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Instance syn05m02hfsg

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Equivalent perspective reformulation of syn05m02.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
3032.73538600 p1 ( gdx sol )
(infeas: 2e-14)
Other points (infeas > 1e-08)  
Dual Bounds
3033.09077000 (ALPHAECP)
3032.73552200 (ANTIGONE)
3032.73545500 (BARON)
3032.73538600 (BONMIN)
3032.73742600 (COUENNE)
3032.73538600 (LINDO)
3032.73576100 (SCIP)
3032.73591100 (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 104
#Binary Variables 20
#Integer Variables 0
#Nonlinear Variables 18
#Nonlinear Binary Variables 6
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 22
#Nonlinear Nonzeros in Objective 0
#Constraints 151
#Linear Constraints 145
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 6
Operands in Gen. Nonlin. Functions div log mul
Constraints curvature convex
#Nonzeros in Jacobian 329
#Nonlinear Nonzeros in Jacobian 18
#Nonzeros in (Upper-Left) Hessian of Lagrangian 36
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 6
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
*        152       71        6       75        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        105       85       20        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        352      334       18        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,b86
          ,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102
          ,b103,b104,b105;

Positive Variables  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;

Binary Variables  b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100
          ,b101,b102,b103,b104,b105;

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;


e1..    objvar + x12 + x13 - 5*x24 - 10*x25 + 2*x34 + x35 - 80*x36 - 90*x37
      - 285*x38 - 390*x39 - 290*x40 - 405*x41 + 5*b96 + 4*b97 + 8*b98 + 7*b99
      + 6*b100 + 9*b101 + 10*b102 + 9*b103 + 6*b104 + 10*b105 =E= 0;

e2..    x12 - x14 - x16 =E= 0;

e3..    x13 - x15 - x17 =E= 0;

e4..  - x18 - x20 + x22 =E= 0;

e5..  - x19 - x21 + x23 =E= 0;

e6..    x22 - x24 - x26 =E= 0;

e7..    x23 - x25 - x27 =E= 0;

e8..    x26 - x28 - x30 - x32 =E= 0;

e9..    x27 - x29 - x31 - x33 =E= 0;

e10.. (x50/(0.001 + 0.999*b86) - log(1 + x42/(0.001 + 0.999*b86)))*(0.001 + 
      0.999*b86) =L= 0;

e11.. (x51/(0.001 + 0.999*b87) - log(1 + x43/(0.001 + 0.999*b87)))*(0.001 + 
      0.999*b87) =L= 0;

e12..    x44 =E= 0;

e13..    x45 =E= 0;

e14..    x52 =E= 0;

e15..    x53 =E= 0;

e16..    x14 - x42 - x44 =E= 0;

e17..    x15 - x43 - x45 =E= 0;

e18..    x18 - x50 - x52 =E= 0;

e19..    x19 - x51 - x53 =E= 0;

e20..    x42 - 40*b86 =L= 0;

e21..    x43 - 40*b87 =L= 0;

e22..    x44 + 40*b86 =L= 40;

e23..    x45 + 40*b87 =L= 40;

e24..    x50 - 3.71357206670431*b86 =L= 0;

e25..    x51 - 3.71357206670431*b87 =L= 0;

e26..    x52 + 3.71357206670431*b86 =L= 3.71357206670431;

e27..    x53 + 3.71357206670431*b87 =L= 3.71357206670431;

e28.. (x54/(0.001 + 0.999*b88) - 1.2*log(1 + x46/(0.001 + 0.999*b88)))*(0.001
       + 0.999*b88) =L= 0;

e29.. (x55/(0.001 + 0.999*b89) - 1.2*log(1 + x47/(0.001 + 0.999*b89)))*(0.001
       + 0.999*b89) =L= 0;

e30..    x48 =E= 0;

e31..    x49 =E= 0;

e32..    x56 =E= 0;

e33..    x57 =E= 0;

e34..    x16 - x46 - x48 =E= 0;

e35..    x17 - x47 - x49 =E= 0;

e36..    x20 - x54 - x56 =E= 0;

e37..    x21 - x55 - x57 =E= 0;

e38..    x46 - 40*b88 =L= 0;

e39..    x47 - 40*b89 =L= 0;

e40..    x48 + 40*b88 =L= 40;

e41..    x49 + 40*b89 =L= 40;

e42..    x54 - 4.45628648004517*b88 =L= 0;

e43..    x55 - 4.45628648004517*b89 =L= 0;

e44..    x56 + 4.45628648004517*b88 =L= 4.45628648004517;

e45..    x57 + 4.45628648004517*b89 =L= 4.45628648004517;

e46..  - 0.75*x58 + x74 =E= 0;

e47..  - 0.75*x59 + x75 =E= 0;

e48..    x60 =E= 0;

e49..    x61 =E= 0;

e50..    x76 =E= 0;

e51..    x77 =E= 0;

e52..    x28 - x58 - x60 =E= 0;

e53..    x29 - x59 - x61 =E= 0;

e54..    x36 - x74 - x76 =E= 0;

e55..    x37 - x75 - x77 =E= 0;

e56..    x58 - 4.45628648004517*b90 =L= 0;

e57..    x59 - 4.45628648004517*b91 =L= 0;

e58..    x60 + 4.45628648004517*b90 =L= 4.45628648004517;

e59..    x61 + 4.45628648004517*b91 =L= 4.45628648004517;

e60..    x74 - 3.34221486003388*b90 =L= 0;

e61..    x75 - 3.34221486003388*b91 =L= 0;

e62..    x76 + 3.34221486003388*b90 =L= 3.34221486003388;

e63..    x77 + 3.34221486003388*b91 =L= 3.34221486003388;

e64.. (x78/(0.001 + 0.999*b92) - 1.5*log(1 + x62/(0.001 + 0.999*b92)))*(0.001
       + 0.999*b92) =L= 0;

e65.. (x79/(0.001 + 0.999*b93) - 1.5*log(1 + x63/(0.001 + 0.999*b93)))*(0.001
       + 0.999*b93) =L= 0;

e66..    x64 =E= 0;

e67..    x65 =E= 0;

e68..    x80 =E= 0;

e69..    x81 =E= 0;

e70..    x30 - x62 - x64 =E= 0;

e71..    x31 - x63 - x65 =E= 0;

e72..    x38 - x78 - x80 =E= 0;

e73..    x39 - x79 - x81 =E= 0;

e74..    x62 - 4.45628648004517*b92 =L= 0;

e75..    x63 - 4.45628648004517*b93 =L= 0;

e76..    x64 + 4.45628648004517*b92 =L= 4.45628648004517;

e77..    x65 + 4.45628648004517*b93 =L= 4.45628648004517;

e78..    x78 - 2.54515263975353*b92 =L= 0;

e79..    x79 - 2.54515263975353*b93 =L= 0;

e80..    x80 + 2.54515263975353*b92 =L= 2.54515263975353;

e81..    x81 + 2.54515263975353*b93 =L= 2.54515263975353;

e82..  - x66 + x82 =E= 0;

e83..  - x67 + x83 =E= 0;

e84..  - 0.5*x70 + x82 =E= 0;

e85..  - 0.5*x71 + x83 =E= 0;

e86..    x68 =E= 0;

e87..    x69 =E= 0;

e88..    x72 =E= 0;

e89..    x73 =E= 0;

e90..    x84 =E= 0;

e91..    x85 =E= 0;

e92..    x32 - x66 - x68 =E= 0;

e93..    x33 - x67 - x69 =E= 0;

e94..    x34 - x70 - x72 =E= 0;

e95..    x35 - x71 - x73 =E= 0;

e96..    x40 - x82 - x84 =E= 0;

e97..    x41 - x83 - x85 =E= 0;

e98..    x66 - 4.45628648004517*b94 =L= 0;

e99..    x67 - 4.45628648004517*b95 =L= 0;

e100..    x68 + 4.45628648004517*b94 =L= 4.45628648004517;

e101..    x69 + 4.45628648004517*b95 =L= 4.45628648004517;

e102..    x70 - 30*b94 =L= 0;

e103..    x71 - 30*b95 =L= 0;

e104..    x72 + 30*b94 =L= 30;

e105..    x73 + 30*b95 =L= 30;

e106..    x82 - 15*b94 =L= 0;

e107..    x83 - 15*b95 =L= 0;

e108..    x84 + 15*b94 =L= 15;

e109..    x85 + 15*b95 =L= 15;

e110..    x2 + 5*b96 =E= 0;

e111..    x3 + 4*b97 =E= 0;

e112..    x4 + 8*b98 =E= 0;

e113..    x5 + 7*b99 =E= 0;

e114..    x6 + 6*b100 =E= 0;

e115..    x7 + 9*b101 =E= 0;

e116..    x8 + 10*b102 =E= 0;

e117..    x9 + 9*b103 =E= 0;

e118..    x10 + 6*b104 =E= 0;

e119..    x11 + 10*b105 =E= 0;

e120..    b86 - b87 =L= 0;

e121..    b88 - b89 =L= 0;

e122..    b90 - b91 =L= 0;

e123..    b92 - b93 =L= 0;

e124..    b94 - b95 =L= 0;

e125..    b96 + b97 =L= 1;

e126..    b96 + b97 =L= 1;

e127..    b98 + b99 =L= 1;

e128..    b98 + b99 =L= 1;

e129..    b100 + b101 =L= 1;

e130..    b100 + b101 =L= 1;

e131..    b102 + b103 =L= 1;

e132..    b102 + b103 =L= 1;

e133..    b104 + b105 =L= 1;

e134..    b104 + b105 =L= 1;

e135..    b86 - b96 =L= 0;

e136..  - b86 + b87 - b97 =L= 0;

e137..    b88 - b98 =L= 0;

e138..  - b88 + b89 - b99 =L= 0;

e139..    b90 - b100 =L= 0;

e140..  - b90 + b91 - b101 =L= 0;

e141..    b92 - b102 =L= 0;

e142..  - b92 + b93 - b103 =L= 0;

e143..    b94 - b104 =L= 0;

e144..  - b94 + b95 - b105 =L= 0;

e145..    b86 + b88 =E= 1;

e146..    b87 + b89 =E= 1;

e147..    b86 + b88 - b90 =G= 0;

e148..    b87 + b89 - b91 =G= 0;

e149..    b86 + b88 - b92 =G= 0;

e150..    b87 + b89 - b93 =G= 0;

e151..    b86 + b88 - b94 =G= 0;

e152..    b87 + b89 - b95 =G= 0;

* set non-default bounds
x12.up = 40;
x13.up = 40;
x34.up = 30;
x35.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: 2022-04-26 Git hash: de668763
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