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Instance syn10m02m

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)
2310.30069100 p1 ( gdx sol )
(infeas: 4e-14)
Other points (infeas > 1e-08)  
Dual Bounds
2310.39180000 (ALPHAECP)
2310.30116200 (ANTIGONE)
2310.30069300 (BARON)
2310.30070000 (BONMIN)
2310.30076900 (COUENNE)
2310.30069300 (LINDO)
2310.30086300 (SCIP)
2310.30133000 (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 Syn10M02M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 110
#Binary Variables 40
#Integer Variables 0
#Nonlinear Variables 12
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 38
#Nonlinear Nonzeros in Objective 0
#Constraints 198
#Linear Constraints 186
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 12
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 462
#Nonlinear Nonzeros in Jacobian 12
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 12
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
*        199       15       50      134        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        111       71       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        501      489       12        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,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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86
          ,b87,b88,b89,b90,b91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111;

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;

Binary Variables  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,b77,b78,b79,b80,b81,b82,b83
          ,b84,b85,b86,b87,b88,b89,b90,b91;

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;


e1..    objvar + x2 + x3 - 5*x14 - 10*x15 + 2*x24 + x25 - 80*x40 - 90*x41
      - 285*x42 - 390*x43 - 290*x44 - 405*x45 - 280*x46 - 400*x47 - 290*x48
      - 300*x49 - 350*x50 - 250*x51 + 5*b72 + 4*b73 + 8*b74 + 7*b75 + 6*b76
      + 9*b77 + 10*b78 + 9*b79 + 6*b80 + 10*b81 + 7*b82 + 7*b83 + 4*b84 + 3*b85
      + 5*b86 + 6*b87 + 2*b88 + 5*b89 + 4*b90 + 7*b91 =E= 0;

e2..    x2 - x4 - x6 =E= 0;

e3..    x3 - x5 - x7 =E= 0;

e4..  - x8 - x10 + x12 =E= 0;

e5..  - x9 - x11 + x13 =E= 0;

e6..    x12 - x14 - x16 =E= 0;

e7..    x13 - x15 - x17 =E= 0;

e8..    x16 - x18 - x20 - x22 =E= 0;

e9..    x17 - x19 - x21 - x23 =E= 0;

e10..    x26 - x32 - x34 =E= 0;

e11..    x27 - x33 - x35 =E= 0;

e12..    x30 - x36 - x38 - x40 =E= 0;

e13..    x31 - x37 - x39 - x41 =E= 0;

e14.. -log(1 + x4) + x8 + b52 =L= 1;

e15.. -log(1 + x5) + x9 + b53 =L= 1;

e16..    x4 - 40*b52 =L= 0;

e17..    x5 - 40*b53 =L= 0;

e18..    x8 - 3.71357206670431*b52 =L= 0;

e19..    x9 - 3.71357206670431*b53 =L= 0;

e20.. -1.2*log(1 + x6) + x10 + b54 =L= 1;

e21.. -1.2*log(1 + x7) + x11 + b55 =L= 1;

e22..    x6 - 40*b54 =L= 0;

e23..    x7 - 40*b55 =L= 0;

e24..    x10 - 4.45628648004517*b54 =L= 0;

e25..    x11 - 4.45628648004517*b55 =L= 0;

e26..  - 0.75*x18 + x26 + b56 =L= 1;

e27..  - 0.75*x19 + x27 + b57 =L= 1;

e28..  - 0.75*x18 + x26 - b56 =G= -1;

e29..  - 0.75*x19 + x27 - b57 =G= -1;

e30..    x18 - 4.45628648004517*b56 =L= 0;

e31..    x19 - 4.45628648004517*b57 =L= 0;

e32..    x26 - 3.34221486003388*b56 =L= 0;

e33..    x27 - 3.34221486003388*b57 =L= 0;

e34.. -1.5*log(1 + x20) + x28 + b58 =L= 1;

e35.. -1.5*log(1 + x21) + x29 + b59 =L= 1;

e36..    x20 - 4.45628648004517*b58 =L= 0;

e37..    x21 - 4.45628648004517*b59 =L= 0;

e38..    x28 - 2.54515263975353*b58 =L= 0;

e39..    x29 - 2.54515263975353*b59 =L= 0;

e40..  - x22 + x30 + b60 =L= 1;

e41..  - x23 + x31 + b61 =L= 1;

e42..  - x22 + x30 - b60 =G= -1;

e43..  - x23 + x31 - b61 =G= -1;

e44..  - 0.5*x24 + x30 + b60 =L= 1;

e45..  - 0.5*x25 + x31 + b61 =L= 1;

e46..  - 0.5*x24 + x30 - b60 =G= -1;

e47..  - 0.5*x25 + x31 - b61 =G= -1;

e48..    x22 - 4.45628648004517*b60 =L= 0;

e49..    x23 - 4.45628648004517*b61 =L= 0;

e50..    x24 - 30*b60 =L= 0;

e51..    x25 - 30*b61 =L= 0;

e52..    x30 - 15*b60 =L= 0;

e53..    x31 - 15*b61 =L= 0;

e54.. -1.25*log(1 + x32) + x42 + b62 =L= 1;

e55.. -1.25*log(1 + x33) + x43 + b63 =L= 1;

e56..    x32 - 3.34221486003388*b62 =L= 0;

e57..    x33 - 3.34221486003388*b63 =L= 0;

e58..    x42 - 1.83548069293539*b62 =L= 0;

e59..    x43 - 1.83548069293539*b63 =L= 0;

e60.. -0.9*log(1 + x34) + x44 + b64 =L= 1;

e61.. -0.9*log(1 + x35) + x45 + b65 =L= 1;

e62..    x34 - 3.34221486003388*b64 =L= 0;

e63..    x35 - 3.34221486003388*b65 =L= 0;

e64..    x44 - 1.32154609891348*b64 =L= 0;

e65..    x45 - 1.32154609891348*b65 =L= 0;

e66.. -log(1 + x28) + x46 + b66 =L= 1;

e67.. -log(1 + x29) + x47 + b67 =L= 1;

e68..    x28 - 2.54515263975353*b66 =L= 0;

e69..    x29 - 2.54515263975353*b67 =L= 0;

e70..    x46 - 1.26558121681553*b66 =L= 0;

e71..    x47 - 1.26558121681553*b67 =L= 0;

e72..  - 0.9*x36 + x48 + b68 =L= 1;

e73..  - 0.9*x37 + x49 + b69 =L= 1;

e74..  - 0.9*x36 + x48 - b68 =G= -1;

e75..  - 0.9*x37 + x49 - b69 =G= -1;

e76..    x36 - 15*b68 =L= 0;

e77..    x37 - 15*b69 =L= 0;

e78..    x48 - 13.5*b68 =L= 0;

e79..    x49 - 13.5*b69 =L= 0;

e80..  - 0.6*x38 + x50 + b70 =L= 1;

e81..  - 0.6*x39 + x51 + b71 =L= 1;

e82..  - 0.6*x38 + x50 - b70 =G= -1;

e83..  - 0.6*x39 + x51 - b71 =G= -1;

e84..    x38 - 15*b70 =L= 0;

e85..    x39 - 15*b71 =L= 0;

e86..    x50 - 9*b70 =L= 0;

e87..    x51 - 9*b71 =L= 0;

e88..    5*b72 + x92 =L= 0;

e89..    4*b73 + x93 =L= 0;

e90..    8*b74 + x94 =L= 0;

e91..    7*b75 + x95 =L= 0;

e92..    6*b76 + x96 =L= 0;

e93..    9*b77 + x97 =L= 0;

e94..    10*b78 + x98 =L= 0;

e95..    9*b79 + x99 =L= 0;

e96..    6*b80 + x100 =L= 0;

e97..    10*b81 + x101 =L= 0;

e98..    7*b82 + x102 =L= 0;

e99..    7*b83 + x103 =L= 0;

e100..    4*b84 + x104 =L= 0;

e101..    3*b85 + x105 =L= 0;

e102..    5*b86 + x106 =L= 0;

e103..    6*b87 + x107 =L= 0;

e104..    2*b88 + x108 =L= 0;

e105..    5*b89 + x109 =L= 0;

e106..    4*b90 + x110 =L= 0;

e107..    7*b91 + x111 =L= 0;

e108..    5*b72 + x92 =G= 0;

e109..    4*b73 + x93 =G= 0;

e110..    8*b74 + x94 =G= 0;

e111..    7*b75 + x95 =G= 0;

e112..    6*b76 + x96 =G= 0;

e113..    9*b77 + x97 =G= 0;

e114..    10*b78 + x98 =G= 0;

e115..    9*b79 + x99 =G= 0;

e116..    6*b80 + x100 =G= 0;

e117..    10*b81 + x101 =G= 0;

e118..    7*b82 + x102 =G= 0;

e119..    7*b83 + x103 =G= 0;

e120..    4*b84 + x104 =G= 0;

e121..    3*b85 + x105 =G= 0;

e122..    5*b86 + x106 =G= 0;

e123..    6*b87 + x107 =G= 0;

e124..    2*b88 + x108 =G= 0;

e125..    5*b89 + x109 =G= 0;

e126..    4*b90 + x110 =G= 0;

e127..    7*b91 + x111 =G= 0;

e128..    b52 - b53 =L= 0;

e129..    b54 - b55 =L= 0;

e130..    b56 - b57 =L= 0;

e131..    b58 - b59 =L= 0;

e132..    b60 - b61 =L= 0;

e133..    b62 - b63 =L= 0;

e134..    b64 - b65 =L= 0;

e135..    b66 - b67 =L= 0;

e136..    b68 - b69 =L= 0;

e137..    b70 - b71 =L= 0;

e138..    b72 + b73 =L= 1;

e139..    b72 + b73 =L= 1;

e140..    b74 + b75 =L= 1;

e141..    b74 + b75 =L= 1;

e142..    b76 + b77 =L= 1;

e143..    b76 + b77 =L= 1;

e144..    b78 + b79 =L= 1;

e145..    b78 + b79 =L= 1;

e146..    b80 + b81 =L= 1;

e147..    b80 + b81 =L= 1;

e148..    b82 + b83 =L= 1;

e149..    b82 + b83 =L= 1;

e150..    b84 + b85 =L= 1;

e151..    b84 + b85 =L= 1;

e152..    b86 + b87 =L= 1;

e153..    b86 + b87 =L= 1;

e154..    b88 + b89 =L= 1;

e155..    b88 + b89 =L= 1;

e156..    b90 + b91 =L= 1;

e157..    b90 + b91 =L= 1;

e158..    b52 - b72 =L= 0;

e159..  - b52 + b53 - b73 =L= 0;

e160..    b54 - b74 =L= 0;

e161..  - b54 + b55 - b75 =L= 0;

e162..    b56 - b76 =L= 0;

e163..  - b56 + b57 - b77 =L= 0;

e164..    b58 - b78 =L= 0;

e165..  - b58 + b59 - b79 =L= 0;

e166..    b60 - b80 =L= 0;

e167..  - b60 + b61 - b81 =L= 0;

e168..    b62 - b82 =L= 0;

e169..  - b62 + b63 - b83 =L= 0;

e170..    b64 - b84 =L= 0;

e171..  - b64 + b65 - b85 =L= 0;

e172..    b66 - b86 =L= 0;

e173..  - b66 + b67 - b87 =L= 0;

e174..    b68 - b88 =L= 0;

e175..  - b68 + b69 - b89 =L= 0;

e176..    b70 - b90 =L= 0;

e177..  - b70 + b71 - b91 =L= 0;

e178..    b52 + b54 =E= 1;

e179..    b53 + b55 =E= 1;

e180..  - b56 + b62 + b64 =G= 0;

e181..  - b57 + b63 + b65 =G= 0;

e182..  - b58 + b66 =G= 0;

e183..  - b59 + b67 =G= 0;

e184..    b52 + b54 - b56 =G= 0;

e185..    b53 + b55 - b57 =G= 0;

e186..    b52 + b54 - b58 =G= 0;

e187..    b53 + b55 - b59 =G= 0;

e188..    b52 + b54 - b60 =G= 0;

e189..    b53 + b55 - b61 =G= 0;

e190..    b56 - b62 =G= 0;

e191..    b57 - b63 =G= 0;

e192..    b56 - b64 =G= 0;

e193..    b57 - b65 =G= 0;

e194..    b58 - b66 =G= 0;

e195..    b59 - b67 =G= 0;

e196..    b60 - b68 =G= 0;

e197..    b61 - b69 =G= 0;

e198..    b60 - b70 =G= 0;

e199..    b61 - b71 =G= 0;

* set non-default bounds
x2.up = 40;
x3.up = 40;
x24.up = 30;
x25.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: 2022-10-14 Git hash: 2be6d7c0
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