MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: clay0304h

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
Formats ams gms mod nl osil
Primal Bounds
40262.42384000 p1 ( gdx sol )
(infeas: 6e-14)
Dual Bounds
40262.38400000 (ALPHAECP)
7914.93695500 (ANTIGONE)
40262.42384000 (BARON)
40262.42384000 (BONMIN)
6605.00000000 (COUENNE)
40262.42384000 (LINDO)
40262.42375000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source CLay0304H.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 176
#Binary Variables 36
#Integer Variables 0
#Nonlinear Variables 36
#Nonlinear Binary Variables 12
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 12
#Nonlinear Nonzeros in Objective 0
#Constraints 258
#Linear Constraints 210
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 48
Operands in Gen. Nonlin. Functions mul div sqr
Constraints curvature convex
#Nonzeros in Jacobian 716
#Nonlinear Nonzeros in Jacobian 144
#Nonzeros in (Upper-Left) Hessian of Lagrangian 84
#Nonzeros in Diagonal of Hessian of Lagrangian 36
#Blocks in Hessian of Lagrangian 12
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 12.5
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
*        259       43       24      192        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        177      141       36        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        729      585      144        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
          ,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
          ,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,x114,x115,x116
          ,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,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,b162,b163,b164,x165,x166,x167,x168
          ,x169,x170,x171,x172,x173,x174,x175,x176,objvar;

Positive Variables  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,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,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,x114,x115,x116,x117,x118,x119
          ,x120,x121,x122,x123,x124,x125,x126,x127,x128,x165,x166,x167,x168
          ,x169,x170,x171,x172,x173,x174,x175,x176;

Binary Variables  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,b162,b163,b164;

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;


e1..  - 300*x165 - 240*x166 - 210*x167 - 100*x168 - 150*x169 - 120*x170
      - 300*x171 - 240*x172 - 210*x173 - 100*x174 - 150*x175 - 120*x176
      + objvar =E= 0;

e2..  - x1 + x2 + x165 =G= 0;

e3..  - x1 + x3 + x166 =G= 0;

e4..  - x1 + x4 + x167 =G= 0;

e5..  - x2 + x3 + x168 =G= 0;

e6..  - x2 + x4 + x169 =G= 0;

e7..  - x3 + x4 + x170 =G= 0;

e8..    x1 - x2 + x165 =G= 0;

e9..    x1 - x3 + x166 =G= 0;

e10..    x1 - x4 + x167 =G= 0;

e11..    x2 - x3 + x168 =G= 0;

e12..    x2 - x4 + x169 =G= 0;

e13..    x3 - x4 + x170 =G= 0;

e14..  - x5 + x6 + x171 =G= 0;

e15..  - x5 + x7 + x172 =G= 0;

e16..  - x5 + x8 + x173 =G= 0;

e17..  - x6 + x7 + x174 =G= 0;

e18..  - x6 + x8 + x175 =G= 0;

e19..  - x7 + x8 + x176 =G= 0;

e20..    x5 - x6 + x171 =G= 0;

e21..    x5 - x7 + x172 =G= 0;

e22..    x5 - x8 + x173 =G= 0;

e23..    x6 - x7 + x174 =G= 0;

e24..    x6 - x8 + x175 =G= 0;

e25..    x7 - x8 + x176 =G= 0;

e26..    x1 - x9 - x12 - x15 - x18 =E= 0;

e27..    x1 - x10 - x13 - x16 - x19 =E= 0;

e28..    x1 - x11 - x14 - x17 - x20 =E= 0;

e29..    x2 - x21 - x24 - x27 - x30 =E= 0;

e30..    x2 - x22 - x25 - x28 - x31 =E= 0;

e31..    x2 - x23 - x26 - x29 - x32 =E= 0;

e32..    x3 - x33 - x36 - x39 - x42 =E= 0;

e33..    x3 - x34 - x37 - x40 - x43 =E= 0;

e34..    x3 - x35 - x38 - x41 - x44 =E= 0;

e35..    x4 - x45 - x48 - x51 - x54 =E= 0;

e36..    x4 - x46 - x49 - x52 - x55 =E= 0;

e37..    x4 - x47 - x50 - x53 - x56 =E= 0;

e38..    x5 - x57 - x60 - x63 - x66 =E= 0;

e39..    x5 - x58 - x61 - x64 - x67 =E= 0;

e40..    x5 - x59 - x62 - x65 - x68 =E= 0;

e41..    x6 - x69 - x72 - x75 - x78 =E= 0;

e42..    x6 - x70 - x73 - x76 - x79 =E= 0;

e43..    x6 - x71 - x74 - x77 - x80 =E= 0;

e44..    x7 - x81 - x84 - x87 - x90 =E= 0;

e45..    x7 - x82 - x85 - x88 - x91 =E= 0;

e46..    x7 - x83 - x86 - x89 - x92 =E= 0;

e47..    x8 - x93 - x96 - x99 - x102 =E= 0;

e48..    x8 - x94 - x97 - x100 - x103 =E= 0;

e49..    x8 - x95 - x98 - x101 - x104 =E= 0;

e50..    x9 - 52.5*b129 =L= 0;

e51..    x10 - 52.5*b130 =L= 0;

e52..    x11 - 52.5*b131 =L= 0;

e53..    x12 - 52.5*b135 =L= 0;

e54..    x13 - 52.5*b136 =L= 0;

e55..    x14 - 52.5*b137 =L= 0;

e56..    x15 - 52.5*b141 =L= 0;

e57..    x16 - 52.5*b142 =L= 0;

e58..    x17 - 52.5*b143 =L= 0;

e59..    x18 - 52.5*b147 =L= 0;

e60..    x19 - 52.5*b148 =L= 0;

e61..    x20 - 52.5*b149 =L= 0;

e62..    x21 - 52.5*b129 =L= 0;

e63..    x22 - 51.5*b132 =L= 0;

e64..    x23 - 51.5*b133 =L= 0;

e65..    x24 - 52.5*b135 =L= 0;

e66..    x25 - 51.5*b138 =L= 0;

e67..    x26 - 51.5*b139 =L= 0;

e68..    x27 - 52.5*b141 =L= 0;

e69..    x28 - 51.5*b144 =L= 0;

e70..    x29 - 51.5*b145 =L= 0;

e71..    x30 - 52.5*b147 =L= 0;

e72..    x31 - 51.5*b150 =L= 0;

e73..    x32 - 51.5*b151 =L= 0;

e74..    x33 - 52.5*b130 =L= 0;

e75..    x34 - 51.5*b132 =L= 0;

e76..    x35 - 53.5*b134 =L= 0;

e77..    x36 - 52.5*b136 =L= 0;

e78..    x37 - 51.5*b138 =L= 0;

e79..    x38 - 53.5*b140 =L= 0;

e80..    x39 - 52.5*b142 =L= 0;

e81..    x40 - 51.5*b144 =L= 0;

e82..    x41 - 53.5*b146 =L= 0;

e83..    x42 - 52.5*b148 =L= 0;

e84..    x43 - 51.5*b150 =L= 0;

e85..    x44 - 53.5*b152 =L= 0;

e86..    x45 - 52.5*b131 =L= 0;

e87..    x46 - 51.5*b133 =L= 0;

e88..    x47 - 53.5*b134 =L= 0;

e89..    x48 - 52.5*b137 =L= 0;

e90..    x49 - 51.5*b139 =L= 0;

e91..    x50 - 53.5*b140 =L= 0;

e92..    x51 - 52.5*b143 =L= 0;

e93..    x52 - 51.5*b145 =L= 0;

e94..    x53 - 53.5*b146 =L= 0;

e95..    x54 - 52.5*b149 =L= 0;

e96..    x55 - 51.5*b151 =L= 0;

e97..    x56 - 53.5*b152 =L= 0;

e98..    x57 - 82*b129 =L= 0;

e99..    x58 - 82*b130 =L= 0;

e100..    x59 - 82*b131 =L= 0;

e101..    x60 - 82*b135 =L= 0;

e102..    x61 - 82*b136 =L= 0;

e103..    x62 - 82*b137 =L= 0;

e104..    x63 - 82*b141 =L= 0;

e105..    x64 - 82*b142 =L= 0;

e106..    x65 - 82*b143 =L= 0;

e107..    x66 - 82*b147 =L= 0;

e108..    x67 - 82*b148 =L= 0;

e109..    x68 - 82*b149 =L= 0;

e110..    x69 - 82*b129 =L= 0;

e111..    x70 - 82.5*b132 =L= 0;

e112..    x71 - 82.5*b133 =L= 0;

e113..    x72 - 82*b135 =L= 0;

e114..    x73 - 82.5*b138 =L= 0;

e115..    x74 - 82.5*b139 =L= 0;

e116..    x75 - 82*b141 =L= 0;

e117..    x76 - 82.5*b144 =L= 0;

e118..    x77 - 82.5*b145 =L= 0;

e119..    x78 - 82*b147 =L= 0;

e120..    x79 - 82.5*b150 =L= 0;

e121..    x80 - 82.5*b151 =L= 0;

e122..    x81 - 82*b130 =L= 0;

e123..    x82 - 82.5*b132 =L= 0;

e124..    x83 - 83.5*b134 =L= 0;

e125..    x84 - 82*b136 =L= 0;

e126..    x85 - 82.5*b138 =L= 0;

e127..    x86 - 83.5*b140 =L= 0;

e128..    x87 - 82*b142 =L= 0;

e129..    x88 - 82.5*b144 =L= 0;

e130..    x89 - 83.5*b146 =L= 0;

e131..    x90 - 82*b148 =L= 0;

e132..    x91 - 82.5*b150 =L= 0;

e133..    x92 - 83.5*b152 =L= 0;

e134..    x93 - 82*b131 =L= 0;

e135..    x94 - 82.5*b133 =L= 0;

e136..    x95 - 83.5*b134 =L= 0;

e137..    x96 - 82*b137 =L= 0;

e138..    x97 - 82.5*b139 =L= 0;

e139..    x98 - 83.5*b140 =L= 0;

e140..    x99 - 82*b143 =L= 0;

e141..    x100 - 82.5*b145 =L= 0;

e142..    x101 - 83.5*b146 =L= 0;

e143..    x102 - 82*b149 =L= 0;

e144..    x103 - 82.5*b151 =L= 0;

e145..    x104 - 83.5*b152 =L= 0;

e146..    x9 - x21 + 6*b129 =L= 0;

e147..    x10 - x33 + 4*b130 =L= 0;

e148..    x11 - x45 + 3.5*b131 =L= 0;

e149..    x22 - x34 + 5*b132 =L= 0;

e150..    x23 - x46 + 4.5*b133 =L= 0;

e151..    x35 - x47 + 2.5*b134 =L= 0;

e152..  - x12 + x24 + 6*b135 =L= 0;

e153..  - x13 + x36 + 4*b136 =L= 0;

e154..  - x14 + x48 + 3.5*b137 =L= 0;

e155..  - x25 + x37 + 5*b138 =L= 0;

e156..  - x26 + x49 + 4.5*b139 =L= 0;

e157..  - x38 + x50 + 2.5*b140 =L= 0;

e158..    x63 - x75 + 5.5*b141 =L= 0;

e159..    x64 - x87 + 4.5*b142 =L= 0;

e160..    x65 - x99 + 4.5*b143 =L= 0;

e161..    x76 - x88 + 4*b144 =L= 0;

e162..    x77 - x100 + 4*b145 =L= 0;

e163..    x89 - x101 + 3*b146 =L= 0;

e164..  - x66 + x78 + 5.5*b147 =L= 0;

e165..  - x67 + x90 + 4.5*b148 =L= 0;

e166..  - x68 + x102 + 4.5*b149 =L= 0;

e167..  - x79 + x91 + 4*b150 =L= 0;

e168..  - x80 + x103 + 4*b151 =L= 0;

e169..  - x92 + x104 + 3*b152 =L= 0;

e170..    b129 + b135 + b141 + b147 =E= 1;

e171..    b130 + b136 + b142 + b148 =E= 1;

e172..    b131 + b137 + b143 + b149 =E= 1;

e173..    b132 + b138 + b144 + b150 =E= 1;

e174..    b133 + b139 + b145 + b151 =E= 1;

e175..    b134 + b140 + b146 + b152 =E= 1;

e176..    x1 - x105 - x109 - x113 =E= 0;

e177..    x2 - x106 - x110 - x114 =E= 0;

e178..    x3 - x107 - x111 - x115 =E= 0;

e179..    x4 - x108 - x112 - x116 =E= 0;

e180..    x5 - x117 - x121 - x125 =E= 0;

e181..    x6 - x118 - x122 - x126 =E= 0;

e182..    x7 - x119 - x123 - x127 =E= 0;

e183..    x8 - x120 - x124 - x128 =E= 0;

e184..    x105 - 18.5*b153 =L= 0;

e185..    x106 - 17.5*b154 =L= 0;

e186..    x107 - 19.5*b155 =L= 0;

e187..    x108 - 20*b156 =L= 0;

e188..    x109 - 52.5*b157 =L= 0;

e189..    x110 - 51.5*b158 =L= 0;

e190..    x111 - 53.5*b159 =L= 0;

e191..    x112 - 54*b160 =L= 0;

e192..    x113 - 31.5*b161 =L= 0;

e193..    x114 - 30.5*b162 =L= 0;

e194..    x115 - 32.5*b163 =L= 0;

e195..    x116 - 33*b164 =L= 0;

e196..    x117 - 13*b153 =L= 0;

e197..    x118 - 13.5*b154 =L= 0;

e198..    x119 - 14.5*b155 =L= 0;

e199..    x120 - 14.5*b156 =L= 0;

e200..    x121 - 82*b157 =L= 0;

e201..    x122 - 82.5*b158 =L= 0;

e202..    x123 - 83.5*b159 =L= 0;

e203..    x124 - 83.5*b160 =L= 0;

e204..    x125 - 51*b161 =L= 0;

e205..    x126 - 51.5*b162 =L= 0;

e206..    x127 - 52.5*b163 =L= 0;

e207..    x128 - 52.5*b164 =L= 0;

e208.. (sqr(x105/(1e-6 + b153)) - 35*x105/(1e-6 + b153) + 306.25*b153 + sqr(
       x117/(1e-6 + b153)) - 14*x117/(1e-6 + b153) + 49*b153 - 36*b153)*(1e-6
        + b153) =L= 0;

e209.. (sqr(x106/(1e-6 + b154)) - 37*x106/(1e-6 + b154) + 342.25*b154 + sqr(
       x118/(1e-6 + b154)) - 15*x118/(1e-6 + b154) + 56.25*b154 - 36*b154)*(
       1e-6 + b154) =L= 0;

e210.. (sqr(x107/(1e-6 + b155)) - 33*x107/(1e-6 + b155) + 272.25*b155 + sqr(
       x119/(1e-6 + b155)) - 17*x119/(1e-6 + b155) + 72.25*b155 - 36*b155)*(
       1e-6 + b155) =L= 0;

e211.. (sqr(x108/(1e-6 + b156)) - 32*x108/(1e-6 + b156) + 256*b156 + sqr(x120/(
       1e-6 + b156)) - 17*x120/(1e-6 + b156) + 72.25*b156 - 36*b156)*(1e-6 + 
       b156) =L= 0;

e212.. (sqr(x109/(1e-6 + b157)) - 105*x109/(1e-6 + b157) + 2756.25*b157 + sqr(
       x121/(1e-6 + b157)) - 154*x121/(1e-6 + b157) + 5929*b157 - 25*b157)*(
       1e-6 + b157) =L= 0;

e213.. (sqr(x110/(1e-6 + b158)) - 107*x110/(1e-6 + b158) + 2862.25*b158 + sqr(
       x122/(1e-6 + b158)) - 155*x122/(1e-6 + b158) + 6006.25*b158 - 25*b158)*(
       1e-6 + b158) =L= 0;

e214.. (sqr(x111/(1e-6 + b159)) - 103*x111/(1e-6 + b159) + 2652.25*b159 + sqr(
       x123/(1e-6 + b159)) - 157*x123/(1e-6 + b159) + 6162.25*b159 - 25*b159)*(
       1e-6 + b159) =L= 0;

e215.. (sqr(x112/(1e-6 + b160)) - 102*x112/(1e-6 + b160) + 2601*b160 + sqr(x124
       /(1e-6 + b160)) - 157*x124/(1e-6 + b160) + 6162.25*b160 - 25*b160)*(1e-6
        + b160) =L= 0;

e216.. (sqr(x113/(1e-6 + b161)) - 65*x113/(1e-6 + b161) + 1056.25*b161 + sqr(
       x125/(1e-6 + b161)) - 94*x125/(1e-6 + b161) + 2209*b161 - 16*b161)*(1e-6
        + b161) =L= 0;

e217.. (sqr(x114/(1e-6 + b162)) - 67*x114/(1e-6 + b162) + 1122.25*b162 + sqr(
       x126/(1e-6 + b162)) - 95*x126/(1e-6 + b162) + 2256.25*b162 - 16*b162)*(
       1e-6 + b162) =L= 0;

e218.. (sqr(x115/(1e-6 + b163)) - 63*x115/(1e-6 + b163) + 992.25*b163 + sqr(
       x127/(1e-6 + b163)) - 97*x127/(1e-6 + b163) + 2352.25*b163 - 16*b163)*(
       1e-6 + b163) =L= 0;

e219.. (sqr(x116/(1e-6 + b164)) - 62*x116/(1e-6 + b164) + 961*b164 + sqr(x128/(
       1e-6 + b164)) - 97*x128/(1e-6 + b164) + 2352.25*b164 - 16*b164)*(1e-6 + 
       b164) =L= 0;

e220.. (sqr(x105/(1e-6 + b153)) - 35*x105/(1e-6 + b153) + 306.25*b153 + sqr(
       x117/(1e-6 + b153)) - 26*x117/(1e-6 + b153) + 169*b153 - 36*b153)*(1e-6
        + b153) =L= 0;

e221.. (sqr(x106/(1e-6 + b154)) - 37*x106/(1e-6 + b154) + 342.25*b154 + sqr(
       x118/(1e-6 + b154)) - 25*x118/(1e-6 + b154) + 156.25*b154 - 36*b154)*(
       1e-6 + b154) =L= 0;

e222.. (sqr(x107/(1e-6 + b155)) - 33*x107/(1e-6 + b155) + 272.25*b155 + sqr(
       x119/(1e-6 + b155)) - 23*x119/(1e-6 + b155) + 132.25*b155 - 36*b155)*(
       1e-6 + b155) =L= 0;

e223.. (sqr(x108/(1e-6 + b156)) - 32*x108/(1e-6 + b156) + 256*b156 + sqr(x120/(
       1e-6 + b156)) - 23*x120/(1e-6 + b156) + 132.25*b156 - 36*b156)*(1e-6 + 
       b156) =L= 0;

e224.. (sqr(x109/(1e-6 + b157)) - 105*x109/(1e-6 + b157) + 2756.25*b157 + sqr(
       x121/(1e-6 + b157)) - 166*x121/(1e-6 + b157) + 6889*b157 - 25*b157)*(
       1e-6 + b157) =L= 0;

e225.. (sqr(x110/(1e-6 + b158)) - 107*x110/(1e-6 + b158) + 2862.25*b158 + sqr(
       x122/(1e-6 + b158)) - 165*x122/(1e-6 + b158) + 6806.25*b158 - 25*b158)*(
       1e-6 + b158) =L= 0;

e226.. (sqr(x111/(1e-6 + b159)) - 103*x111/(1e-6 + b159) + 2652.25*b159 + sqr(
       x123/(1e-6 + b159)) - 163*x123/(1e-6 + b159) + 6642.25*b159 - 25*b159)*(
       1e-6 + b159) =L= 0;

e227.. (sqr(x112/(1e-6 + b160)) - 102*x112/(1e-6 + b160) + 2601*b160 + sqr(x124
       /(1e-6 + b160)) - 163*x124/(1e-6 + b160) + 6642.25*b160 - 25*b160)*(1e-6
        + b160) =L= 0;

e228.. (sqr(x113/(1e-6 + b161)) - 65*x113/(1e-6 + b161) + 1056.25*b161 + sqr(
       x125/(1e-6 + b161)) - 106*x125/(1e-6 + b161) + 2809*b161 - 16*b161)*(
       1e-6 + b161) =L= 0;

e229.. (sqr(x114/(1e-6 + b162)) - 67*x114/(1e-6 + b162) + 1122.25*b162 + sqr(
       x126/(1e-6 + b162)) - 105*x126/(1e-6 + b162) + 2756.25*b162 - 16*b162)*(
       1e-6 + b162) =L= 0;

e230.. (sqr(x115/(1e-6 + b163)) - 63*x115/(1e-6 + b163) + 992.25*b163 + sqr(
       x127/(1e-6 + b163)) - 103*x127/(1e-6 + b163) + 2652.25*b163 - 16*b163)*(
       1e-6 + b163) =L= 0;

e231.. (sqr(x116/(1e-6 + b164)) - 62*x116/(1e-6 + b164) + 961*b164 + sqr(x128/(
       1e-6 + b164)) - 103*x128/(1e-6 + b164) + 2652.25*b164 - 16*b164)*(1e-6
        + b164) =L= 0;

e232.. (sqr(x105/(1e-6 + b153)) - 25*x105/(1e-6 + b153) + 156.25*b153 + sqr(
       x117/(1e-6 + b153)) - 14*x117/(1e-6 + b153) + 49*b153 - 36*b153)*(1e-6
        + b153) =L= 0;

e233.. (sqr(x106/(1e-6 + b154)) - 23*x106/(1e-6 + b154) + 132.25*b154 + sqr(
       x118/(1e-6 + b154)) - 15*x118/(1e-6 + b154) + 56.25*b154 - 36*b154)*(
       1e-6 + b154) =L= 0;

e234.. (sqr(x107/(1e-6 + b155)) - 27*x107/(1e-6 + b155) + 182.25*b155 + sqr(
       x119/(1e-6 + b155)) - 17*x119/(1e-6 + b155) + 72.25*b155 - 36*b155)*(
       1e-6 + b155) =L= 0;

e235.. (sqr(x108/(1e-6 + b156)) - 28*x108/(1e-6 + b156) + 196*b156 + sqr(x120/(
       1e-6 + b156)) - 17*x120/(1e-6 + b156) + 72.25*b156 - 36*b156)*(1e-6 + 
       b156) =L= 0;

e236.. (sqr(x109/(1e-6 + b157)) - 95*x109/(1e-6 + b157) + 2256.25*b157 + sqr(
       x121/(1e-6 + b157)) - 154*x121/(1e-6 + b157) + 5929*b157 - 25*b157)*(
       1e-6 + b157) =L= 0;

e237.. (sqr(x110/(1e-6 + b158)) - 93*x110/(1e-6 + b158) + 2162.25*b158 + sqr(
       x122/(1e-6 + b158)) - 155*x122/(1e-6 + b158) + 6006.25*b158 - 25*b158)*(
       1e-6 + b158) =L= 0;

e238.. (sqr(x111/(1e-6 + b159)) - 97*x111/(1e-6 + b159) + 2352.25*b159 + sqr(
       x123/(1e-6 + b159)) - 157*x123/(1e-6 + b159) + 6162.25*b159 - 25*b159)*(
       1e-6 + b159) =L= 0;

e239.. (sqr(x112/(1e-6 + b160)) - 98*x112/(1e-6 + b160) + 2401*b160 + sqr(x124/
       (1e-6 + b160)) - 157*x124/(1e-6 + b160) + 6162.25*b160 - 25*b160)*(1e-6
        + b160) =L= 0;

e240.. (sqr(x113/(1e-6 + b161)) - 55*x113/(1e-6 + b161) + 756.25*b161 + sqr(
       x125/(1e-6 + b161)) - 94*x125/(1e-6 + b161) + 2209*b161 - 16*b161)*(1e-6
        + b161) =L= 0;

e241.. (sqr(x114/(1e-6 + b162)) - 53*x114/(1e-6 + b162) + 702.25*b162 + sqr(
       x126/(1e-6 + b162)) - 95*x126/(1e-6 + b162) + 2256.25*b162 - 16*b162)*(
       1e-6 + b162) =L= 0;

e242.. (sqr(x115/(1e-6 + b163)) - 57*x115/(1e-6 + b163) + 812.25*b163 + sqr(
       x127/(1e-6 + b163)) - 97*x127/(1e-6 + b163) + 2352.25*b163 - 16*b163)*(
       1e-6 + b163) =L= 0;

e243.. (sqr(x116/(1e-6 + b164)) - 58*x116/(1e-6 + b164) + 841*b164 + sqr(x128/(
       1e-6 + b164)) - 97*x128/(1e-6 + b164) + 2352.25*b164 - 16*b164)*(1e-6 + 
       b164) =L= 0;

e244.. (sqr(x105/(1e-6 + b153)) - 25*x105/(1e-6 + b153) + 156.25*b153 + sqr(
       x117/(1e-6 + b153)) - 26*x117/(1e-6 + b153) + 169*b153 - 36*b153)*(1e-6
        + b153) =L= 0;

e245.. (sqr(x106/(1e-6 + b154)) - 23*x106/(1e-6 + b154) + 132.25*b154 + sqr(
       x118/(1e-6 + b154)) - 25*x118/(1e-6 + b154) + 156.25*b154 - 36*b154)*(
       1e-6 + b154) =L= 0;

e246.. (sqr(x107/(1e-6 + b155)) - 27*x107/(1e-6 + b155) + 182.25*b155 + sqr(
       x119/(1e-6 + b155)) - 23*x119/(1e-6 + b155) + 132.25*b155 - 36*b155)*(
       1e-6 + b155) =L= 0;

e247.. (sqr(x108/(1e-6 + b156)) - 28*x108/(1e-6 + b156) + 196*b156 + sqr(x120/(
       1e-6 + b156)) - 23*x120/(1e-6 + b156) + 132.25*b156 - 36*b156)*(1e-6 + 
       b156) =L= 0;

e248.. (sqr(x109/(1e-6 + b157)) - 95*x109/(1e-6 + b157) + 2256.25*b157 + sqr(
       x121/(1e-6 + b157)) - 166*x121/(1e-6 + b157) + 6889*b157 - 25*b157)*(
       1e-6 + b157) =L= 0;

e249.. (sqr(x110/(1e-6 + b158)) - 93*x110/(1e-6 + b158) + 2162.25*b158 + sqr(
       x122/(1e-6 + b158)) - 165*x122/(1e-6 + b158) + 6806.25*b158 - 25*b158)*(
       1e-6 + b158) =L= 0;

e250.. (sqr(x111/(1e-6 + b159)) - 97*x111/(1e-6 + b159) + 2352.25*b159 + sqr(
       x123/(1e-6 + b159)) - 163*x123/(1e-6 + b159) + 6642.25*b159 - 25*b159)*(
       1e-6 + b159) =L= 0;

e251.. (sqr(x112/(1e-6 + b160)) - 98*x112/(1e-6 + b160) + 2401*b160 + sqr(x124/
       (1e-6 + b160)) - 163*x124/(1e-6 + b160) + 6642.25*b160 - 25*b160)*(1e-6
        + b160) =L= 0;

e252.. (sqr(x113/(1e-6 + b161)) - 55*x113/(1e-6 + b161) + 756.25*b161 + sqr(
       x125/(1e-6 + b161)) - 106*x125/(1e-6 + b161) + 2809*b161 - 16*b161)*(
       1e-6 + b161) =L= 0;

e253.. (sqr(x114/(1e-6 + b162)) - 53*x114/(1e-6 + b162) + 702.25*b162 + sqr(
       x126/(1e-6 + b162)) - 105*x126/(1e-6 + b162) + 2756.25*b162 - 16*b162)*(
       1e-6 + b162) =L= 0;

e254.. (sqr(x115/(1e-6 + b163)) - 57*x115/(1e-6 + b163) + 812.25*b163 + sqr(
       x127/(1e-6 + b163)) - 103*x127/(1e-6 + b163) + 2652.25*b163 - 16*b163)*(
       1e-6 + b163) =L= 0;

e255.. (sqr(x116/(1e-6 + b164)) - 58*x116/(1e-6 + b164) + 841*b164 + sqr(x128/(
       1e-6 + b164)) - 103*x128/(1e-6 + b164) + 2652.25*b164 - 16*b164)*(1e-6
        + b164) =L= 0;

e256..    b153 + b157 + b161 =E= 1;

e257..    b154 + b158 + b162 =E= 1;

e258..    b155 + b159 + b163 =E= 1;

e259..    b156 + b160 + b164 =E= 1;

* set non-default bounds
x1.lo = 11.5; x1.up = 52.5;
x2.lo = 12.5; x2.up = 51.5;
x3.lo = 10.5; x3.up = 53.5;
x4.lo = 10; x4.up = 54;
x5.lo = 7; x5.up = 82;
x6.lo = 6.5; x6.up = 82.5;
x7.lo = 5.5; x7.up = 83.5;
x8.lo = 5.5; x8.up = 83.5;

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: 2018-08-07 Git hash: fccdb193
Imprint / Privacy Policy