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Instance fo7_ar4_1
Optimization of block layout design problems with unequal areas
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 20.72852509 (ALPHAECP) 20.72982440 (ANTIGONE) 20.72982505 (BARON) 15.37955100 (BONMIN) 20.72982505 (COUENNE) 20.72982182 (LINDO) 20.72982504 (SCIP) 20.72981848 (SHOT) |
| Referencesⓘ | Castillo, Ignacio, Westerlund, Joakim, Emet, Stefan, and Westerlund, Tapio, Optimization of block layout design problems with unequal areas: A comparison of MILP and MINLP optimization methods, Computers and Chemical Engineering, 30:1, 2005, 54-69. |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 19 Dec 2005 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 112 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 42 |
| #Nonlinear Variablesⓘ | 14 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 269 |
| #Linear Constraintsⓘ | 255 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 14 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 1042 |
| #Nonlinear Nonzeros in Jacobianⓘ | 14 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 14 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 14 |
| #Blocks in Hessian of Lagrangianⓘ | 14 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 8.3333e-02 |
| Maximal coefficientⓘ | 3.6000e+01 |
| Infeasibility of initial pointⓘ | 7.785 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 270 2 2 266 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 113 71 0 42 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1055 1041 14 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36
,i37,i38,i39,i40,i41,i42,objvar,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,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
,i18,i19,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34
,i35,i36,i37,i38,i39,i40,i41,i42;
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;
e1.. objvar - x44 - x45 - x46 - x47 - x48 - x49 - x50 - x51 - x52 - x53
- x54 - x55 =E= 0;
e2.. x56 - x57 =G= 0;
e3.. x58 - x59 =G= 0;
e4.. i1 - i2 =E= 0;
e5.. - 8.54*i1 - x44 + 0.5*x60 + 0.5*x61 =L= 0;
e6.. 13*i1 - x45 + 0.5*x62 + 0.5*x63 =L= 13;
e7.. - 8.54*i3 + 0.5*x60 + 0.5*x64 - x65 =L= 0;
e8.. 13*i3 + 0.5*x62 + 0.5*x66 - x67 =L= 13;
e9.. - 8.54*i5 + 0.5*x60 + 0.5*x68 - x69 =L= 0;
e10.. 13*i5 + 0.5*x62 + 0.5*x70 - x71 =L= 13;
e11.. - 8.54*i7 + 0.5*x60 + 0.5*x72 - x73 =L= 0;
e12.. 13*i7 + 0.5*x62 + 0.5*x74 - x75 =L= 13;
e13.. - 8.54*i9 + 0.5*x60 + 0.5*x76 - x77 =L= 0;
e14.. 13*i9 + 0.5*x62 + 0.5*x78 - x79 =L= 13;
e15.. - 8.54*i11 + 0.5*x60 + 0.5*x80 - x81 =L= 0;
e16.. 13*i11 + 0.5*x62 + 0.5*x82 - x83 =L= 13;
e17.. - 8.54*i13 - x46 + 0.5*x61 + 0.5*x64 =L= 0;
e18.. 13*i13 - x47 + 0.5*x63 + 0.5*x66 =L= 13;
e19.. - 8.54*i15 + 0.5*x61 + 0.5*x68 - x84 =L= 0;
e20.. 13*i15 + 0.5*x63 + 0.5*x70 - x85 =L= 13;
e21.. - 8.54*i17 + 0.5*x61 + 0.5*x72 - x86 =L= 0;
e22.. 13*i17 + 0.5*x63 + 0.5*x74 - x87 =L= 13;
e23.. - 8.54*i19 + 0.5*x61 + 0.5*x76 - x88 =L= 0;
e24.. 13*i19 + 0.5*x63 + 0.5*x78 - x89 =L= 13;
e25.. - 8.54*i21 + 0.5*x61 + 0.5*x80 - x90 =L= 0;
e26.. 13*i21 + 0.5*x63 + 0.5*x82 - x91 =L= 13;
e27.. - 8.54*i23 - x48 + 0.5*x64 + 0.5*x68 =L= 0;
e28.. 13*i23 - x49 + 0.5*x66 + 0.5*x70 =L= 13;
e29.. - 8.54*i25 + 0.5*x64 + 0.5*x72 - x92 =L= 0;
e30.. 13*i25 + 0.5*x66 + 0.5*x74 - x93 =L= 13;
e31.. - 8.54*i27 + 0.5*x64 + 0.5*x76 - x94 =L= 0;
e32.. 13*i27 + 0.5*x66 + 0.5*x78 - x95 =L= 13;
e33.. - 8.54*i29 + 0.5*x64 + 0.5*x80 - x96 =L= 0;
e34.. 13*i29 + 0.5*x66 + 0.5*x82 - x97 =L= 13;
e35.. - 8.54*i31 - x50 + 0.5*x68 + 0.5*x72 =L= 0;
e36.. 13*i31 - x51 + 0.5*x70 + 0.5*x74 =L= 13;
e37.. - 8.54*i33 + 0.5*x68 + 0.5*x76 - x98 =L= 0;
e38.. 13*i33 + 0.5*x70 + 0.5*x78 - x99 =L= 13;
e39.. - 8.54*i35 + 0.5*x68 + 0.5*x80 - x100 =L= 0;
e40.. 13*i35 + 0.5*x70 + 0.5*x82 - x101 =L= 13;
e41.. - 8.54*i37 - x52 + 0.5*x72 + 0.5*x76 =L= 0;
e42.. 13*i37 - x53 + 0.5*x74 + 0.5*x78 =L= 13;
e43.. - 8.54*i39 + 0.5*x72 + 0.5*x80 - x102 =L= 0;
e44.. 13*i39 + 0.5*x74 + 0.5*x82 - x103 =L= 13;
e45.. - 8.54*i41 - x54 + 0.5*x76 + 0.5*x80 =L= 0;
e46.. 13*i41 - x55 + 0.5*x78 + 0.5*x82 =L= 13;
e47.. - 0.5*x60 - 0.125*x62 =L= -2;
e48.. - 0.125*x60 - 0.5*x62 =L= -2;
e49.. - 0.5*x61 - 0.125*x63 =L= -2;
e50.. - 0.125*x61 - 0.5*x63 =L= -2;
e51.. - 0.5*x64 - 0.125*x66 =L= -2;
e52.. - 0.125*x64 - 0.5*x66 =L= -2;
e53.. - 0.333333*x68 - 0.083333*x70 =L= -2;
e54.. - 0.117096*x68 - 0.237222*x70 =L= -2;
e55.. - 0.666667*x72 - 0.166667*x74 =L= -2;
e56.. - 0.166667*x72 - 0.666667*x74 =L= -2;
e57.. - 0.666667*x76 - 0.166667*x78 =L= -2;
e58.. - 0.166667*x76 - 0.666667*x78 =L= -2;
e59.. - 0.666667*x80 - 0.166667*x82 =L= -2;
e60.. - 0.166667*x80 - 0.666667*x82 =L= -2;
e61.. x56 + 0.5*x60 =L= 8.54;
e62.. - x56 + 0.5*x60 =L= 0;
e63.. x59 + 0.5*x62 =L= 13;
e64.. - x59 + 0.5*x62 =L= 0;
e65.. x57 + 0.5*x61 =L= 8.54;
e66.. - x57 + 0.5*x61 =L= 0;
e67.. x58 + 0.5*x63 =L= 13;
e68.. - x58 + 0.5*x63 =L= 0;
e69.. 0.5*x64 + x104 =L= 8.54;
e70.. 0.5*x64 - x104 =L= 0;
e71.. 0.5*x66 + x105 =L= 13;
e72.. 0.5*x66 - x105 =L= 0;
e73.. 0.5*x68 + x106 =L= 8.54;
e74.. 0.5*x68 - x106 =L= 0;
e75.. 0.5*x70 + x107 =L= 13;
e76.. 0.5*x70 - x107 =L= 0;
e77.. 0.5*x72 + x108 =L= 8.54;
e78.. 0.5*x72 - x108 =L= 0;
e79.. 0.5*x74 + x109 =L= 13;
e80.. 0.5*x74 - x109 =L= 0;
e81.. 0.5*x76 + x110 =L= 8.54;
e82.. 0.5*x76 - x110 =L= 0;
e83.. 0.5*x78 + x111 =L= 13;
e84.. 0.5*x78 - x111 =L= 0;
e85.. 0.5*x80 + x112 =L= 8.54;
e86.. 0.5*x80 - x112 =L= 0;
e87.. 0.5*x82 + x113 =L= 13;
e88.. 0.5*x82 - x113 =L= 0;
e89.. - x44 + x56 - x57 =L= 0;
e90.. - x44 - x56 + x57 =L= 0;
e91.. - x45 - x58 + x59 =L= 0;
e92.. - x45 + x58 - x59 =L= 0;
e93.. - 8.54*i1 - 8.54*i2 - x56 + x57 + 0.5*x60 + 0.5*x61 =L= 0;
e94.. - 8.54*i1 + 8.54*i2 + x56 - x57 + 0.5*x60 + 0.5*x61 =L= 8.54;
e95.. 13*i1 - 13*i2 + x58 - x59 + 0.5*x62 + 0.5*x63 =L= 13;
e96.. 13*i1 + 13*i2 - x58 + x59 + 0.5*x62 + 0.5*x63 =L= 26;
e97.. x56 - x65 - x104 =L= 0;
e98.. - x56 - x65 + x104 =L= 0;
e99.. x59 - x67 - x105 =L= 0;
e100.. - x59 - x67 + x105 =L= 0;
e101.. - 8.54*i3 - 8.54*i4 - x56 + 0.5*x60 + 0.5*x64 + x104 =L= 0;
e102.. - 8.54*i3 + 8.54*i4 + x56 + 0.5*x60 + 0.5*x64 - x104 =L= 8.54;
e103.. 13*i3 - 13*i4 - x59 + 0.5*x62 + 0.5*x66 + x105 =L= 13;
e104.. 13*i3 + 13*i4 + x59 + 0.5*x62 + 0.5*x66 - x105 =L= 26;
e105.. x56 - x69 - x106 =L= 0;
e106.. - x56 - x69 + x106 =L= 0;
e107.. x59 - x71 - x107 =L= 0;
e108.. - x59 - x71 + x107 =L= 0;
e109.. - 8.54*i5 - 8.54*i6 - x56 + 0.5*x60 + 0.5*x68 + x106 =L= 0;
e110.. - 8.54*i5 + 8.54*i6 + x56 + 0.5*x60 + 0.5*x68 - x106 =L= 8.54;
e111.. 13*i5 - 13*i6 - x59 + 0.5*x62 + 0.5*x70 + x107 =L= 13;
e112.. 13*i5 + 13*i6 + x59 + 0.5*x62 + 0.5*x70 - x107 =L= 26;
e113.. x56 - x73 - x108 =L= 0;
e114.. - x56 - x73 + x108 =L= 0;
e115.. x59 - x75 - x109 =L= 0;
e116.. - x59 - x75 + x109 =L= 0;
e117.. - 8.54*i7 - 8.54*i8 - x56 + 0.5*x60 + 0.5*x72 + x108 =L= 0;
e118.. - 8.54*i7 + 8.54*i8 + x56 + 0.5*x60 + 0.5*x72 - x108 =L= 8.54;
e119.. 13*i7 - 13*i8 - x59 + 0.5*x62 + 0.5*x74 + x109 =L= 13;
e120.. 13*i7 + 13*i8 + x59 + 0.5*x62 + 0.5*x74 - x109 =L= 26;
e121.. x56 - x77 - x110 =L= 0;
e122.. - x56 - x77 + x110 =L= 0;
e123.. x59 - x79 - x111 =L= 0;
e124.. - x59 - x79 + x111 =L= 0;
e125.. - 8.54*i9 - 8.54*i10 - x56 + 0.5*x60 + 0.5*x76 + x110 =L= 0;
e126.. - 8.54*i9 + 8.54*i10 + x56 + 0.5*x60 + 0.5*x76 - x110 =L= 8.54;
e127.. 13*i9 - 13*i10 - x59 + 0.5*x62 + 0.5*x78 + x111 =L= 13;
e128.. 13*i9 + 13*i10 + x59 + 0.5*x62 + 0.5*x78 - x111 =L= 26;
e129.. x56 - x81 - x112 =L= 0;
e130.. - x56 - x81 + x112 =L= 0;
e131.. x59 - x83 - x113 =L= 0;
e132.. - x59 - x83 + x113 =L= 0;
e133.. - 8.54*i11 - 8.54*i12 - x56 + 0.5*x60 + 0.5*x80 + x112 =L= 0;
e134.. - 8.54*i11 + 8.54*i12 + x56 + 0.5*x60 + 0.5*x80 - x112 =L= 8.54;
e135.. 13*i11 - 13*i12 - x59 + 0.5*x62 + 0.5*x82 + x113 =L= 13;
e136.. 13*i11 + 13*i12 + x59 + 0.5*x62 + 0.5*x82 - x113 =L= 26;
e137.. - x46 + x57 - x104 =L= 0;
e138.. - x46 - x57 + x104 =L= 0;
e139.. - x47 + x58 - x105 =L= 0;
e140.. - x47 - x58 + x105 =L= 0;
e141.. - 8.54*i13 - 8.54*i14 - x57 + 0.5*x61 + 0.5*x64 + x104 =L= 0;
e142.. - 8.54*i13 + 8.54*i14 + x57 + 0.5*x61 + 0.5*x64 - x104 =L= 8.54;
e143.. 13*i13 - 13*i14 - x58 + 0.5*x63 + 0.5*x66 + x105 =L= 13;
e144.. 13*i13 + 13*i14 + x58 + 0.5*x63 + 0.5*x66 - x105 =L= 26;
e145.. x57 - x84 - x106 =L= 0;
e146.. - x57 - x84 + x106 =L= 0;
e147.. x58 - x85 - x107 =L= 0;
e148.. - x58 - x85 + x107 =L= 0;
e149.. - 8.54*i15 - 8.54*i16 - x57 + 0.5*x61 + 0.5*x68 + x106 =L= 0;
e150.. - 8.54*i15 + 8.54*i16 + x57 + 0.5*x61 + 0.5*x68 - x106 =L= 8.54;
e151.. 13*i15 - 13*i16 - x58 + 0.5*x63 + 0.5*x70 + x107 =L= 13;
e152.. 13*i15 + 13*i16 + x58 + 0.5*x63 + 0.5*x70 - x107 =L= 26;
e153.. x57 - x86 - x108 =L= 0;
e154.. - x57 - x86 + x108 =L= 0;
e155.. x58 - x87 - x109 =L= 0;
e156.. - x58 - x87 + x109 =L= 0;
e157.. - 8.54*i17 - 8.54*i18 - x57 + 0.5*x61 + 0.5*x72 + x108 =L= 0;
e158.. - 8.54*i17 + 8.54*i18 + x57 + 0.5*x61 + 0.5*x72 - x108 =L= 8.54;
e159.. 13*i17 - 13*i18 - x58 + 0.5*x63 + 0.5*x74 + x109 =L= 13;
e160.. 13*i17 + 13*i18 + x58 + 0.5*x63 + 0.5*x74 - x109 =L= 26;
e161.. x57 - x88 - x110 =L= 0;
e162.. - x57 - x88 + x110 =L= 0;
e163.. x58 - x89 - x111 =L= 0;
e164.. - x58 - x89 + x111 =L= 0;
e165.. - 8.54*i19 - 8.54*i20 - x57 + 0.5*x61 + 0.5*x76 + x110 =L= 0;
e166.. - 8.54*i19 + 8.54*i20 + x57 + 0.5*x61 + 0.5*x76 - x110 =L= 8.54;
e167.. 13*i19 - 13*i20 - x58 + 0.5*x63 + 0.5*x78 + x111 =L= 13;
e168.. 13*i19 + 13*i20 + x58 + 0.5*x63 + 0.5*x78 - x111 =L= 26;
e169.. x57 - x90 - x112 =L= 0;
e170.. - x57 - x90 + x112 =L= 0;
e171.. x58 - x91 - x113 =L= 0;
e172.. - x58 - x91 + x113 =L= 0;
e173.. - 8.54*i21 - 8.54*i22 - x57 + 0.5*x61 + 0.5*x80 + x112 =L= 0;
e174.. - 8.54*i21 + 8.54*i22 + x57 + 0.5*x61 + 0.5*x80 - x112 =L= 8.54;
e175.. 13*i21 - 13*i22 - x58 + 0.5*x63 + 0.5*x82 + x113 =L= 13;
e176.. 13*i21 + 13*i22 + x58 + 0.5*x63 + 0.5*x82 - x113 =L= 26;
e177.. - x48 + x104 - x106 =L= 0;
e178.. - x48 - x104 + x106 =L= 0;
e179.. - x49 + x105 - x107 =L= 0;
e180.. - x49 - x105 + x107 =L= 0;
e181.. - 8.54*i23 - 8.54*i24 + 0.5*x64 + 0.5*x68 - x104 + x106 =L= 0;
e182.. - 8.54*i23 + 8.54*i24 + 0.5*x64 + 0.5*x68 + x104 - x106 =L= 8.54;
e183.. 13*i23 - 13*i24 + 0.5*x66 + 0.5*x70 - x105 + x107 =L= 13;
e184.. 13*i23 + 13*i24 + 0.5*x66 + 0.5*x70 + x105 - x107 =L= 26;
e185.. - x92 + x104 - x108 =L= 0;
e186.. - x92 - x104 + x108 =L= 0;
e187.. - x93 + x105 - x109 =L= 0;
e188.. - x93 - x105 + x109 =L= 0;
e189.. - 8.54*i25 - 8.54*i26 + 0.5*x64 + 0.5*x72 - x104 + x108 =L= 0;
e190.. - 8.54*i25 + 8.54*i26 + 0.5*x64 + 0.5*x72 + x104 - x108 =L= 8.54;
e191.. 13*i25 - 13*i26 + 0.5*x66 + 0.5*x74 - x105 + x109 =L= 13;
e192.. 13*i25 + 13*i26 + 0.5*x66 + 0.5*x74 + x105 - x109 =L= 26;
e193.. - x94 + x104 - x110 =L= 0;
e194.. - x94 - x104 + x110 =L= 0;
e195.. - x95 + x105 - x111 =L= 0;
e196.. - x95 - x105 + x111 =L= 0;
e197.. - 8.54*i27 - 8.54*i28 + 0.5*x64 + 0.5*x76 - x104 + x110 =L= 0;
e198.. - 8.54*i27 + 8.54*i28 + 0.5*x64 + 0.5*x76 + x104 - x110 =L= 8.54;
e199.. 13*i27 - 13*i28 + 0.5*x66 + 0.5*x78 - x105 + x111 =L= 13;
e200.. 13*i27 + 13*i28 + 0.5*x66 + 0.5*x78 + x105 - x111 =L= 26;
e201.. - x96 + x104 - x112 =L= 0;
e202.. - x96 - x104 + x112 =L= 0;
e203.. - x97 + x105 - x113 =L= 0;
e204.. - x97 - x105 + x113 =L= 0;
e205.. - 8.54*i29 - 8.54*i30 + 0.5*x64 + 0.5*x80 - x104 + x112 =L= 0;
e206.. - 8.54*i29 + 8.54*i30 + 0.5*x64 + 0.5*x80 + x104 - x112 =L= 8.54;
e207.. 13*i29 - 13*i30 + 0.5*x66 + 0.5*x82 - x105 + x113 =L= 13;
e208.. 13*i29 + 13*i30 + 0.5*x66 + 0.5*x82 + x105 - x113 =L= 26;
e209.. - x50 + x106 - x108 =L= 0;
e210.. - x50 - x106 + x108 =L= 0;
e211.. - x51 + x107 - x109 =L= 0;
e212.. - x51 - x107 + x109 =L= 0;
e213.. - 8.54*i31 - 8.54*i32 + 0.5*x68 + 0.5*x72 - x106 + x108 =L= 0;
e214.. - 8.54*i31 + 8.54*i32 + 0.5*x68 + 0.5*x72 + x106 - x108 =L= 8.54;
e215.. 13*i31 - 13*i32 + 0.5*x70 + 0.5*x74 - x107 + x109 =L= 13;
e216.. 13*i31 + 13*i32 + 0.5*x70 + 0.5*x74 + x107 - x109 =L= 26;
e217.. - x98 + x106 - x110 =L= 0;
e218.. - x98 - x106 + x110 =L= 0;
e219.. - x99 + x107 - x111 =L= 0;
e220.. - x99 - x107 + x111 =L= 0;
e221.. - 8.54*i33 - 8.54*i34 + 0.5*x68 + 0.5*x76 - x106 + x110 =L= 0;
e222.. - 8.54*i33 + 8.54*i34 + 0.5*x68 + 0.5*x76 + x106 - x110 =L= 8.54;
e223.. 13*i33 - 13*i34 + 0.5*x70 + 0.5*x78 - x107 + x111 =L= 13;
e224.. 13*i33 + 13*i34 + 0.5*x70 + 0.5*x78 + x107 - x111 =L= 26;
e225.. - x100 + x106 - x112 =L= 0;
e226.. - x100 - x106 + x112 =L= 0;
e227.. - x101 + x107 - x113 =L= 0;
e228.. - x101 - x107 + x113 =L= 0;
e229.. - 8.54*i35 - 8.54*i36 + 0.5*x68 + 0.5*x80 - x106 + x112 =L= 0;
e230.. - 8.54*i35 + 8.54*i36 + 0.5*x68 + 0.5*x80 + x106 - x112 =L= 8.54;
e231.. 13*i35 - 13*i36 + 0.5*x70 + 0.5*x82 - x107 + x113 =L= 13;
e232.. 13*i35 + 13*i36 + 0.5*x70 + 0.5*x82 + x107 - x113 =L= 26;
e233.. - x52 + x108 - x110 =L= 0;
e234.. - x52 - x108 + x110 =L= 0;
e235.. - x53 + x109 - x111 =L= 0;
e236.. - x53 - x109 + x111 =L= 0;
e237.. - 8.54*i37 - 8.54*i38 + 0.5*x72 + 0.5*x76 - x108 + x110 =L= 0;
e238.. - 8.54*i37 + 8.54*i38 + 0.5*x72 + 0.5*x76 + x108 - x110 =L= 8.54;
e239.. 13*i37 - 13*i38 + 0.5*x74 + 0.5*x78 - x109 + x111 =L= 13;
e240.. 13*i37 + 13*i38 + 0.5*x74 + 0.5*x78 + x109 - x111 =L= 26;
e241.. - x102 + x108 - x112 =L= 0;
e242.. - x102 - x108 + x112 =L= 0;
e243.. - x103 + x109 - x113 =L= 0;
e244.. - x103 - x109 + x113 =L= 0;
e245.. - 8.54*i39 - 8.54*i40 + 0.5*x72 + 0.5*x80 - x108 + x112 =L= 0;
e246.. - 8.54*i39 + 8.54*i40 + 0.5*x72 + 0.5*x80 + x108 - x112 =L= 8.54;
e247.. 13*i39 - 13*i40 + 0.5*x74 + 0.5*x82 - x109 + x113 =L= 13;
e248.. 13*i39 + 13*i40 + 0.5*x74 + 0.5*x82 + x109 - x113 =L= 26;
e249.. - x54 + x110 - x112 =L= 0;
e250.. - x54 - x110 + x112 =L= 0;
e251.. - x55 + x111 - x113 =L= 0;
e252.. - x55 - x111 + x113 =L= 0;
e253.. - 8.54*i41 - 8.54*i42 + 0.5*x76 + 0.5*x80 - x110 + x112 =L= 0;
e254.. - 8.54*i41 + 8.54*i42 + 0.5*x76 + 0.5*x80 + x110 - x112 =L= 8.54;
e255.. 13*i41 - 13*i42 + 0.5*x78 + 0.5*x82 - x111 + x113 =L= 13;
e256.. 13*i41 + 13*i42 + 0.5*x78 + 0.5*x82 + x111 - x113 =L= 26;
e257.. 16/x60 - x62 =L= 0;
e258.. 16/x62 - x60 =L= 0;
e259.. 16/x61 - x63 =L= 0;
e260.. 16/x63 - x61 =L= 0;
e261.. 16/x64 - x66 =L= 0;
e262.. 16/x66 - x64 =L= 0;
e263.. 36/x68 - x70 =L= 0;
e264.. 36/x70 - x68 =L= 0;
e265.. 9/x72 - x74 =L= 0;
e266.. 9/x74 - x72 =L= 0;
e267.. 9/x76 - x78 =L= 0;
e268.. 9/x78 - x76 =L= 0;
e269.. 9/x80 - x82 =L= 0;
e270.. 9/x82 - x80 =L= 0;
* set non-default bounds
i1.up = 100;
i2.up = 100;
i3.up = 100;
i4.up = 100;
i5.up = 100;
i6.up = 100;
i7.up = 100;
i8.up = 100;
i9.up = 100;
i10.up = 100;
i11.up = 100;
i12.up = 100;
i13.up = 100;
i14.up = 100;
i15.up = 100;
i16.up = 100;
i17.up = 100;
i18.up = 100;
i19.up = 100;
i20.up = 100;
i21.up = 100;
i22.up = 100;
i23.up = 100;
i24.up = 100;
i25.up = 100;
i26.up = 100;
i27.up = 100;
i28.up = 100;
i29.up = 100;
i30.up = 100;
i31.up = 100;
i32.up = 100;
i33.up = 100;
i34.up = 100;
i35.up = 100;
i36.up = 100;
i37.up = 100;
i38.up = 100;
i39.up = 100;
i40.up = 100;
i41.up = 100;
i42.up = 100;
x60.lo = 2; x60.up = 8;
x61.lo = 2; x61.up = 8;
x62.lo = 2; x62.up = 8;
x63.lo = 2; x63.up = 8;
x64.lo = 2; x64.up = 8;
x66.lo = 2; x66.up = 8;
x68.lo = 3; x68.up = 8.54;
x70.lo = 4.2155; x70.up = 12;
x72.lo = 1.5; x72.up = 6;
x74.lo = 1.5; x74.up = 6;
x76.lo = 1.5; x76.up = 6;
x78.lo = 1.5; x78.up = 6;
x80.lo = 1.5; x80.up = 6;
x82.lo = 1.5; x82.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: 2025-08-07 Git hash: e62cedfc