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Instance syn05m04m

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)
5510.38734500 p1 ( gdx sol )
(infeas: 5e-12)
Other points (infeas > 1e-08)  
Dual Bounds
5510.55800000 (ALPHAECP)
5510.38780000 (ANTIGONE)
5510.38735200 (BARON)
5510.38734500 (BONMIN)
5510.38744600 (COUENNE)
5510.38734500 (LINDO)
5510.38768300 (SCIP)
5510.38764800 (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 Syn05M04M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 120
#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 44
#Nonlinear Nonzeros in Objective 0
#Constraints 262
#Linear Constraints 250
#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 622
#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
*        263       21       44      198        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        121       81       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        667      655       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,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,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,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
          ,x116,x117,x118,x119,x120,x121;

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;

Binary Variables  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,b92,b93
          ,b94,b95,b96,b97,b98,b99,b100,b101;

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,e251,e252,e253,e254,e255,e256,e257,e258,e259
          ,e260,e261,e262,e263;


e1..    objvar + x2 + x3 + x4 + x5 - 5*x26 - 10*x27 - 5*x28 - 10*x29 + 2*x46
      + x47 + 2*x48 + x49 - 80*x50 - 90*x51 - 120*x52 - 100*x53 - 285*x54
      - 390*x55 - 350*x56 - 300*x57 - 290*x58 - 405*x59 - 190*x60 - 340*x61
      + 5*b82 + 4*b83 + 6*b84 + 3*b85 + 8*b86 + 7*b87 + 6*b88 + 5*b89 + 6*b90
      + 9*b91 + 4*b92 + 3*b93 + 10*b94 + 9*b95 + 5*b96 + 6*b97 + 6*b98 + 10*b99
      + 6*b100 + 9*b101 =E= 0;

e2..    x2 - x6 - x10 =E= 0;

e3..    x3 - x7 - x11 =E= 0;

e4..    x4 - x8 - x12 =E= 0;

e5..    x5 - x9 - x13 =E= 0;

e6..  - x14 - x18 + x22 =E= 0;

e7..  - x15 - x19 + x23 =E= 0;

e8..  - x16 - x20 + x24 =E= 0;

e9..  - x17 - x21 + x25 =E= 0;

e10..    x22 - x26 - x30 =E= 0;

e11..    x23 - x27 - x31 =E= 0;

e12..    x24 - x28 - x32 =E= 0;

e13..    x25 - x29 - x33 =E= 0;

e14..    x30 - x34 - x38 - x42 =E= 0;

e15..    x31 - x35 - x39 - x43 =E= 0;

e16..    x32 - x36 - x40 - x44 =E= 0;

e17..    x33 - x37 - x41 - x45 =E= 0;

e18.. -log(1 + x6) + x14 + b62 =L= 1;

e19.. -log(1 + x7) + x15 + b63 =L= 1;

e20.. -log(1 + x8) + x16 + b64 =L= 1;

e21.. -log(1 + x9) + x17 + b65 =L= 1;

e22..    x6 - 40*b62 =L= 0;

e23..    x7 - 40*b63 =L= 0;

e24..    x8 - 40*b64 =L= 0;

e25..    x9 - 40*b65 =L= 0;

e26..    x14 - 3.71357206670431*b62 =L= 0;

e27..    x15 - 3.71357206670431*b63 =L= 0;

e28..    x16 - 3.71357206670431*b64 =L= 0;

e29..    x17 - 3.71357206670431*b65 =L= 0;

e30.. -1.2*log(1 + x10) + x18 + b66 =L= 1;

e31.. -1.2*log(1 + x11) + x19 + b67 =L= 1;

e32.. -1.2*log(1 + x12) + x20 + b68 =L= 1;

e33.. -1.2*log(1 + x13) + x21 + b69 =L= 1;

e34..    x10 - 40*b66 =L= 0;

e35..    x11 - 40*b67 =L= 0;

e36..    x12 - 40*b68 =L= 0;

e37..    x13 - 40*b69 =L= 0;

e38..    x18 - 4.45628648004517*b66 =L= 0;

e39..    x19 - 4.45628648004517*b67 =L= 0;

e40..    x20 - 4.45628648004517*b68 =L= 0;

e41..    x21 - 4.45628648004517*b69 =L= 0;

e42..  - 0.75*x34 + x50 + b70 =L= 1;

e43..  - 0.75*x35 + x51 + b71 =L= 1;

e44..  - 0.75*x36 + x52 + b72 =L= 1;

e45..  - 0.75*x37 + x53 + b73 =L= 1;

e46..  - 0.75*x34 + x50 - b70 =G= -1;

e47..  - 0.75*x35 + x51 - b71 =G= -1;

e48..  - 0.75*x36 + x52 - b72 =G= -1;

e49..  - 0.75*x37 + x53 - b73 =G= -1;

e50..    x34 - 4.45628648004517*b70 =L= 0;

e51..    x35 - 4.45628648004517*b71 =L= 0;

e52..    x36 - 4.45628648004517*b72 =L= 0;

e53..    x37 - 4.45628648004517*b73 =L= 0;

e54..    x50 - 3.34221486003388*b70 =L= 0;

e55..    x51 - 3.34221486003388*b71 =L= 0;

e56..    x52 - 3.34221486003388*b72 =L= 0;

e57..    x53 - 3.34221486003388*b73 =L= 0;

e58.. -1.5*log(1 + x38) + x54 + b74 =L= 1;

e59.. -1.5*log(1 + x39) + x55 + b75 =L= 1;

e60.. -1.5*log(1 + x40) + x56 + b76 =L= 1;

e61.. -1.5*log(1 + x41) + x57 + b77 =L= 1;

e62..    x38 - 4.45628648004517*b74 =L= 0;

e63..    x39 - 4.45628648004517*b75 =L= 0;

e64..    x40 - 4.45628648004517*b76 =L= 0;

e65..    x41 - 4.45628648004517*b77 =L= 0;

e66..    x54 - 2.54515263975353*b74 =L= 0;

e67..    x55 - 2.54515263975353*b75 =L= 0;

e68..    x56 - 2.54515263975353*b76 =L= 0;

e69..    x57 - 2.54515263975353*b77 =L= 0;

e70..  - x42 + x58 + b78 =L= 1;

e71..  - x43 + x59 + b79 =L= 1;

e72..  - x44 + x60 + b80 =L= 1;

e73..  - x45 + x61 + b81 =L= 1;

e74..  - x42 + x58 - b78 =G= -1;

e75..  - x43 + x59 - b79 =G= -1;

e76..  - x44 + x60 - b80 =G= -1;

e77..  - x45 + x61 - b81 =G= -1;

e78..  - 0.5*x46 + x58 + b78 =L= 1;

e79..  - 0.5*x47 + x59 + b79 =L= 1;

e80..  - 0.5*x48 + x60 + b80 =L= 1;

e81..  - 0.5*x49 + x61 + b81 =L= 1;

e82..  - 0.5*x46 + x58 - b78 =G= -1;

e83..  - 0.5*x47 + x59 - b79 =G= -1;

e84..  - 0.5*x48 + x60 - b80 =G= -1;

e85..  - 0.5*x49 + x61 - b81 =G= -1;

e86..    x42 - 4.45628648004517*b78 =L= 0;

e87..    x43 - 4.45628648004517*b79 =L= 0;

e88..    x44 - 4.45628648004517*b80 =L= 0;

e89..    x45 - 4.45628648004517*b81 =L= 0;

e90..    x46 - 30*b78 =L= 0;

e91..    x47 - 30*b79 =L= 0;

e92..    x48 - 30*b80 =L= 0;

e93..    x49 - 30*b81 =L= 0;

e94..    x58 - 15*b78 =L= 0;

e95..    x59 - 15*b79 =L= 0;

e96..    x60 - 15*b80 =L= 0;

e97..    x61 - 15*b81 =L= 0;

e98..    5*b82 + x102 =L= 0;

e99..    4*b83 + x103 =L= 0;

e100..    6*b84 + x104 =L= 0;

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

e102..    8*b86 + x106 =L= 0;

e103..    7*b87 + x107 =L= 0;

e104..    6*b88 + x108 =L= 0;

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

e106..    6*b90 + x110 =L= 0;

e107..    9*b91 + x111 =L= 0;

e108..    4*b92 + x112 =L= 0;

e109..    3*b93 + x113 =L= 0;

e110..    10*b94 + x114 =L= 0;

e111..    9*b95 + x115 =L= 0;

e112..    5*b96 + x116 =L= 0;

e113..    6*b97 + x117 =L= 0;

e114..    6*b98 + x118 =L= 0;

e115..    10*b99 + x119 =L= 0;

e116..    6*b100 + x120 =L= 0;

e117..    9*b101 + x121 =L= 0;

e118..    5*b82 + x102 =G= 0;

e119..    4*b83 + x103 =G= 0;

e120..    6*b84 + x104 =G= 0;

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

e122..    8*b86 + x106 =G= 0;

e123..    7*b87 + x107 =G= 0;

e124..    6*b88 + x108 =G= 0;

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

e126..    6*b90 + x110 =G= 0;

e127..    9*b91 + x111 =G= 0;

e128..    4*b92 + x112 =G= 0;

e129..    3*b93 + x113 =G= 0;

e130..    10*b94 + x114 =G= 0;

e131..    9*b95 + x115 =G= 0;

e132..    5*b96 + x116 =G= 0;

e133..    6*b97 + x117 =G= 0;

e134..    6*b98 + x118 =G= 0;

e135..    10*b99 + x119 =G= 0;

e136..    6*b100 + x120 =G= 0;

e137..    9*b101 + x121 =G= 0;

e138..    b62 - b63 =L= 0;

e139..    b62 - b64 =L= 0;

e140..    b62 - b65 =L= 0;

e141..    b63 - b64 =L= 0;

e142..    b63 - b65 =L= 0;

e143..    b64 - b65 =L= 0;

e144..    b66 - b67 =L= 0;

e145..    b66 - b68 =L= 0;

e146..    b66 - b69 =L= 0;

e147..    b67 - b68 =L= 0;

e148..    b67 - b69 =L= 0;

e149..    b68 - b69 =L= 0;

e150..    b70 - b71 =L= 0;

e151..    b70 - b72 =L= 0;

e152..    b70 - b73 =L= 0;

e153..    b71 - b72 =L= 0;

e154..    b71 - b73 =L= 0;

e155..    b72 - b73 =L= 0;

e156..    b74 - b75 =L= 0;

e157..    b74 - b76 =L= 0;

e158..    b74 - b77 =L= 0;

e159..    b75 - b76 =L= 0;

e160..    b75 - b77 =L= 0;

e161..    b76 - b77 =L= 0;

e162..    b78 - b79 =L= 0;

e163..    b78 - b80 =L= 0;

e164..    b78 - b81 =L= 0;

e165..    b79 - b80 =L= 0;

e166..    b79 - b81 =L= 0;

e167..    b80 - b81 =L= 0;

e168..    b82 + b83 =L= 1;

e169..    b82 + b84 =L= 1;

e170..    b82 + b85 =L= 1;

e171..    b82 + b83 =L= 1;

e172..    b83 + b84 =L= 1;

e173..    b83 + b85 =L= 1;

e174..    b82 + b84 =L= 1;

e175..    b83 + b84 =L= 1;

e176..    b84 + b85 =L= 1;

e177..    b82 + b85 =L= 1;

e178..    b83 + b85 =L= 1;

e179..    b84 + b85 =L= 1;

e180..    b86 + b87 =L= 1;

e181..    b86 + b88 =L= 1;

e182..    b86 + b89 =L= 1;

e183..    b86 + b87 =L= 1;

e184..    b87 + b88 =L= 1;

e185..    b87 + b89 =L= 1;

e186..    b86 + b88 =L= 1;

e187..    b87 + b88 =L= 1;

e188..    b88 + b89 =L= 1;

e189..    b86 + b89 =L= 1;

e190..    b87 + b89 =L= 1;

e191..    b88 + b89 =L= 1;

e192..    b90 + b91 =L= 1;

e193..    b90 + b92 =L= 1;

e194..    b90 + b93 =L= 1;

e195..    b90 + b91 =L= 1;

e196..    b91 + b92 =L= 1;

e197..    b91 + b93 =L= 1;

e198..    b90 + b92 =L= 1;

e199..    b91 + b92 =L= 1;

e200..    b92 + b93 =L= 1;

e201..    b90 + b93 =L= 1;

e202..    b91 + b93 =L= 1;

e203..    b92 + b93 =L= 1;

e204..    b94 + b95 =L= 1;

e205..    b94 + b96 =L= 1;

e206..    b94 + b97 =L= 1;

e207..    b94 + b95 =L= 1;

e208..    b95 + b96 =L= 1;

e209..    b95 + b97 =L= 1;

e210..    b94 + b96 =L= 1;

e211..    b95 + b96 =L= 1;

e212..    b96 + b97 =L= 1;

e213..    b94 + b97 =L= 1;

e214..    b95 + b97 =L= 1;

e215..    b96 + b97 =L= 1;

e216..    b98 + b99 =L= 1;

e217..    b98 + b100 =L= 1;

e218..    b98 + b101 =L= 1;

e219..    b98 + b99 =L= 1;

e220..    b99 + b100 =L= 1;

e221..    b99 + b101 =L= 1;

e222..    b98 + b100 =L= 1;

e223..    b99 + b100 =L= 1;

e224..    b100 + b101 =L= 1;

e225..    b98 + b101 =L= 1;

e226..    b99 + b101 =L= 1;

e227..    b100 + b101 =L= 1;

e228..    b62 - b82 =L= 0;

e229..  - b62 + b63 - b83 =L= 0;

e230..  - b62 - b63 + b64 - b84 =L= 0;

e231..  - b62 - b63 - b64 + b65 - b85 =L= 0;

e232..    b66 - b86 =L= 0;

e233..  - b66 + b67 - b87 =L= 0;

e234..  - b66 - b67 + b68 - b88 =L= 0;

e235..  - b66 - b67 - b68 + b69 - b89 =L= 0;

e236..    b70 - b90 =L= 0;

e237..  - b70 + b71 - b91 =L= 0;

e238..  - b70 - b71 + b72 - b92 =L= 0;

e239..  - b70 - b71 - b72 + b73 - b93 =L= 0;

e240..    b74 - b94 =L= 0;

e241..  - b74 + b75 - b95 =L= 0;

e242..  - b74 - b75 + b76 - b96 =L= 0;

e243..  - b74 - b75 - b76 + b77 - b97 =L= 0;

e244..    b78 - b98 =L= 0;

e245..  - b78 + b79 - b99 =L= 0;

e246..  - b78 - b79 + b80 - b100 =L= 0;

e247..  - b78 - b79 - b80 + b81 - b101 =L= 0;

e248..    b62 + b66 =E= 1;

e249..    b63 + b67 =E= 1;

e250..    b64 + b68 =E= 1;

e251..    b65 + b69 =E= 1;

e252..    b62 + b66 - b70 =G= 0;

e253..    b63 + b67 - b71 =G= 0;

e254..    b64 + b68 - b72 =G= 0;

e255..    b65 + b69 - b73 =G= 0;

e256..    b62 + b66 - b74 =G= 0;

e257..    b63 + b67 - b75 =G= 0;

e258..    b64 + b68 - b76 =G= 0;

e259..    b65 + b69 - b77 =G= 0;

e260..    b62 + b66 - b78 =G= 0;

e261..    b63 + b67 - b79 =G= 0;

e262..    b64 + b68 - b80 =G= 0;

e263..    b65 + b69 - b81 =G= 0;

* set non-default bounds
x2.up = 40;
x3.up = 40;
x4.up = 40;
x5.up = 40;
x46.up = 30;
x47.up = 30;
x48.up = 30;
x49.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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