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Instance syn05m03hfsg

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Equivalent perspective reformulation of syn05m03.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
4027.37175500 p1 ( gdx sol )
(infeas: 1e-13)
Other points (infeas > 1e-08)  
Dual Bounds
4027.89698100 (ALPHAECP)
4027.37224100 (ANTIGONE)
4027.37321900 (BARON)
4027.37175600 (BONMIN)
4027.37328500 (COUENNE)
4027.37175600 (LINDO)
4027.37214700 (SCIP)
6484.03212600 (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.
Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019.
Application Synthesis of processing system
Added to library 25 Sep 2019
Problem type MBNLP
#Variables 156
#Binary Variables 30
#Integer Variables 0
#Nonlinear Variables 27
#Nonlinear Binary Variables 9
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 33
#Nonlinear Nonzeros in Objective 0
#Constraints 249
#Linear Constraints 240
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 9
Operands in Gen. Nonlin. Functions div log mul
Constraints curvature convex
#Nonzeros in Jacobian 546
#Nonlinear Nonzeros in Jacobian 27
#Nonzeros in (Upper-Left) Hessian of Lagrangian 54
#Nonzeros in Diagonal of Hessian of Lagrangian 18
#Blocks in Hessian of Lagrangian 9
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
Minimal coefficient 1.0000e-03
Maximal coefficient 4.0500e+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
*        250      106        9      135        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        157      127       30        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        580      553       27        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,b128
          ,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;

Positive Variables  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;

Binary Variables  b128,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;

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;


e1..    objvar + x17 + x18 + x19 - 5*x35 - 10*x36 - 5*x37 + 2*x50 + x51 + 2*x52
      - 80*x53 - 90*x54 - 120*x55 - 285*x56 - 390*x57 - 350*x58 - 290*x59
      - 405*x60 - 190*x61 + 5*b143 + 4*b144 + 6*b145 + 8*b146 + 7*b147 + 6*b148
      + 6*b149 + 9*b150 + 4*b151 + 10*b152 + 9*b153 + 5*b154 + 6*b155 + 10*b156
      + 6*b157 =E= 0;

e2..    x17 - x20 - x23 =E= 0;

e3..    x18 - x21 - x24 =E= 0;

e4..    x19 - x22 - x25 =E= 0;

e5..  - x26 - x29 + x32 =E= 0;

e6..  - x27 - x30 + x33 =E= 0;

e7..  - x28 - x31 + x34 =E= 0;

e8..    x32 - x35 - x38 =E= 0;

e9..    x33 - x36 - x39 =E= 0;

e10..    x34 - x37 - x40 =E= 0;

e11..    x38 - x41 - x44 - x47 =E= 0;

e12..    x39 - x42 - x45 - x48 =E= 0;

e13..    x40 - x43 - x46 - x49 =E= 0;

e14.. (x74/(0.001 + 0.999*b128) - log(1 + x62/(0.001 + 0.999*b128)))*(0.001 + 
      0.999*b128) =L= 0;

e15.. (x75/(0.001 + 0.999*b129) - log(1 + x63/(0.001 + 0.999*b129)))*(0.001 + 
      0.999*b129) =L= 0;

e16.. (x76/(0.001 + 0.999*b130) - log(1 + x64/(0.001 + 0.999*b130)))*(0.001 + 
      0.999*b130) =L= 0;

e17..    x65 =E= 0;

e18..    x66 =E= 0;

e19..    x67 =E= 0;

e20..    x77 =E= 0;

e21..    x78 =E= 0;

e22..    x79 =E= 0;

e23..    x20 - x62 - x65 =E= 0;

e24..    x21 - x63 - x66 =E= 0;

e25..    x22 - x64 - x67 =E= 0;

e26..    x26 - x74 - x77 =E= 0;

e27..    x27 - x75 - x78 =E= 0;

e28..    x28 - x76 - x79 =E= 0;

e29..    x62 - 40*b128 =L= 0;

e30..    x63 - 40*b129 =L= 0;

e31..    x64 - 40*b130 =L= 0;

e32..    x65 + 40*b128 =L= 40;

e33..    x66 + 40*b129 =L= 40;

e34..    x67 + 40*b130 =L= 40;

e35..    x74 - 3.71357206670431*b128 =L= 0;

e36..    x75 - 3.71357206670431*b129 =L= 0;

e37..    x76 - 3.71357206670431*b130 =L= 0;

e38..    x77 + 3.71357206670431*b128 =L= 3.71357206670431;

e39..    x78 + 3.71357206670431*b129 =L= 3.71357206670431;

e40..    x79 + 3.71357206670431*b130 =L= 3.71357206670431;

e41.. (x80/(0.001 + 0.999*b131) - 1.2*log(1 + x68/(0.001 + 0.999*b131)))*(0.001
       + 0.999*b131) =L= 0;

e42.. (x81/(0.001 + 0.999*b132) - 1.2*log(1 + x69/(0.001 + 0.999*b132)))*(0.001
       + 0.999*b132) =L= 0;

e43.. (x82/(0.001 + 0.999*b133) - 1.2*log(1 + x70/(0.001 + 0.999*b133)))*(0.001
       + 0.999*b133) =L= 0;

e44..    x71 =E= 0;

e45..    x72 =E= 0;

e46..    x73 =E= 0;

e47..    x83 =E= 0;

e48..    x84 =E= 0;

e49..    x85 =E= 0;

e50..    x23 - x68 - x71 =E= 0;

e51..    x24 - x69 - x72 =E= 0;

e52..    x25 - x70 - x73 =E= 0;

e53..    x29 - x80 - x83 =E= 0;

e54..    x30 - x81 - x84 =E= 0;

e55..    x31 - x82 - x85 =E= 0;

e56..    x68 - 40*b131 =L= 0;

e57..    x69 - 40*b132 =L= 0;

e58..    x70 - 40*b133 =L= 0;

e59..    x71 + 40*b131 =L= 40;

e60..    x72 + 40*b132 =L= 40;

e61..    x73 + 40*b133 =L= 40;

e62..    x80 - 4.45628648004517*b131 =L= 0;

e63..    x81 - 4.45628648004517*b132 =L= 0;

e64..    x82 - 4.45628648004517*b133 =L= 0;

e65..    x83 + 4.45628648004517*b131 =L= 4.45628648004517;

e66..    x84 + 4.45628648004517*b132 =L= 4.45628648004517;

e67..    x85 + 4.45628648004517*b133 =L= 4.45628648004517;

e68..  - 0.75*x86 + x110 =E= 0;

e69..  - 0.75*x87 + x111 =E= 0;

e70..  - 0.75*x88 + x112 =E= 0;

e71..    x89 =E= 0;

e72..    x90 =E= 0;

e73..    x91 =E= 0;

e74..    x113 =E= 0;

e75..    x114 =E= 0;

e76..    x115 =E= 0;

e77..    x41 - x86 - x89 =E= 0;

e78..    x42 - x87 - x90 =E= 0;

e79..    x43 - x88 - x91 =E= 0;

e80..    x53 - x110 - x113 =E= 0;

e81..    x54 - x111 - x114 =E= 0;

e82..    x55 - x112 - x115 =E= 0;

e83..    x86 - 4.45628648004517*b134 =L= 0;

e84..    x87 - 4.45628648004517*b135 =L= 0;

e85..    x88 - 4.45628648004517*b136 =L= 0;

e86..    x89 + 4.45628648004517*b134 =L= 4.45628648004517;

e87..    x90 + 4.45628648004517*b135 =L= 4.45628648004517;

e88..    x91 + 4.45628648004517*b136 =L= 4.45628648004517;

e89..    x110 - 3.34221486003388*b134 =L= 0;

e90..    x111 - 3.34221486003388*b135 =L= 0;

e91..    x112 - 3.34221486003388*b136 =L= 0;

e92..    x113 + 3.34221486003388*b134 =L= 3.34221486003388;

e93..    x114 + 3.34221486003388*b135 =L= 3.34221486003388;

e94..    x115 + 3.34221486003388*b136 =L= 3.34221486003388;

e95.. (x116/(0.001 + 0.999*b137) - 1.5*log(1 + x92/(0.001 + 0.999*b137)))*(
      0.001 + 0.999*b137) =L= 0;

e96.. (x117/(0.001 + 0.999*b138) - 1.5*log(1 + x93/(0.001 + 0.999*b138)))*(
      0.001 + 0.999*b138) =L= 0;

e97.. (x118/(0.001 + 0.999*b139) - 1.5*log(1 + x94/(0.001 + 0.999*b139)))*(
      0.001 + 0.999*b139) =L= 0;

e98..    x95 =E= 0;

e99..    x96 =E= 0;

e100..    x97 =E= 0;

e101..    x119 =E= 0;

e102..    x120 =E= 0;

e103..    x121 =E= 0;

e104..    x44 - x92 - x95 =E= 0;

e105..    x45 - x93 - x96 =E= 0;

e106..    x46 - x94 - x97 =E= 0;

e107..    x56 - x116 - x119 =E= 0;

e108..    x57 - x117 - x120 =E= 0;

e109..    x58 - x118 - x121 =E= 0;

e110..    x92 - 4.45628648004517*b137 =L= 0;

e111..    x93 - 4.45628648004517*b138 =L= 0;

e112..    x94 - 4.45628648004517*b139 =L= 0;

e113..    x95 + 4.45628648004517*b137 =L= 4.45628648004517;

e114..    x96 + 4.45628648004517*b138 =L= 4.45628648004517;

e115..    x97 + 4.45628648004517*b139 =L= 4.45628648004517;

e116..    x116 - 2.54515263975353*b137 =L= 0;

e117..    x117 - 2.54515263975353*b138 =L= 0;

e118..    x118 - 2.54515263975353*b139 =L= 0;

e119..    x119 + 2.54515263975353*b137 =L= 2.54515263975353;

e120..    x120 + 2.54515263975353*b138 =L= 2.54515263975353;

e121..    x121 + 2.54515263975353*b139 =L= 2.54515263975353;

e122..  - x98 + x122 =E= 0;

e123..  - x99 + x123 =E= 0;

e124..  - x100 + x124 =E= 0;

e125..  - 0.5*x104 + x122 =E= 0;

e126..  - 0.5*x105 + x123 =E= 0;

e127..  - 0.5*x106 + x124 =E= 0;

e128..    x101 =E= 0;

e129..    x102 =E= 0;

e130..    x103 =E= 0;

e131..    x107 =E= 0;

e132..    x108 =E= 0;

e133..    x109 =E= 0;

e134..    x125 =E= 0;

e135..    x126 =E= 0;

e136..    x127 =E= 0;

e137..    x47 - x98 - x101 =E= 0;

e138..    x48 - x99 - x102 =E= 0;

e139..    x49 - x100 - x103 =E= 0;

e140..    x50 - x104 - x107 =E= 0;

e141..    x51 - x105 - x108 =E= 0;

e142..    x52 - x106 - x109 =E= 0;

e143..    x59 - x122 - x125 =E= 0;

e144..    x60 - x123 - x126 =E= 0;

e145..    x61 - x124 - x127 =E= 0;

e146..    x98 - 4.45628648004517*b140 =L= 0;

e147..    x99 - 4.45628648004517*b141 =L= 0;

e148..    x100 - 4.45628648004517*b142 =L= 0;

e149..    x101 + 4.45628648004517*b140 =L= 4.45628648004517;

e150..    x102 + 4.45628648004517*b141 =L= 4.45628648004517;

e151..    x103 + 4.45628648004517*b142 =L= 4.45628648004517;

e152..    x104 - 30*b140 =L= 0;

e153..    x105 - 30*b141 =L= 0;

e154..    x106 - 30*b142 =L= 0;

e155..    x107 + 30*b140 =L= 30;

e156..    x108 + 30*b141 =L= 30;

e157..    x109 + 30*b142 =L= 30;

e158..    x122 - 15*b140 =L= 0;

e159..    x123 - 15*b141 =L= 0;

e160..    x124 - 15*b142 =L= 0;

e161..    x125 + 15*b140 =L= 15;

e162..    x126 + 15*b141 =L= 15;

e163..    x127 + 15*b142 =L= 15;

e164..    x2 + 5*b143 =E= 0;

e165..    x3 + 4*b144 =E= 0;

e166..    x4 + 6*b145 =E= 0;

e167..    x5 + 8*b146 =E= 0;

e168..    x6 + 7*b147 =E= 0;

e169..    x7 + 6*b148 =E= 0;

e170..    x8 + 6*b149 =E= 0;

e171..    x9 + 9*b150 =E= 0;

e172..    x10 + 4*b151 =E= 0;

e173..    x11 + 10*b152 =E= 0;

e174..    x12 + 9*b153 =E= 0;

e175..    x13 + 5*b154 =E= 0;

e176..    x14 + 6*b155 =E= 0;

e177..    x15 + 10*b156 =E= 0;

e178..    x16 + 6*b157 =E= 0;

e179..    b128 - b129 =L= 0;

e180..    b128 - b130 =L= 0;

e181..    b129 - b130 =L= 0;

e182..    b131 - b132 =L= 0;

e183..    b131 - b133 =L= 0;

e184..    b132 - b133 =L= 0;

e185..    b134 - b135 =L= 0;

e186..    b134 - b136 =L= 0;

e187..    b135 - b136 =L= 0;

e188..    b137 - b138 =L= 0;

e189..    b137 - b139 =L= 0;

e190..    b138 - b139 =L= 0;

e191..    b140 - b141 =L= 0;

e192..    b140 - b142 =L= 0;

e193..    b141 - b142 =L= 0;

e194..    b143 + b144 =L= 1;

e195..    b143 + b145 =L= 1;

e196..    b143 + b144 =L= 1;

e197..    b144 + b145 =L= 1;

e198..    b143 + b145 =L= 1;

e199..    b144 + b145 =L= 1;

e200..    b146 + b147 =L= 1;

e201..    b146 + b148 =L= 1;

e202..    b146 + b147 =L= 1;

e203..    b147 + b148 =L= 1;

e204..    b146 + b148 =L= 1;

e205..    b147 + b148 =L= 1;

e206..    b149 + b150 =L= 1;

e207..    b149 + b151 =L= 1;

e208..    b149 + b150 =L= 1;

e209..    b150 + b151 =L= 1;

e210..    b149 + b151 =L= 1;

e211..    b150 + b151 =L= 1;

e212..    b152 + b153 =L= 1;

e213..    b152 + b154 =L= 1;

e214..    b152 + b153 =L= 1;

e215..    b153 + b154 =L= 1;

e216..    b152 + b154 =L= 1;

e217..    b153 + b154 =L= 1;

e218..    b155 + b156 =L= 1;

e219..    b155 + b157 =L= 1;

e220..    b155 + b156 =L= 1;

e221..    b156 + b157 =L= 1;

e222..    b155 + b157 =L= 1;

e223..    b156 + b157 =L= 1;

e224..    b128 - b143 =L= 0;

e225..  - b128 + b129 - b144 =L= 0;

e226..  - b128 - b129 + b130 - b145 =L= 0;

e227..    b131 - b146 =L= 0;

e228..  - b131 + b132 - b147 =L= 0;

e229..  - b131 - b132 + b133 - b148 =L= 0;

e230..    b134 - b149 =L= 0;

e231..  - b134 + b135 - b150 =L= 0;

e232..  - b134 - b135 + b136 - b151 =L= 0;

e233..    b137 - b152 =L= 0;

e234..  - b137 + b138 - b153 =L= 0;

e235..  - b137 - b138 + b139 - b154 =L= 0;

e236..    b140 - b155 =L= 0;

e237..  - b140 + b141 - b156 =L= 0;

e238..  - b140 - b141 + b142 - b157 =L= 0;

e239..    b128 + b131 =E= 1;

e240..    b129 + b132 =E= 1;

e241..    b130 + b133 =E= 1;

e242..    b128 + b131 - b134 =G= 0;

e243..    b129 + b132 - b135 =G= 0;

e244..    b130 + b133 - b136 =G= 0;

e245..    b128 + b131 - b137 =G= 0;

e246..    b129 + b132 - b138 =G= 0;

e247..    b130 + b133 - b139 =G= 0;

e248..    b128 + b131 - b140 =G= 0;

e249..    b129 + b132 - b141 =G= 0;

e250..    b130 + b133 - b142 =G= 0;

* set non-default bounds
x17.up = 40;
x18.up = 40;
x19.up = 40;
x50.up = 30;
x51.up = 30;
x52.up = 30;

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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