MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance no7_ar2_1

Optimization of block layout design problems with unequal areas
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
107.81530830 p1 ( gdx sol )
(infeas: 8e-14)
Other points (infeas > 1e-08)  
Dual Bounds
107.80736000 (ALPHAECP)
107.81530830 (ANTIGONE)
107.81530830 (BARON)
79.49395000 (BONMIN)
107.81527290 (COUENNE)
107.81530710 (LINDO)
107.81530020 (SCIP)
107.81525940 (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 18
#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 1.1785e-01
Maximal coefficient 3.6000e+01
Infeasibility of initial point 4.243
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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
*       1061     1047       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 - 5*x44 - 5*x45 - x46 - x47 - 3*x48 - 3*x49 - x50 - x51 - 2*x52
      - 2*x53 - x54 - x55 - 4*x56 - 4*x57 - 2*x58 - 2*x59 - x60 - x61 =E= 0;

e2..    x62 - x63 =G= 0;

e3..    x64 - x65 =G= 0;

e4..    i1 - i2 =E= 0;

e5..  - 8.54*i1 + 0.5*x66 + 0.5*x67 - x68 =L= 0;

e6..    13*i1 + 0.5*x69 + 0.5*x70 - x71 =L= 13;

e7..  - 8.54*i3 + 0.5*x66 + 0.5*x72 - x73 =L= 0;

e8..    13*i3 + 0.5*x69 + 0.5*x74 - x75 =L= 13;

e9..  - 8.54*i5 - x44 + 0.5*x66 + 0.5*x76 =L= 0;

e10..    13*i5 - x45 + 0.5*x69 + 0.5*x77 =L= 13;

e11..  - 8.54*i7 + 0.5*x66 + 0.5*x78 - x79 =L= 0;

e12..    13*i7 + 0.5*x69 + 0.5*x80 - x81 =L= 13;

e13..  - 8.54*i9 + 0.5*x66 + 0.5*x82 - x83 =L= 0;

e14..    13*i9 + 0.5*x69 + 0.5*x84 - x85 =L= 13;

e15..  - 8.54*i11 - x46 + 0.5*x66 + 0.5*x86 =L= 0;

e16..    13*i11 - x47 + 0.5*x69 + 0.5*x87 =L= 13;

e17..  - 8.54*i13 + 0.5*x67 + 0.5*x72 - x88 =L= 0;

e18..    13*i13 + 0.5*x70 + 0.5*x74 - x89 =L= 13;

e19..  - 8.54*i15 - x48 + 0.5*x67 + 0.5*x76 =L= 0;

e20..    13*i15 - x49 + 0.5*x70 + 0.5*x77 =L= 13;

e21..  - 8.54*i17 + 0.5*x67 + 0.5*x78 - x90 =L= 0;

e22..    13*i17 + 0.5*x70 + 0.5*x80 - x91 =L= 13;

e23..  - 8.54*i19 + 0.5*x67 + 0.5*x82 - x92 =L= 0;

e24..    13*i19 + 0.5*x70 + 0.5*x84 - x93 =L= 13;

e25..  - 8.54*i21 - x50 + 0.5*x67 + 0.5*x86 =L= 0;

e26..    13*i21 - x51 + 0.5*x70 + 0.5*x87 =L= 13;

e27..  - 8.54*i23 - x52 + 0.5*x72 + 0.5*x76 =L= 0;

e28..    13*i23 - x53 + 0.5*x74 + 0.5*x77 =L= 13;

e29..  - 8.54*i25 + 0.5*x72 + 0.5*x78 - x94 =L= 0;

e30..    13*i25 + 0.5*x74 + 0.5*x80 - x95 =L= 13;

e31..  - 8.54*i27 + 0.5*x72 + 0.5*x82 - x96 =L= 0;

e32..    13*i27 + 0.5*x74 + 0.5*x84 - x97 =L= 13;

e33..  - 8.54*i29 - x54 + 0.5*x72 + 0.5*x86 =L= 0;

e34..    13*i29 - x55 + 0.5*x74 + 0.5*x87 =L= 13;

e35..  - 8.54*i31 - x56 + 0.5*x76 + 0.5*x78 =L= 0;

e36..    13*i31 - x57 + 0.5*x77 + 0.5*x80 =L= 13;

e37..  - 8.54*i33 + 0.5*x76 + 0.5*x82 - x98 =L= 0;

e38..    13*i33 + 0.5*x77 + 0.5*x84 - x99 =L= 13;

e39..  - 8.54*i35 + 0.5*x76 + 0.5*x86 - x100 =L= 0;

e40..    13*i35 + 0.5*x77 + 0.5*x87 - x101 =L= 13;

e41..  - 8.54*i37 + 0.5*x78 + 0.5*x82 - x102 =L= 0;

e42..    13*i37 + 0.5*x80 + 0.5*x84 - x103 =L= 13;

e43..  - 8.54*i39 - x58 + 0.5*x78 + 0.5*x86 =L= 0;

e44..    13*i39 - x59 + 0.5*x80 + 0.5*x87 =L= 13;

e45..  - 8.54*i41 - x60 + 0.5*x82 + 0.5*x86 =L= 0;

e46..    13*i41 - x61 + 0.5*x84 + 0.5*x87 =L= 13;

e47..  - 0.353557*x66 - 0.176775*x69 =L= -2;

e48..  - 0.176775*x66 - 0.353556*x69 =L= -2;

e49..  - 0.353557*x67 - 0.176775*x70 =L= -2;

e50..  - 0.176775*x67 - 0.353556*x70 =L= -2;

e51..  - 0.353557*x72 - 0.176775*x74 =L= -2;

e52..  - 0.176775*x72 - 0.353556*x74 =L= -2;

e53..  - 0.235705*x76 - 0.11785*x77 =L= -2;

e54..  - 0.117851*x76 - 0.235703*x77 =L= -2;

e55..  - 0.471409*x78 - 0.2357*x80 =L= -2;

e56..  - 0.235705*x78 - 0.4714*x80 =L= -2;

e57..  - 0.471409*x82 - 0.2357*x84 =L= -2;

e58..  - 0.235705*x82 - 0.4714*x84 =L= -2;

e59..  - 0.471409*x86 - 0.2357*x87 =L= -2;

e60..  - 0.235705*x86 - 0.4714*x87 =L= -2;

e61..    x62 + 0.5*x66 =L= 8.54;

e62..  - x62 + 0.5*x66 =L= 0;

e63..    x65 + 0.5*x69 =L= 13;

e64..  - x65 + 0.5*x69 =L= 0;

e65..    x63 + 0.5*x67 =L= 8.54;

e66..  - x63 + 0.5*x67 =L= 0;

e67..    x64 + 0.5*x70 =L= 13;

e68..  - x64 + 0.5*x70 =L= 0;

e69..    0.5*x72 + x104 =L= 8.54;

e70..    0.5*x72 - x104 =L= 0;

e71..    0.5*x74 + x105 =L= 13;

e72..    0.5*x74 - x105 =L= 0;

e73..    0.5*x76 + x106 =L= 8.54;

e74..    0.5*x76 - x106 =L= 0;

e75..    0.5*x77 + x107 =L= 13;

e76..    0.5*x77 - x107 =L= 0;

e77..    0.5*x78 + x108 =L= 8.54;

e78..    0.5*x78 - x108 =L= 0;

e79..    0.5*x80 + x109 =L= 13;

e80..    0.5*x80 - x109 =L= 0;

e81..    0.5*x82 + x110 =L= 8.54;

e82..    0.5*x82 - x110 =L= 0;

e83..    0.5*x84 + x111 =L= 13;

e84..    0.5*x84 - x111 =L= 0;

e85..    0.5*x86 + x112 =L= 8.54;

e86..    0.5*x86 - x112 =L= 0;

e87..    0.5*x87 + x113 =L= 13;

e88..    0.5*x87 - x113 =L= 0;

e89..    x62 - x63 - x68 =L= 0;

e90..  - x62 + x63 - x68 =L= 0;

e91..  - x64 + x65 - x71 =L= 0;

e92..    x64 - x65 - x71 =L= 0;

e93..  - 8.54*i1 - 8.54*i2 - x62 + x63 + 0.5*x66 + 0.5*x67 =L= 0;

e94..  - 8.54*i1 + 8.54*i2 + x62 - x63 + 0.5*x66 + 0.5*x67 =L= 8.54;

e95..    13*i1 - 13*i2 + x64 - x65 + 0.5*x69 + 0.5*x70 =L= 13;

e96..    13*i1 + 13*i2 - x64 + x65 + 0.5*x69 + 0.5*x70 =L= 26;

e97..    x62 - x73 - x104 =L= 0;

e98..  - x62 - x73 + x104 =L= 0;

e99..    x65 - x75 - x105 =L= 0;

e100..  - x65 - x75 + x105 =L= 0;

e101..  - 8.54*i3 - 8.54*i4 - x62 + 0.5*x66 + 0.5*x72 + x104 =L= 0;

e102..  - 8.54*i3 + 8.54*i4 + x62 + 0.5*x66 + 0.5*x72 - x104 =L= 8.54;

e103..    13*i3 - 13*i4 - x65 + 0.5*x69 + 0.5*x74 + x105 =L= 13;

e104..    13*i3 + 13*i4 + x65 + 0.5*x69 + 0.5*x74 - x105 =L= 26;

e105..  - x44 + x62 - x106 =L= 0;

e106..  - x44 - x62 + x106 =L= 0;

e107..  - x45 + x65 - x107 =L= 0;

e108..  - x45 - x65 + x107 =L= 0;

e109..  - 8.54*i5 - 8.54*i6 - x62 + 0.5*x66 + 0.5*x76 + x106 =L= 0;

e110..  - 8.54*i5 + 8.54*i6 + x62 + 0.5*x66 + 0.5*x76 - x106 =L= 8.54;

e111..    13*i5 - 13*i6 - x65 + 0.5*x69 + 0.5*x77 + x107 =L= 13;

e112..    13*i5 + 13*i6 + x65 + 0.5*x69 + 0.5*x77 - x107 =L= 26;

e113..    x62 - x79 - x108 =L= 0;

e114..  - x62 - x79 + x108 =L= 0;

e115..    x65 - x81 - x109 =L= 0;

e116..  - x65 - x81 + x109 =L= 0;

e117..  - 8.54*i7 - 8.54*i8 - x62 + 0.5*x66 + 0.5*x78 + x108 =L= 0;

e118..  - 8.54*i7 + 8.54*i8 + x62 + 0.5*x66 + 0.5*x78 - x108 =L= 8.54;

e119..    13*i7 - 13*i8 - x65 + 0.5*x69 + 0.5*x80 + x109 =L= 13;

e120..    13*i7 + 13*i8 + x65 + 0.5*x69 + 0.5*x80 - x109 =L= 26;

e121..    x62 - x83 - x110 =L= 0;

e122..  - x62 - x83 + x110 =L= 0;

e123..    x65 - x85 - x111 =L= 0;

e124..  - x65 - x85 + x111 =L= 0;

e125..  - 8.54*i9 - 8.54*i10 - x62 + 0.5*x66 + 0.5*x82 + x110 =L= 0;

e126..  - 8.54*i9 + 8.54*i10 + x62 + 0.5*x66 + 0.5*x82 - x110 =L= 8.54;

e127..    13*i9 - 13*i10 - x65 + 0.5*x69 + 0.5*x84 + x111 =L= 13;

e128..    13*i9 + 13*i10 + x65 + 0.5*x69 + 0.5*x84 - x111 =L= 26;

e129..  - x46 + x62 - x112 =L= 0;

e130..  - x46 - x62 + x112 =L= 0;

e131..  - x47 + x65 - x113 =L= 0;

e132..  - x47 - x65 + x113 =L= 0;

e133..  - 8.54*i11 - 8.54*i12 - x62 + 0.5*x66 + 0.5*x86 + x112 =L= 0;

e134..  - 8.54*i11 + 8.54*i12 + x62 + 0.5*x66 + 0.5*x86 - x112 =L= 8.54;

e135..    13*i11 - 13*i12 - x65 + 0.5*x69 + 0.5*x87 + x113 =L= 13;

e136..    13*i11 + 13*i12 + x65 + 0.5*x69 + 0.5*x87 - x113 =L= 26;

e137..    x63 - x88 - x104 =L= 0;

e138..  - x63 - x88 + x104 =L= 0;

e139..    x64 - x89 - x105 =L= 0;

e140..  - x64 - x89 + x105 =L= 0;

e141..  - 8.54*i13 - 8.54*i14 - x63 + 0.5*x67 + 0.5*x72 + x104 =L= 0;

e142..  - 8.54*i13 + 8.54*i14 + x63 + 0.5*x67 + 0.5*x72 - x104 =L= 8.54;

e143..    13*i13 - 13*i14 - x64 + 0.5*x70 + 0.5*x74 + x105 =L= 13;

e144..    13*i13 + 13*i14 + x64 + 0.5*x70 + 0.5*x74 - x105 =L= 26;

e145..  - x48 + x63 - x106 =L= 0;

e146..  - x48 - x63 + x106 =L= 0;

e147..  - x49 + x64 - x107 =L= 0;

e148..  - x49 - x64 + x107 =L= 0;

e149..  - 8.54*i15 - 8.54*i16 - x63 + 0.5*x67 + 0.5*x76 + x106 =L= 0;

e150..  - 8.54*i15 + 8.54*i16 + x63 + 0.5*x67 + 0.5*x76 - x106 =L= 8.54;

e151..    13*i15 - 13*i16 - x64 + 0.5*x70 + 0.5*x77 + x107 =L= 13;

e152..    13*i15 + 13*i16 + x64 + 0.5*x70 + 0.5*x77 - x107 =L= 26;

e153..    x63 - x90 - x108 =L= 0;

e154..  - x63 - x90 + x108 =L= 0;

e155..    x64 - x91 - x109 =L= 0;

e156..  - x64 - x91 + x109 =L= 0;

e157..  - 8.54*i17 - 8.54*i18 - x63 + 0.5*x67 + 0.5*x78 + x108 =L= 0;

e158..  - 8.54*i17 + 8.54*i18 + x63 + 0.5*x67 + 0.5*x78 - x108 =L= 8.54;

e159..    13*i17 - 13*i18 - x64 + 0.5*x70 + 0.5*x80 + x109 =L= 13;

e160..    13*i17 + 13*i18 + x64 + 0.5*x70 + 0.5*x80 - x109 =L= 26;

e161..    x63 - x92 - x110 =L= 0;

e162..  - x63 - x92 + x110 =L= 0;

e163..    x64 - x93 - x111 =L= 0;

e164..  - x64 - x93 + x111 =L= 0;

e165..  - 8.54*i19 - 8.54*i20 - x63 + 0.5*x67 + 0.5*x82 + x110 =L= 0;

e166..  - 8.54*i19 + 8.54*i20 + x63 + 0.5*x67 + 0.5*x82 - x110 =L= 8.54;

e167..    13*i19 - 13*i20 - x64 + 0.5*x70 + 0.5*x84 + x111 =L= 13;

e168..    13*i19 + 13*i20 + x64 + 0.5*x70 + 0.5*x84 - x111 =L= 26;

e169..  - x50 + x63 - x112 =L= 0;

e170..  - x50 - x63 + x112 =L= 0;

e171..  - x51 + x64 - x113 =L= 0;

e172..  - x51 - x64 + x113 =L= 0;

e173..  - 8.54*i21 - 8.54*i22 - x63 + 0.5*x67 + 0.5*x86 + x112 =L= 0;

e174..  - 8.54*i21 + 8.54*i22 + x63 + 0.5*x67 + 0.5*x86 - x112 =L= 8.54;

e175..    13*i21 - 13*i22 - x64 + 0.5*x70 + 0.5*x87 + x113 =L= 13;

e176..    13*i21 + 13*i22 + x64 + 0.5*x70 + 0.5*x87 - x113 =L= 26;

e177..  - x52 + x104 - x106 =L= 0;

e178..  - x52 - x104 + x106 =L= 0;

e179..  - x53 + x105 - x107 =L= 0;

e180..  - x53 - x105 + x107 =L= 0;

e181..  - 8.54*i23 - 8.54*i24 + 0.5*x72 + 0.5*x76 - x104 + x106 =L= 0;

e182..  - 8.54*i23 + 8.54*i24 + 0.5*x72 + 0.5*x76 + x104 - x106 =L= 8.54;

e183..    13*i23 - 13*i24 + 0.5*x74 + 0.5*x77 - x105 + x107 =L= 13;

e184..    13*i23 + 13*i24 + 0.5*x74 + 0.5*x77 + x105 - x107 =L= 26;

e185..  - x94 + x104 - x108 =L= 0;

e186..  - x94 - x104 + x108 =L= 0;

e187..  - x95 + x105 - x109 =L= 0;

e188..  - x95 - x105 + x109 =L= 0;

e189..  - 8.54*i25 - 8.54*i26 + 0.5*x72 + 0.5*x78 - x104 + x108 =L= 0;

e190..  - 8.54*i25 + 8.54*i26 + 0.5*x72 + 0.5*x78 + x104 - x108 =L= 8.54;

e191..    13*i25 - 13*i26 + 0.5*x74 + 0.5*x80 - x105 + x109 =L= 13;

e192..    13*i25 + 13*i26 + 0.5*x74 + 0.5*x80 + x105 - x109 =L= 26;

e193..  - x96 + x104 - x110 =L= 0;

e194..  - x96 - x104 + x110 =L= 0;

e195..  - x97 + x105 - x111 =L= 0;

e196..  - x97 - x105 + x111 =L= 0;

e197..  - 8.54*i27 - 8.54*i28 + 0.5*x72 + 0.5*x82 - x104 + x110 =L= 0;

e198..  - 8.54*i27 + 8.54*i28 + 0.5*x72 + 0.5*x82 + x104 - x110 =L= 8.54;

e199..    13*i27 - 13*i28 + 0.5*x74 + 0.5*x84 - x105 + x111 =L= 13;

e200..    13*i27 + 13*i28 + 0.5*x74 + 0.5*x84 + x105 - x111 =L= 26;

e201..  - x54 + x104 - x112 =L= 0;

e202..  - x54 - x104 + x112 =L= 0;

e203..  - x55 + x105 - x113 =L= 0;

e204..  - x55 - x105 + x113 =L= 0;

e205..  - 8.54*i29 - 8.54*i30 + 0.5*x72 + 0.5*x86 - x104 + x112 =L= 0;

e206..  - 8.54*i29 + 8.54*i30 + 0.5*x72 + 0.5*x86 + x104 - x112 =L= 8.54;

e207..    13*i29 - 13*i30 + 0.5*x74 + 0.5*x87 - x105 + x113 =L= 13;

e208..    13*i29 + 13*i30 + 0.5*x74 + 0.5*x87 + x105 - x113 =L= 26;

e209..  - x56 + x106 - x108 =L= 0;

e210..  - x56 - x106 + x108 =L= 0;

e211..  - x57 + x107 - x109 =L= 0;

e212..  - x57 - x107 + x109 =L= 0;

e213..  - 8.54*i31 - 8.54*i32 + 0.5*x76 + 0.5*x78 - x106 + x108 =L= 0;

e214..  - 8.54*i31 + 8.54*i32 + 0.5*x76 + 0.5*x78 + x106 - x108 =L= 8.54;

e215..    13*i31 - 13*i32 + 0.5*x77 + 0.5*x80 - x107 + x109 =L= 13;

e216..    13*i31 + 13*i32 + 0.5*x77 + 0.5*x80 + 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*x76 + 0.5*x82 - x106 + x110 =L= 0;

e222..  - 8.54*i33 + 8.54*i34 + 0.5*x76 + 0.5*x82 + x106 - x110 =L= 8.54;

e223..    13*i33 - 13*i34 + 0.5*x77 + 0.5*x84 - x107 + x111 =L= 13;

e224..    13*i33 + 13*i34 + 0.5*x77 + 0.5*x84 + 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*x76 + 0.5*x86 - x106 + x112 =L= 0;

e230..  - 8.54*i35 + 8.54*i36 + 0.5*x76 + 0.5*x86 + x106 - x112 =L= 8.54;

e231..    13*i35 - 13*i36 + 0.5*x77 + 0.5*x87 - x107 + x113 =L= 13;

e232..    13*i35 + 13*i36 + 0.5*x77 + 0.5*x87 + x107 - x113 =L= 26;

e233..  - x102 + x108 - x110 =L= 0;

e234..  - x102 - x108 + x110 =L= 0;

e235..  - x103 + x109 - x111 =L= 0;

e236..  - x103 - x109 + x111 =L= 0;

e237..  - 8.54*i37 - 8.54*i38 + 0.5*x78 + 0.5*x82 - x108 + x110 =L= 0;

e238..  - 8.54*i37 + 8.54*i38 + 0.5*x78 + 0.5*x82 + x108 - x110 =L= 8.54;

e239..    13*i37 - 13*i38 + 0.5*x80 + 0.5*x84 - x109 + x111 =L= 13;

e240..    13*i37 + 13*i38 + 0.5*x80 + 0.5*x84 + x109 - x111 =L= 26;

e241..  - x58 + x108 - x112 =L= 0;

e242..  - x58 - x108 + x112 =L= 0;

e243..  - x59 + x109 - x113 =L= 0;

e244..  - x59 - x109 + x113 =L= 0;

e245..  - 8.54*i39 - 8.54*i40 + 0.5*x78 + 0.5*x86 - x108 + x112 =L= 0;

e246..  - 8.54*i39 + 8.54*i40 + 0.5*x78 + 0.5*x86 + x108 - x112 =L= 8.54;

e247..    13*i39 - 13*i40 + 0.5*x80 + 0.5*x87 - x109 + x113 =L= 13;

e248..    13*i39 + 13*i40 + 0.5*x80 + 0.5*x87 + x109 - x113 =L= 26;

e249..  - x60 + x110 - x112 =L= 0;

e250..  - x60 - x110 + x112 =L= 0;

e251..  - x61 + x111 - x113 =L= 0;

e252..  - x61 - x111 + x113 =L= 0;

e253..  - 8.54*i41 - 8.54*i42 + 0.5*x82 + 0.5*x86 - x110 + x112 =L= 0;

e254..  - 8.54*i41 + 8.54*i42 + 0.5*x82 + 0.5*x86 + x110 - x112 =L= 8.54;

e255..    13*i41 - 13*i42 + 0.5*x84 + 0.5*x87 - x111 + x113 =L= 13;

e256..    13*i41 + 13*i42 + 0.5*x84 + 0.5*x87 + x111 - x113 =L= 26;

e257.. 16/x66 - x69 =L= 0;

e258.. 16/x69 - x66 =L= 0;

e259.. 16/x67 - x70 =L= 0;

e260.. 16/x70 - x67 =L= 0;

e261.. 16/x72 - x74 =L= 0;

e262.. 16/x74 - x72 =L= 0;

e263.. 36/x76 - x77 =L= 0;

e264.. 36/x77 - x76 =L= 0;

e265.. 9/x78 - x80 =L= 0;

e266.. 9/x80 - x78 =L= 0;

e267.. 9/x82 - x84 =L= 0;

e268.. 9/x84 - x82 =L= 0;

e269.. 9/x86 - x87 =L= 0;

e270.. 9/x87 - x86 =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;
x66.lo = 2.8284; x66.up = 5.6569;
x67.lo = 2.8284; x67.up = 5.6569;
x69.lo = 2.8284; x69.up = 5.6569;
x70.lo = 2.8284; x70.up = 5.6569;
x72.lo = 2.8284; x72.up = 5.6569;
x74.lo = 2.8284; x74.up = 5.6569;
x76.lo = 4.2426; x76.up = 8.4853;
x77.lo = 4.2426; x77.up = 8.4853;
x78.lo = 2.1213; x78.up = 4.2426;
x80.lo = 2.1213; x80.up = 4.2426;
x82.lo = 2.1213; x82.up = 4.2426;
x84.lo = 2.1213; x84.up = 4.2426;
x86.lo = 2.1213; x86.up = 4.2426;
x87.lo = 2.1213; x87.up = 4.2426;

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: 2024-11-25 Git hash: de62f3e5
Imprint / Privacy Policy / License: CC-BY 4.0