MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance syn05m03m

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)
4027.37175500 p1 ( gdx sol )
(infeas: 8e-14)
Other points (infeas > 1e-08)  
Dual Bounds
4027.37300000 (ALPHAECP)
4027.37220000 (ANTIGONE)
4027.37176000 (BARON)
4027.37180000 (BONMIN)
4027.37178500 (COUENNE)
4027.37175500 (LINDO)
4027.37201700 (SCIP)
4027.37198300 (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 Syn05M03M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 90
#Binary Variables 30
#Integer Variables 0
#Nonlinear Variables 9
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 33
#Nonlinear Nonzeros in Objective 0
#Constraints 174
#Linear Constraints 165
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 9
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 414
#Nonlinear Nonzeros in Jacobian 9
#Nonzeros in (Upper-Left) Hessian of Lagrangian 9
#Nonzeros in Diagonal of Hessian of Lagrangian 9
#Blocks in Hessian of Lagrangian 9
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.0000e-01
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
*        175       16       33      126        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         91       61       30        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        448      439        9        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,b47,b48,b49,b50,b51,b52
          ,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69
          ,b70,b71,b72,b73,b74,b75,b76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91;

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;

Binary Variables  b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61
          ,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76;

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;


e1..    objvar + x2 + x3 + x4 - 5*x20 - 10*x21 - 5*x22 + 2*x35 + x36 + 2*x37
      - 80*x38 - 90*x39 - 120*x40 - 285*x41 - 390*x42 - 350*x43 - 290*x44
      - 405*x45 - 190*x46 + 5*b62 + 4*b63 + 6*b64 + 8*b65 + 7*b66 + 6*b67
      + 6*b68 + 9*b69 + 4*b70 + 10*b71 + 9*b72 + 5*b73 + 6*b74 + 10*b75 + 6*b76
      =E= 0;

e2..    x2 - x5 - x8 =E= 0;

e3..    x3 - x6 - x9 =E= 0;

e4..    x4 - x7 - x10 =E= 0;

e5..  - x11 - x14 + x17 =E= 0;

e6..  - x12 - x15 + x18 =E= 0;

e7..  - x13 - x16 + x19 =E= 0;

e8..    x17 - x20 - x23 =E= 0;

e9..    x18 - x21 - x24 =E= 0;

e10..    x19 - x22 - x25 =E= 0;

e11..    x23 - x26 - x29 - x32 =E= 0;

e12..    x24 - x27 - x30 - x33 =E= 0;

e13..    x25 - x28 - x31 - x34 =E= 0;

e14.. -log(1 + x5) + x11 + b47 =L= 1;

e15.. -log(1 + x6) + x12 + b48 =L= 1;

e16.. -log(1 + x7) + x13 + b49 =L= 1;

e17..    x5 - 40*b47 =L= 0;

e18..    x6 - 40*b48 =L= 0;

e19..    x7 - 40*b49 =L= 0;

e20..    x11 - 3.71357206670431*b47 =L= 0;

e21..    x12 - 3.71357206670431*b48 =L= 0;

e22..    x13 - 3.71357206670431*b49 =L= 0;

e23.. -1.2*log(1 + x8) + x14 + b50 =L= 1;

e24.. -1.2*log(1 + x9) + x15 + b51 =L= 1;

e25.. -1.2*log(1 + x10) + x16 + b52 =L= 1;

e26..    x8 - 40*b50 =L= 0;

e27..    x9 - 40*b51 =L= 0;

e28..    x10 - 40*b52 =L= 0;

e29..    x14 - 4.45628648004517*b50 =L= 0;

e30..    x15 - 4.45628648004517*b51 =L= 0;

e31..    x16 - 4.45628648004517*b52 =L= 0;

e32..  - 0.75*x26 + x38 + b53 =L= 1;

e33..  - 0.75*x27 + x39 + b54 =L= 1;

e34..  - 0.75*x28 + x40 + b55 =L= 1;

e35..  - 0.75*x26 + x38 - b53 =G= -1;

e36..  - 0.75*x27 + x39 - b54 =G= -1;

e37..  - 0.75*x28 + x40 - b55 =G= -1;

e38..    x26 - 4.45628648004517*b53 =L= 0;

e39..    x27 - 4.45628648004517*b54 =L= 0;

e40..    x28 - 4.45628648004517*b55 =L= 0;

e41..    x38 - 3.34221486003388*b53 =L= 0;

e42..    x39 - 3.34221486003388*b54 =L= 0;

e43..    x40 - 3.34221486003388*b55 =L= 0;

e44.. -1.5*log(1 + x29) + x41 + b56 =L= 1;

e45.. -1.5*log(1 + x30) + x42 + b57 =L= 1;

e46.. -1.5*log(1 + x31) + x43 + b58 =L= 1;

e47..    x29 - 4.45628648004517*b56 =L= 0;

e48..    x30 - 4.45628648004517*b57 =L= 0;

e49..    x31 - 4.45628648004517*b58 =L= 0;

e50..    x41 - 2.54515263975353*b56 =L= 0;

e51..    x42 - 2.54515263975353*b57 =L= 0;

e52..    x43 - 2.54515263975353*b58 =L= 0;

e53..  - x32 + x44 + b59 =L= 1;

e54..  - x33 + x45 + b60 =L= 1;

e55..  - x34 + x46 + b61 =L= 1;

e56..  - x32 + x44 - b59 =G= -1;

e57..  - x33 + x45 - b60 =G= -1;

e58..  - x34 + x46 - b61 =G= -1;

e59..  - 0.5*x35 + x44 + b59 =L= 1;

e60..  - 0.5*x36 + x45 + b60 =L= 1;

e61..  - 0.5*x37 + x46 + b61 =L= 1;

e62..  - 0.5*x35 + x44 - b59 =G= -1;

e63..  - 0.5*x36 + x45 - b60 =G= -1;

e64..  - 0.5*x37 + x46 - b61 =G= -1;

e65..    x32 - 4.45628648004517*b59 =L= 0;

e66..    x33 - 4.45628648004517*b60 =L= 0;

e67..    x34 - 4.45628648004517*b61 =L= 0;

e68..    x35 - 30*b59 =L= 0;

e69..    x36 - 30*b60 =L= 0;

e70..    x37 - 30*b61 =L= 0;

e71..    x44 - 15*b59 =L= 0;

e72..    x45 - 15*b60 =L= 0;

e73..    x46 - 15*b61 =L= 0;

e74..    5*b62 + x77 =L= 0;

e75..    4*b63 + x78 =L= 0;

e76..    6*b64 + x79 =L= 0;

e77..    8*b65 + x80 =L= 0;

e78..    7*b66 + x81 =L= 0;

e79..    6*b67 + x82 =L= 0;

e80..    6*b68 + x83 =L= 0;

e81..    9*b69 + x84 =L= 0;

e82..    4*b70 + x85 =L= 0;

e83..    10*b71 + x86 =L= 0;

e84..    9*b72 + x87 =L= 0;

e85..    5*b73 + x88 =L= 0;

e86..    6*b74 + x89 =L= 0;

e87..    10*b75 + x90 =L= 0;

e88..    6*b76 + x91 =L= 0;

e89..    5*b62 + x77 =G= 0;

e90..    4*b63 + x78 =G= 0;

e91..    6*b64 + x79 =G= 0;

e92..    8*b65 + x80 =G= 0;

e93..    7*b66 + x81 =G= 0;

e94..    6*b67 + x82 =G= 0;

e95..    6*b68 + x83 =G= 0;

e96..    9*b69 + x84 =G= 0;

e97..    4*b70 + x85 =G= 0;

e98..    10*b71 + x86 =G= 0;

e99..    9*b72 + x87 =G= 0;

e100..    5*b73 + x88 =G= 0;

e101..    6*b74 + x89 =G= 0;

e102..    10*b75 + x90 =G= 0;

e103..    6*b76 + x91 =G= 0;

e104..    b47 - b48 =L= 0;

e105..    b47 - b49 =L= 0;

e106..    b48 - b49 =L= 0;

e107..    b50 - b51 =L= 0;

e108..    b50 - b52 =L= 0;

e109..    b51 - b52 =L= 0;

e110..    b53 - b54 =L= 0;

e111..    b53 - b55 =L= 0;

e112..    b54 - b55 =L= 0;

e113..    b56 - b57 =L= 0;

e114..    b56 - b58 =L= 0;

e115..    b57 - b58 =L= 0;

e116..    b59 - b60 =L= 0;

e117..    b59 - b61 =L= 0;

e118..    b60 - b61 =L= 0;

e119..    b62 + b63 =L= 1;

e120..    b62 + b64 =L= 1;

e121..    b62 + b63 =L= 1;

e122..    b63 + b64 =L= 1;

e123..    b62 + b64 =L= 1;

e124..    b63 + b64 =L= 1;

e125..    b65 + b66 =L= 1;

e126..    b65 + b67 =L= 1;

e127..    b65 + b66 =L= 1;

e128..    b66 + b67 =L= 1;

e129..    b65 + b67 =L= 1;

e130..    b66 + b67 =L= 1;

e131..    b68 + b69 =L= 1;

e132..    b68 + b70 =L= 1;

e133..    b68 + b69 =L= 1;

e134..    b69 + b70 =L= 1;

e135..    b68 + b70 =L= 1;

e136..    b69 + b70 =L= 1;

e137..    b71 + b72 =L= 1;

e138..    b71 + b73 =L= 1;

e139..    b71 + b72 =L= 1;

e140..    b72 + b73 =L= 1;

e141..    b71 + b73 =L= 1;

e142..    b72 + b73 =L= 1;

e143..    b74 + b75 =L= 1;

e144..    b74 + b76 =L= 1;

e145..    b74 + b75 =L= 1;

e146..    b75 + b76 =L= 1;

e147..    b74 + b76 =L= 1;

e148..    b75 + b76 =L= 1;

e149..    b47 - b62 =L= 0;

e150..  - b47 + b48 - b63 =L= 0;

e151..  - b47 - b48 + b49 - b64 =L= 0;

e152..    b50 - b65 =L= 0;

e153..  - b50 + b51 - b66 =L= 0;

e154..  - b50 - b51 + b52 - b67 =L= 0;

e155..    b53 - b68 =L= 0;

e156..  - b53 + b54 - b69 =L= 0;

e157..  - b53 - b54 + b55 - b70 =L= 0;

e158..    b56 - b71 =L= 0;

e159..  - b56 + b57 - b72 =L= 0;

e160..  - b56 - b57 + b58 - b73 =L= 0;

e161..    b59 - b74 =L= 0;

e162..  - b59 + b60 - b75 =L= 0;

e163..  - b59 - b60 + b61 - b76 =L= 0;

e164..    b47 + b50 =E= 1;

e165..    b48 + b51 =E= 1;

e166..    b49 + b52 =E= 1;

e167..    b47 + b50 - b53 =G= 0;

e168..    b48 + b51 - b54 =G= 0;

e169..    b49 + b52 - b55 =G= 0;

e170..    b47 + b50 - b56 =G= 0;

e171..    b48 + b51 - b57 =G= 0;

e172..    b49 + b52 - b58 =G= 0;

e173..    b47 + b50 - b59 =G= 0;

e174..    b48 + b51 - b60 =G= 0;

e175..    b49 + b52 - b61 =G= 0;

* set non-default bounds
x2.up = 40;
x3.up = 40;
x4.up = 40;
x35.up = 30;
x36.up = 30;
x37.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
Imprint / Privacy Policy / License: CC-BY 4.0