0;
e148.. - b32 - x75 - x76 =L= 0;
e149.. - b33 - x77 - x78 =L= 0;
e150.. - b34 - x79 - x80 =L= 0;
e151.. - b35 - x81 - x82 =L= 0;
e152.. - b36 - x83 - x84 =L= 0;
e153.. b25 - x61 - x62 =L= 0;
e154.. b26 - x63 - x64 =L= 0;
e155.. b27 - x65 - x66 =L= 0;
e156.. b28 - x67 - x68 =L= 0;
e157.. b29 - x69 - x70 =L= 0;
e158.. b30 - x71 - x72 =L= 0;
e159.. b31 - x73 - x74 =L= 0;
e160.. b32 - x75 - x76 =L= 0;
e161.. b33 - x77 - x78 =L= 0;
e162.. b34 - x79 - x80 =L= 0;
e163.. b35 - x81 - x82 =L= 0;
e164.. b36 - x83 - x84 =L= 0;
e165.. - b25 - x37 - x38 =L= 0;
e166.. - b26 - x39 - x40 =L= 0;
e167.. - b27 - x41 - x42 =L= 0;
e168.. - b28 - x43 - x44 =L= 0;
e169.. - b29 - x45 - x46 =L= 0;
e170.. - b30 - x47 - x48 =L= 0;
e171.. - b31 - x49 - x50 =L= 0;
e172.. - b32 - x51 - x52 =L= 0;
e173.. - b33 - x53 - x54 =L= 0;
e174.. - b34 - x55 - x56 =L= 0;
e175.. - b35 - x57 - x58 =L= 0;
e176.. - b36 - x59 - x60 =L= 0;
e177.. b25 - x37 - x38 =L= 0;
e178.. b26 - x39 - x40 =L= 0;
e179.. b27 - x41 - x42 =L= 0;
e180.. b28 - x43 - x44 =L= 0;
e181.. b29 - x45 - x46 =L= 0;
e182.. b30 - x47 - x48 =L= 0;
e183.. b31 - x49 - x50 =L= 0;
e184.. b32 - x51 - x52 =L= 0;
e185.. b33 - x53 - x54 =L= 0;
e186.. b34 - x55 - x56 =L= 0;
e187.. b35 - x57 - x58 =L= 0;
e188.. b36 - x59 - x60 =L= 0;
e189.. - b25 - x61 - x62 =G= -2;
e190.. - b26 - x63 - x64 =G= -2;
e191.. - b27 - x65 - x66 =G= -2;
e192.. - b28 - x67 - x68 =G= -2;
e193.. - b29 - x69 - x70 =G= -2;
e194.. - b30 - x71 - x72 =G= -2;
e195.. - b31 - x73 - x74 =G= -2;
e196.. - b32 - x75 - x76 =G= -2;
e197.. - b33 - x77 - x78 =G= -2;
e198.. - b34 - x79 - x80 =G= -2;
e199.. - b35 - x81 - x82 =G= -2;
e200.. - b36 - x83 - x84 =G= -2;
e201.. b25 - x61 - x62 =G= -2;
e202.. b26 - x63 - x64 =G= -2;
e203.. b27 - x65 - x66 =G= -2;
e204.. b28 - x67 - x68 =G= -2;
e205.. b29 - x69 - x70 =G= -2;
e206.. b30 - x71 - x72 =G= -2;
e207.. b31 - x73 - x74 =G= -2;
e208.. b32 - x75 - x76 =G= -2;
e209.. b33 - x77 - x78 =G= -2;
e210.. b34 - x79 - x80 =G= -2;
e211.. b35 - x81 - x82 =G= -2;
e212.. b36 - x83 - x84 =G= -2;
e213.. - b25 - x37 - x38 =G= -2;
e214.. - b26 - x39 - x40 =G= -2;
e215.. - b27 - x41 - x42 =G= -2;
e216.. - b28 - x43 - x44 =G= -2;
e217.. - b29 - x45 - x46 =G= -2;
e218.. - b30 - x47 - x48 =G= -2;
e219.. - b31 - x49 - x50 =G= -2;
e220.. - b32 - x51 - x52 =G= -2;
e221.. - b33 - x53 - x54 =G= -2;
e222.. - b34 - x55 - x56 =G= -2;
e223.. - b35 - x57 - x58 =G= -2;
e224.. - b36 - x59 - x60 =G= -2;
e225.. b25 - x37 - x38 =G= -2;
e226.. b26 - x39 - x40 =G= -2;
e227.. b27 - x41 - x42 =G= -2;
e228.. b28 - x43 - x44 =G= -2;
e229.. b29 - x45 - x46 =G= -2;
e230.. b30 - x47 - x48 =G= -2;
e231.. b31 - x49 - x50 =G= -2;
e232.. b32 - x51 - x52 =G= -2;
e233.. b33 - x53 - x54 =G= -2;
e234.. b34 - x55 - x56 =G= -2;
e235.. b35 - x57 - x58 =G= -2;
e236.. b36 - x59 - x60 =G= -2;
e237.. (x37 + 5.13435*x38)*x61 - x37 + 1000*b25 =L= 1000;
e238.. (x37 + 5.13435*x38)*x62 - 5.13435*x38 + 1000*b25 =L= 1000;
e239.. (x39 + 5.13435*x40)*x63 - x39 + 1000*b26 =L= 1000;
e240.. (x39 + 5.13435*x40)*x64 - 5.13435*x40 + 1000*b26 =L= 1000;
e241.. (x41 + 5.13435*x42)*x65 - x41 + 1000*b27 =L= 1000;
e242.. (x41 + 5.13435*x42)*x66 - 5.13435*x42 + 1000*b27 =L= 1000;
e243.. (x43 + 5.13435*x44)*x67 - x43 + 1000*b28 =L= 1000;
e244.. (x43 + 5.13435*x44)*x68 - 5.13435*x44 + 1000*b28 =L= 1000;
e245.. (x45 + 5.13435*x46)*x69 - x45 + 1000*b29 =L= 1000;
e246.. (x45 + 5.13435*x46)*x70 - 5.13435*x46 + 1000*b29 =L= 1000;
e247.. (x47 + 5.13435*x48)*x71 - x47 + 1000*b30 =L= 1000;
e248.. (x47 + 5.13435*x48)*x72 - 5.13435*x48 + 1000*b30 =L= 1000;
e249.. (x49 + 5.13435*x50)*x73 - x49 + 1000*b31 =L= 1000;
e250.. (x49 + 5.13435*x50)*x74 - 5.13435*x50 + 1000*b31 =L= 1000;
e251.. (x51 + 5.13435*x52)*x75 - x51 + 1000*b32 =L= 1000;
e252.. (x51 + 5.13435*x52)*x76 - 5.13435*x52 + 1000*b32 =L= 1000;
e253.. (x53 + 5.13435*x54)*x77 - x53 + 1000*b33 =L= 1000;
e254.. (x53 + 5.13435*x54)*x78 - 5.13435*x54 + 1000*b33 =L= 1000;
e255.. (x55 + 5.13435*x56)*x79 - x55 + 1000*b34 =L= 1000;
e256.. (x55 + 5.13435*x56)*x80 - 5.13435*x56 + 1000*b34 =L= 1000;
e257.. (x57 + 5.13435*x58)*x81 - x57 + 1000*b35 =L= 1000;
e258.. (x57 + 5.13435*x58)*x82 - 5.13435*x58 + 1000*b35 =L= 1000;
e259.. (x59 + 5.13435*x60)*x83 - x59 + 1000*b36 =L= 1000;
e260.. (x59 + 5.13435*x60)*x84 - 5.13435*x60 + 1000*b36 =L= 1000;
e261.. (x37 + 5.13435*x38)*x61 - x37 - 1000*b25 =G= -1000;
e262.. (x37 + 5.13435*x38)*x62 - 5.13435*x38 - 1000*b25 =G= -1000;
e263.. (x39 + 5.13435*x40)*x63 - x39 - 1000*b26 =G= -1000;
e264.. (x39 + 5.13435*x40)*x64 - 5.13435*x40 - 1000*b26 =G= -1000;
e265.. (x41 + 5.13435*x42)*x65 - x41 - 1000*b27 =G= -1000;
e266.. (x41 + 5.13435*x42)*x66 - 5.13435*x42 - 1000*b27 =G= -1000;
e267.. (x43 + 5.13435*x44)*x67 - x43 - 1000*b28 =G= -1000;
e268.. (x43 + 5.13435*x44)*x68 - 5.13435*x44 - 1000*b28 =G= -1000;
e269.. (x45 + 5.13435*x46)*x69 - x45 - 1000*b29 =G= -1000;
e270.. (x45 + 5.13435*x46)*x70 - 5.13435*x46 - 1000*b29 =G= -1000;
e271.. (x47 + 5.13435*x48)*x71 - x47 - 1000*b30 =G= -1000;
e272.. (x47 + 5.13435*x48)*x72 - 5.13435*x48 - 1000*b30 =G= -1000;
e273.. (x49 + 5.13435*x50)*x73 - x49 - 1000*b31 =G= -1000;
e274.. (x49 + 5.13435*x50)*x74 - 5.13435*x50 - 1000*b31 =G= -1000;
e275.. (x51 + 5.13435*x52)*x75 - x51 - 1000*b32 =G= -1000;
e276.. (x51 + 5.13435*x52)*x76 - 5.13435*x52 - 1000*b32 =G= -1000;
e277.. (x53 + 5.13435*x54)*x77 - x53 - 1000*b33 =G= -1000;
e278.. (x53 + 5.13435*x54)*x78 - 5.13435*x54 - 1000*b33 =G= -1000;
e279.. (x55 + 5.13435*x56)*x79 - x55 - 1000*b34 =G= -1000;
e280.. (x55 + 5.13435*x56)*x80 - 5.13435*x56 - 1000*b34 =G= -1000;
e281.. (x57 + 5.13435*x58)*x81 - x57 - 1000*b35 =G= -1000;
e282.. (x57 + 5.13435*x58)*x82 - 5.13435*x58 - 1000*b35 =G= -1000;
e283.. (x59 + 5.13435*x60)*x83 - x59 - 1000*b36 =G= -1000;
e284.. (x59 + 5.13435*x60)*x84 - 5.13435*x60 - 1000*b36 =G= -1000;
* set non-default bounds
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1;
x63.up = 1;
x64.up = 1;
x65.up = 1;
x66.up = 1;
x67.up = 1;
x68.up = 1;
x69.up = 1;
x70.up = 1;
x71.up = 1;
x72.up = 1;
x73.up = 1;
x74.up = 1;
x75.up = 1;
x76.up = 1;
x77.up = 1;
x78.up = 1;
x79.up = 1;
x80.up = 1;
x81.up = 1;
x82.up = 1;
x83.up = 1;
x84.up = 1;
x87.up = 100;
objvar.lo = 0; objvar.up = 5;
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