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Instance syn15hfsg

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Equivalent perspective reformulation of syn15.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
853.28472920 p1 ( gdx sol )
(infeas: 1e-15)
Other points (infeas > 1e-08)  
Dual Bounds
853.28472920 (ALPHAECP)
853.28502380 (ANTIGONE)
853.28499290 (BARON)
853.28472920 (BONMIN)
853.28507850 (COUENNE)
853.28472930 (LINDO)
853.28482220 (SCIP)
853.28477360 (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 121
#Binary Variables 15
#Integer Variables 0
#Nonlinear Variables 31
#Nonlinear Binary Variables 10
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 22
#Nonlinear Nonzeros in Objective 0
#Constraints 181
#Linear Constraints 170
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 11
Operands in Gen. Nonlin. Functions div log mul
Constraints curvature convex
#Nonzeros in Jacobian 393
#Nonlinear Nonzeros in Jacobian 33
#Nonzeros in (Upper-Left) Hessian of Lagrangian 63
#Nonzeros in Diagonal of Hessian of Lagrangian 21
#Blocks in Hessian of Lagrangian 10
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 3.1
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-03
Maximal coefficient 5.0000e+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
*        182       85       20       77        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        122      107       15        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        416      383       33        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,b108,b109,b110,b111,b112,b113,b114,b115
          ,b116,b117,b118,b119,b120,b121,b122;

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;

Binary Variables  b108,b109,b110,b111,b112,b113,b114,b115,b116,b117,b118,b119
          ,b120,b121,b122;

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;


e1..    objvar - 5*x8 - 500*x26 - 350*x27 - 200*x38 - 250*x39 - 200*x40
      - 200*x41 + 5*b108 + 8*b109 + 6*b110 + 10*b111 + 6*b112 + 7*b113 + 4*b114
      + 5*b115 + 2*b116 + 4*b117 + 3*b118 + 7*b119 + 3*b120 + 2*b121 + 4*b122
      =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.. (x46/(0.001 + 0.999*b108) - log(1 + x42/(0.001 + 0.999*b108)))*(0.001 + 
      0.999*b108) =L= 0;

e13..    x43 =E= 0;

e14..    x47 =E= 0;

e15..    x3 - x42 - x43 =E= 0;

e16..    x5 - x46 - x47 =E= 0;

e17..    x42 - 10*b108 =L= 0;

e18..    x43 + 10*b108 =L= 10;

e19..    x46 - 2.39789527279837*b108 =L= 0;

e20..    x47 + 2.39789527279837*b108 =L= 2.39789527279837;

e21.. (x48/(0.001 + 0.999*b109) - 1.2*log(1 + x44/(0.001 + 0.999*b109)))*(0.001
       + 0.999*b109) =L= 0;

e22..    x45 =E= 0;

e23..    x49 =E= 0;

e24..    x4 - x44 - x45 =E= 0;

e25..    x6 - x48 - x49 =E= 0;

e26..    x44 - 10*b109 =L= 0;

e27..    x45 + 10*b109 =L= 10;

e28..    x48 - 2.87747432735804*b109 =L= 0;

e29..    x49 + 2.87747432735804*b109 =L= 2.87747432735804;

e30..  - 0.75*x50 + x58 =E= 0;

e31..    x51 =E= 0;

e32..    x59 =E= 0;

e33..    x10 - x50 - x51 =E= 0;

e34..    x14 - x58 - x59 =E= 0;

e35..    x50 - 2.87747432735804*b110 =L= 0;

e36..    x51 + 2.87747432735804*b110 =L= 2.87747432735804;

e37..    x58 - 2.15810574551853*b110 =L= 0;

e38..    x59 + 2.15810574551853*b110 =L= 2.15810574551853;

e39.. (x60/(0.001 + 0.999*b111) - 1.5*log(1 + x52/(0.001 + 0.999*b111)))*(0.001
       + 0.999*b111) =L= 0;

e40..    x53 =E= 0;

e41..    x62 =E= 0;

e42..    x11 - x52 - x53 =E= 0;

e43..    x15 - x60 - x62 =E= 0;

e44..    x52 - 2.87747432735804*b111 =L= 0;

e45..    x53 + 2.87747432735804*b111 =L= 2.87747432735804;

e46..    x60 - 2.03277599268042*b111 =L= 0;

e47..    x62 + 2.03277599268042*b111 =L= 2.03277599268042;

e48..  - x54 + x64 =E= 0;

e49..  - 0.5*x56 + x64 =E= 0;

e50..    x55 =E= 0;

e51..    x57 =E= 0;

e52..    x65 =E= 0;

e53..    x12 - x54 - x55 =E= 0;

e54..    x13 - x56 - x57 =E= 0;

e55..    x16 - x64 - x65 =E= 0;

e56..    x54 - 2.87747432735804*b112 =L= 0;

e57..    x55 + 2.87747432735804*b112 =L= 2.87747432735804;

e58..    x56 - 7*b112 =L= 0;

e59..    x57 + 7*b112 =L= 7;

e60..    x64 - 3.5*b112 =L= 0;

e61..    x65 + 3.5*b112 =L= 3.5;

e62.. (x76/(0.001 + 0.999*b113) - 1.25*log(1 + x66/(0.001 + 0.999*b113)))*(
      0.001 + 0.999*b113) =L= 0;

e63..    x67 =E= 0;

e64..    x78 =E= 0;

e65..    x17 - x66 - x67 =E= 0;

e66..    x22 - x76 - x78 =E= 0;

e67..    x66 - 2.15810574551853*b113 =L= 0;

e68..    x67 + 2.15810574551853*b113 =L= 2.15810574551853;

e69..    x76 - 1.43746550029693*b113 =L= 0;

e70..    x78 + 1.43746550029693*b113 =L= 1.43746550029693;

e71.. (x80/(0.001 + 0.999*b114) - 0.9*log(1 + x68/(0.001 + 0.999*b114)))*(0.001
       + 0.999*b114) =L= 0;

e72..    x69 =E= 0;

e73..    x82 =E= 0;

e74..    x18 - x68 - x69 =E= 0;

e75..    x23 - x80 - x82 =E= 0;

e76..    x68 - 2.15810574551853*b114 =L= 0;

e77..    x69 + 2.15810574551853*b114 =L= 2.15810574551853;

e78..    x80 - 1.03497516021379*b114 =L= 0;

e79..    x82 + 1.03497516021379*b114 =L= 1.03497516021379;

e80.. (x84/(0.001 + 0.999*b115) - log(1 + x61/(0.001 + 0.999*b115)))*(0.001 + 
      0.999*b115) =L= 0;

e81..    x63 =E= 0;

e82..    x85 =E= 0;

e83..    x15 - x61 - x63 =E= 0;

e84..    x24 - x84 - x85 =E= 0;

e85..    x61 - 2.03277599268042*b115 =L= 0;

e86..    x63 + 2.03277599268042*b115 =L= 2.03277599268042;

e87..    x84 - 1.10947836929589*b115 =L= 0;

e88..    x85 + 1.10947836929589*b115 =L= 1.10947836929589;

e89..  - 0.9*x70 + x86 =E= 0;

e90..    x71 =E= 0;

e91..    x87 =E= 0;

e92..    x19 - x70 - x71 =E= 0;

e93..    x25 - x86 - x87 =E= 0;

e94..    x70 - 3.5*b116 =L= 0;

e95..    x71 + 3.5*b116 =L= 3.5;

e96..    x86 - 3.15*b116 =L= 0;

e97..    x87 + 3.15*b116 =L= 3.15;

e98..  - 0.6*x72 + x88 =E= 0;

e99..    x73 =E= 0;

e100..    x89 =E= 0;

e101..    x20 - x72 - x73 =E= 0;

e102..    x26 - x88 - x89 =E= 0;

e103..    x72 - 3.5*b117 =L= 0;

e104..    x73 + 3.5*b117 =L= 3.5;

e105..    x88 - 2.1*b117 =L= 0;

e106..    x89 + 2.1*b117 =L= 2.1;

e107.. (x90/(0.001 + 0.999*b118) - 1.1*log(1 + x74/(0.001 + 0.999*b118)))*(
       0.001 + 0.999*b118) =L= 0;

e108..    x75 =E= 0;

e109..    x91 =E= 0;

e110..    x21 - x74 - x75 =E= 0;

e111..    x27 - x90 - x91 =E= 0;

e112..    x74 - 3.5*b118 =L= 0;

e113..    x75 + 3.5*b118 =L= 3.5;

e114..    x90 - 1.6544851364539*b118 =L= 0;

e115..    x91 + 1.6544851364539*b118 =L= 1.6544851364539;

e116..  - 0.9*x77 + x100 =E= 0;

e117..  - x96 + x100 =E= 0;

e118..    x79 =E= 0;

e119..    x97 =E= 0;

e120..    x101 =E= 0;

e121..    x22 - x77 - x79 =E= 0;

e122..    x30 - x96 - x97 =E= 0;

e123..    x38 - x100 - x101 =E= 0;

e124..    x77 - 1.43746550029693*b119 =L= 0;

e125..    x79 + 1.43746550029693*b119 =L= 1.43746550029693;

e126..    x96 - 5*b119 =L= 0;

e127..    x97 + 5*b119 =L= 5;

e128..    x100 - 5*b119 =L= 0;

e129..    x101 + 5*b119 =L= 5;

e130.. (x102/(0.001 + 0.999*b120) - log(1 + x81/(0.001 + 0.999*b120)))*(0.001
        + 0.999*b120) =L= 0;

e131..    x83 =E= 0;

e132..    x103 =E= 0;

e133..    x23 - x81 - x83 =E= 0;

e134..    x39 - x102 - x103 =E= 0;

e135..    x81 - 1.03497516021379*b120 =L= 0;

e136..    x83 + 1.03497516021379*b120 =L= 1.03497516021379;

e137..    x102 - 0.710483612536911*b120 =L= 0;

e138..    x103 + 0.710483612536911*b120 =L= 0.710483612536911;

e139.. (x104/(0.001 + 0.999*b121) - 0.7*log(1 + x92/(0.001 + 0.999*b121)))*(
       0.001 + 0.999*b121) =L= 0;

e140..    x93 =E= 0;

e141..    x105 =E= 0;

e142..    x28 - x92 - x93 =E= 0;

e143..    x40 - x104 - x105 =E= 0;

e144..    x92 - 1.10947836929589*b121 =L= 0;

e145..    x93 + 1.10947836929589*b121 =L= 1.10947836929589;

e146..    x104 - 0.522508489006913*b121 =L= 0;

e147..    x105 + 0.522508489006913*b121 =L= 0.522508489006913;

e148.. (x106/(0.001 + 0.999*b122) - 0.65*log(1 + x94/(0.001 + 0.999*b122)))*(
       0.001 + 0.999*b122) =L= 0;

e149.. (x106/(0.001 + 0.999*b122) - 0.65*log(1 + x98/(0.001 + 0.999*b122)))*(
       0.001 + 0.999*b122) =L= 0;

e150..    x95 =E= 0;

e151..    x99 =E= 0;

e152..    x107 =E= 0;

e153..    x29 - x94 - x95 =E= 0;

e154..    x32 - x98 - x99 =E= 0;

e155..    x41 - x106 - x107 =E= 0;

e156..    x94 - 1.10947836929589*b122 =L= 0;

e157..    x95 + 1.10947836929589*b122 =L= 1.10947836929589;

e158..    x98 - 8.15*b122 =L= 0;

e159..    x99 + 8.15*b122 =L= 8.15;

e160..    x106 - 1.43894002153683*b122 =L= 0;

e161..    x107 + 1.43894002153683*b122 =L= 1.43894002153683;

e162..    b108 + b109 =E= 1;

e163..  - b110 + b113 + b114 =G= 0;

e164..  - b113 + b119 =G= 0;

e165..  - b114 + b120 =G= 0;

e166..  - b111 + b115 =G= 0;

e167..  - b115 + b121 + b122 =G= 0;

e168..  - b112 + b116 + b117 + b118 =G= 0;

e169..  - b116 + b122 =G= 0;

e170..    b108 + b109 - b110 =G= 0;

e171..    b108 + b109 - b111 =G= 0;

e172..    b108 + b109 - b112 =G= 0;

e173..    b110 - b113 =G= 0;

e174..    b110 - b114 =G= 0;

e175..    b111 - b115 =G= 0;

e176..    b112 - b116 =G= 0;

e177..    b112 - b117 =G= 0;

e178..    b112 - b118 =G= 0;

e179..    b113 - b119 =G= 0;

e180..    b114 - b120 =G= 0;

e181..    b115 - b121 =G= 0;

e182..    b115 - b122 =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: 2022-04-26 Git hash: de668763
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