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Removed Instance syn20h

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
924.26342450 p1 ( gdx sol )
(infeas: 3e-16)
Other points (infeas > 1e-08)  
Dual Bounds
924.73989400 (ALPHAECP)
2445.56520300 (ANTIGONE)
924.26342650 (BARON)
924.26342510 (BONMIN)
924.26361690 (COUENNE)
924.26342450 (LINDO)
924.26363330 (SCIP)
924.26435400 (SHOT)
References Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339.
Türkay, Metin and Grossmann, I E, Logic-based MINLP Algorithms for optimal synthesis of process networks, Computers and Chemical Engineering, 20:8, 1996, 959-978.
Source Syn20H.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Removed from library 16 Feb 2022
Removed because Superseded by syn20hfsg.
Problem type MBNLP
#Variables 151
#Binary Variables 20
#Integer Variables 0
#Nonlinear Variables 40
#Nonlinear Binary Variables 13
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 0
#Constraints 233
#Linear Constraints 219
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 14
Operands in Gen. Nonlin. Functions div log mul
Constraints curvature convex
#Nonzeros in Jacobian 503
#Nonlinear Nonzeros in Jacobian 42
#Nonzeros in (Upper-Left) Hessian of Lagrangian 81
#Nonzeros in Diagonal of Hessian of Lagrangian 27
#Blocks in Hessian of Lagrangian 13
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 3.076923
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-06
Maximal coefficient 7.0000e+02
Infeasibility of initial point 1
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
*        234      107       27      100        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        152      132       20        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        534      492       42        0
*
*  Solve m using MINLP maximizing objvar;


Variables  objvar,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
          ,x129,x130,x131,x132,b133,b134,b135,b136,b137,b138,b139,b140,b141
          ,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152;

Positive Variables  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,x129,x130,x131,x132;

Binary Variables  b133,b134,b135,b136,b137,b138,b139,b140,b141,b142,b143,b144
          ,b145,b146,b147,b148,b149,b150,b151,b152;

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;


e1..    objvar - 5*x8 - 200*x38 - 250*x39 - 200*x40 - 700*x41 - 400*x42
      - 500*x43 - 400*x44 - 600*x45 - 700*x46 + 5*b133 + 8*b134 + 6*b135
      + 10*b136 + 6*b137 + 7*b138 + 4*b139 + 5*b140 + 2*b141 + 4*b142 + 3*b143
      + 7*b144 + 3*b145 + 2*b146 + 4*b147 + 2*b148 + 3*b149 + 5*b150 + 2*b151
      + 8*b152 =E= 0;

e2..    x2 - x3 - x4 =E= 0;

e3..  - x5 - x6 + x7 =E= 0;

e4..    x7 - x8 - x9 =E= 0;

e5..    x9 - x10 - x11 - x12 =E= 0;

e6..    x14 - x17 - x18 =E= 0;

e7..    x16 - x19 - x20 - x21 =E= 0;

e8..    x24 - x28 - x29 =E= 0;

e9..  - x25 - x31 + x32 =E= 0;

e10..    x26 - x33 - x34 =E= 0;

e11..    x27 - x35 - x36 - x37 =E= 0;

e12.. (x51/(1e-6 + b133) - log(1 + x47/(1e-6 + b133)))*(1e-6 + b133) =L= 0;

e13..    x48 =E= 0;

e14..    x52 =E= 0;

e15..    x3 - x47 - x48 =E= 0;

e16..    x5 - x51 - x52 =E= 0;

e17..    x47 - 10*b133 =L= 0;

e18..    x48 + 10*b133 =L= 10;

e19..    x51 - 2.39789527279837*b133 =L= 0;

e20..    x52 + 2.39789527279837*b133 =L= 2.39789527279837;

e21.. (x53/(1e-6 + b134) - 1.2*log(1 + x49/(1e-6 + b134)))*(1e-6 + b134) =L= 0;

e22..    x50 =E= 0;

e23..    x54 =E= 0;

e24..    x4 - x49 - x50 =E= 0;

e25..    x6 - x53 - x54 =E= 0;

e26..    x49 - 10*b134 =L= 0;

e27..    x50 + 10*b134 =L= 10;

e28..    x53 - 2.87747432735804*b134 =L= 0;

e29..    x54 + 2.87747432735804*b134 =L= 2.87747432735804;

e30..  - 0.75*x55 + x63 =E= 0;

e31..    x56 =E= 0;

e32..    x64 =E= 0;

e33..    x10 - x55 - x56 =E= 0;

e34..    x14 - x63 - x64 =E= 0;

e35..    x55 - 2.87747432735804*b135 =L= 0;

e36..    x56 + 2.87747432735804*b135 =L= 2.87747432735804;

e37..    x63 - 2.15810574551853*b135 =L= 0;

e38..    x64 + 2.15810574551853*b135 =L= 2.15810574551853;

e39.. (x65/(1e-6 + b136) - 1.5*log(1 + x57/(1e-6 + b136)))*(1e-6 + b136) =L= 0;

e40..    x58 =E= 0;

e41..    x67 =E= 0;

e42..    x11 - x57 - x58 =E= 0;

e43..    x15 - x65 - x67 =E= 0;

e44..    x57 - 2.87747432735804*b136 =L= 0;

e45..    x58 + 2.87747432735804*b136 =L= 2.87747432735804;

e46..    x65 - 2.03277599268042*b136 =L= 0;

e47..    x67 + 2.03277599268042*b136 =L= 2.03277599268042;

e48..  - x59 + x69 =E= 0;

e49..  - 0.5*x61 + x69 =E= 0;

e50..    x60 =E= 0;

e51..    x62 =E= 0;

e52..    x70 =E= 0;

e53..    x12 - x59 - x60 =E= 0;

e54..    x13 - x61 - x62 =E= 0;

e55..    x16 - x69 - x70 =E= 0;

e56..    x59 - 2.87747432735804*b137 =L= 0;

e57..    x60 + 2.87747432735804*b137 =L= 2.87747432735804;

e58..    x61 - 7*b137 =L= 0;

e59..    x62 + 7*b137 =L= 7;

e60..    x69 - 3.5*b137 =L= 0;

e61..    x70 + 3.5*b137 =L= 3.5;

e62.. (x81/(1e-6 + b138) - 1.25*log(1 + x71/(1e-6 + b138)))*(1e-6 + b138) =L= 0
      ;

e63..    x72 =E= 0;

e64..    x83 =E= 0;

e65..    x17 - x71 - x72 =E= 0;

e66..    x22 - x81 - x83 =E= 0;

e67..    x71 - 2.15810574551853*b138 =L= 0;

e68..    x72 + 2.15810574551853*b138 =L= 2.15810574551853;

e69..    x81 - 1.43746550029693*b138 =L= 0;

e70..    x83 + 1.43746550029693*b138 =L= 1.43746550029693;

e71.. (x85/(1e-6 + b139) - 0.9*log(1 + x73/(1e-6 + b139)))*(1e-6 + b139) =L= 0;

e72..    x74 =E= 0;

e73..    x87 =E= 0;

e74..    x18 - x73 - x74 =E= 0;

e75..    x23 - x85 - x87 =E= 0;

e76..    x73 - 2.15810574551853*b139 =L= 0;

e77..    x74 + 2.15810574551853*b139 =L= 2.15810574551853;

e78..    x85 - 1.03497516021379*b139 =L= 0;

e79..    x87 + 1.03497516021379*b139 =L= 1.03497516021379;

e80.. (x89/(1e-6 + b140) - log(1 + x66/(1e-6 + b140)))*(1e-6 + b140) =L= 0;

e81..    x68 =E= 0;

e82..    x90 =E= 0;

e83..    x15 - x66 - x68 =E= 0;

e84..    x24 - x89 - x90 =E= 0;

e85..    x66 - 2.03277599268042*b140 =L= 0;

e86..    x68 + 2.03277599268042*b140 =L= 2.03277599268042;

e87..    x89 - 1.10947836929589*b140 =L= 0;

e88..    x90 + 1.10947836929589*b140 =L= 1.10947836929589;

e89..  - 0.9*x75 + x91 =E= 0;

e90..    x76 =E= 0;

e91..    x92 =E= 0;

e92..    x19 - x75 - x76 =E= 0;

e93..    x25 - x91 - x92 =E= 0;

e94..    x75 - 3.5*b141 =L= 0;

e95..    x76 + 3.5*b141 =L= 3.5;

e96..    x91 - 3.15*b141 =L= 0;

e97..    x92 + 3.15*b141 =L= 3.15;

e98..  - 0.6*x77 + x93 =E= 0;

e99..    x78 =E= 0;

e100..    x94 =E= 0;

e101..    x20 - x77 - x78 =E= 0;

e102..    x26 - x93 - x94 =E= 0;

e103..    x77 - 3.5*b142 =L= 0;

e104..    x78 + 3.5*b142 =L= 3.5;

e105..    x93 - 2.1*b142 =L= 0;

e106..    x94 + 2.1*b142 =L= 2.1;

e107.. (x95/(1e-6 + b143) - 1.1*log(1 + x79/(1e-6 + b143)))*(1e-6 + b143) =L= 0
       ;

e108..    x80 =E= 0;

e109..    x96 =E= 0;

e110..    x21 - x79 - x80 =E= 0;

e111..    x27 - x95 - x96 =E= 0;

e112..    x79 - 3.5*b143 =L= 0;

e113..    x80 + 3.5*b143 =L= 3.5;

e114..    x95 - 1.6544851364539*b143 =L= 0;

e115..    x96 + 1.6544851364539*b143 =L= 1.6544851364539;

e116..  - 0.9*x82 + x115 =E= 0;

e117..  - x101 + x115 =E= 0;

e118..    x84 =E= 0;

e119..    x102 =E= 0;

e120..    x116 =E= 0;

e121..    x22 - x82 - x84 =E= 0;

e122..    x30 - x101 - x102 =E= 0;

e123..    x38 - x115 - x116 =E= 0;

e124..    x82 - 1.43746550029693*b144 =L= 0;

e125..    x84 + 1.43746550029693*b144 =L= 1.43746550029693;

e126..    x101 - 5*b144 =L= 0;

e127..    x102 + 5*b144 =L= 5;

e128..    x115 - 5*b144 =L= 0;

e129..    x116 + 5*b144 =L= 5;

e130.. (x117/(1e-6 + b145) - log(1 + x86/(1e-6 + b145)))*(1e-6 + b145) =L= 0;

e131..    x88 =E= 0;

e132..    x118 =E= 0;

e133..    x23 - x86 - x88 =E= 0;

e134..    x39 - x117 - x118 =E= 0;

e135..    x86 - 1.03497516021379*b145 =L= 0;

e136..    x88 + 1.03497516021379*b145 =L= 1.03497516021379;

e137..    x117 - 0.710483612536911*b145 =L= 0;

e138..    x118 + 0.710483612536911*b145 =L= 0.710483612536911;

e139.. (x119/(1e-6 + b146) - 0.7*log(1 + x97/(1e-6 + b146)))*(1e-6 + b146)
        =L= 0;

e140..    x98 =E= 0;

e141..    x120 =E= 0;

e142..    x28 - x97 - x98 =E= 0;

e143..    x40 - x119 - x120 =E= 0;

e144..    x97 - 1.10947836929589*b146 =L= 0;

e145..    x98 + 1.10947836929589*b146 =L= 1.10947836929589;

e146..    x119 - 0.522508489006913*b146 =L= 0;

e147..    x120 + 0.522508489006913*b146 =L= 0.522508489006913;

e148.. (x121/(1e-6 + b147) - 0.65*log(1 + x99/(1e-6 + b147)))*(1e-6 + b147)
        =L= 0;

e149.. (x121/(1e-6 + b147) - 0.65*log(1 + x103/(1e-6 + b147)))*(1e-6 + b147)
        =L= 0;

e150..    x100 =E= 0;

e151..    x104 =E= 0;

e152..    x122 =E= 0;

e153..    x29 - x99 - x100 =E= 0;

e154..    x32 - x103 - x104 =E= 0;

e155..    x41 - x121 - x122 =E= 0;

e156..    x99 - 1.10947836929589*b147 =L= 0;

e157..    x100 + 1.10947836929589*b147 =L= 1.10947836929589;

e158..    x103 - 8.15*b147 =L= 0;

e159..    x104 + 8.15*b147 =L= 8.15;

e160..    x121 - 1.43894002153683*b147 =L= 0;

e161..    x122 + 1.43894002153683*b147 =L= 1.43894002153683;

e162..  - x105 + x123 =E= 0;

e163..    x106 =E= 0;

e164..    x124 =E= 0;

e165..    x33 - x105 - x106 =E= 0;

e166..    x42 - x123 - x124 =E= 0;

e167..    x105 - 2.1*b148 =L= 0;

e168..    x106 + 2.1*b148 =L= 2.1;

e169..    x123 - 2.1*b148 =L= 0;

e170..    x124 + 2.1*b148 =L= 2.1;

e171..  - x107 + x125 =E= 0;

e172..    x108 =E= 0;

e173..    x126 =E= 0;

e174..    x34 - x107 - x108 =E= 0;

e175..    x43 - x125 - x126 =E= 0;

e176..    x107 - 2.1*b149 =L= 0;

e177..    x108 + 2.1*b149 =L= 2.1;

e178..    x125 - 2.1*b149 =L= 0;

e179..    x126 + 2.1*b149 =L= 2.1;

e180.. (x127/(1e-6 + b150) - 0.75*log(1 + x109/(1e-6 + b150)))*(1e-6 + b150)
        =L= 0;

e181..    x110 =E= 0;

e182..    x128 =E= 0;

e183..    x35 - x109 - x110 =E= 0;

e184..    x44 - x127 - x128 =E= 0;

e185..    x109 - 1.6544851364539*b150 =L= 0;

e186..    x110 + 1.6544851364539*b150 =L= 1.6544851364539;

e187..    x127 - 0.732188035236726*b150 =L= 0;

e188..    x128 + 0.732188035236726*b150 =L= 0.732188035236726;

e189.. (x129/(1e-6 + b151) - 0.8*log(1 + x111/(1e-6 + b151)))*(1e-6 + b151)
        =L= 0;

e190..    x112 =E= 0;

e191..    x130 =E= 0;

e192..    x36 - x111 - x112 =E= 0;

e193..    x45 - x129 - x130 =E= 0;

e194..    x111 - 1.6544851364539*b151 =L= 0;

e195..    x112 + 1.6544851364539*b151 =L= 1.6544851364539;

e196..    x129 - 0.781000570919175*b151 =L= 0;

e197..    x130 + 0.781000570919175*b151 =L= 0.781000570919175;

e198.. (x131/(1e-6 + b152) - 0.85*log(1 + x113/(1e-6 + b152)))*(1e-6 + b152)
        =L= 0;

e199..    x114 =E= 0;

e200..    x132 =E= 0;

e201..    x37 - x113 - x114 =E= 0;

e202..    x46 - x131 - x132 =E= 0;

e203..    x113 - 1.6544851364539*b152 =L= 0;

e204..    x114 + 1.6544851364539*b152 =L= 1.6544851364539;

e205..    x131 - 0.829813106601623*b152 =L= 0;

e206..    x132 + 0.829813106601623*b152 =L= 0.829813106601623;

e207..    b133 + b134 =E= 1;

e208..  - b135 + b138 + b139 =G= 0;

e209..  - b138 + b144 =G= 0;

e210..  - b139 + b145 =G= 0;

e211..  - b136 + b140 =G= 0;

e212..  - b140 + b146 + b147 =G= 0;

e213..  - b137 + b141 + b142 + b143 =G= 0;

e214..  - b141 + b147 =G= 0;

e215..  - b142 + b148 + b149 =G= 0;

e216..  - b143 + b150 + b151 + b152 =G= 0;

e217..    b133 + b134 - b135 =G= 0;

e218..    b133 + b134 - b136 =G= 0;

e219..    b133 + b134 - b137 =G= 0;

e220..    b135 - b138 =G= 0;

e221..    b135 - b139 =G= 0;

e222..    b136 - b140 =G= 0;

e223..    b137 - b141 =G= 0;

e224..    b137 - b142 =G= 0;

e225..    b137 - b143 =G= 0;

e226..    b138 - b144 =G= 0;

e227..    b139 - b145 =G= 0;

e228..    b140 - b146 =G= 0;

e229..    b140 - b147 =G= 0;

e230..    b142 - b148 =G= 0;

e231..    b142 - b149 =G= 0;

e232..    b143 - b150 =G= 0;

e233..    b143 - b151 =G= 0;

e234..    b143 - b152 =G= 0;

* set non-default bounds
x2.up = 10;
x13.up = 7;
x30.up = 5;
x31.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% maximizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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