MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance syn40m

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)
67.71325586 p1 ( gdx sol )
(infeas: 3e-10)
Other points (infeas > 1e-08)  
Dual Bounds
67.71736100 (ALPHAECP)
67.71343158 (ANTIGONE)
67.71326996 (BARON)
67.71325600 (BONMIN)
949.55011770 (COUENNE)
67.71325586 (LINDO)
67.71336160 (SCIP)
67.71352452 (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 Syn40M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 130
#Binary Variables 40
#Integer Variables 0
#Nonlinear Variables 28
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 66
#Nonlinear Nonzeros in Objective 0
#Constraints 226
#Linear Constraints 198
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 28
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 560
#Nonlinear Nonzeros in Jacobian 28
#Nonzeros in (Upper-Left) Hessian of Lagrangian 28
#Nonzeros in Diagonal of Hessian of Lagrangian 28
#Blocks in Hessian of Lagrangian 28
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 3.6739e-01
Maximal coefficient 3.5000e+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
*        227       23       72      132        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        131       91       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        627      599       28        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,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102
          ,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
          ,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
          ,b129,b130,b131;

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;

Binary Variables  b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103,b104
          ,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116,b117
          ,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129,b130
          ,b131;

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;


e1..    objvar + x2 - 5*x8 + 2*x13 + 10*x30 + 5*x31 - 40*x38 - 15*x39 - 10*x40
      - 30*x41 - 35*x42 - 20*x43 - 25*x44 - 15*x45 - 30*x53 + x58 + 5*x75 + x76
      - 120*x83 - 140*x84 - 90*x85 - 80*x86 - 285*x87 - 290*x88 - 280*x89
      - 290*x90 - 350*x91 + 5*b92 + 8*b93 + 6*b94 + 10*b95 + 6*b96 + 7*b97
      + 4*b98 + 5*b99 + 2*b100 + 4*b101 + 3*b102 + 7*b103 + 3*b104 + 2*b105
      + 4*b106 + 2*b107 + 3*b108 + 5*b109 + 2*b110 + b111 + 2*b112 + 9*b113
      + 5*b114 + 2*b115 + 10*b116 + 4*b117 + 7*b118 + 4*b119 + 2*b120 + 8*b121
      + 9*b122 + 3*b123 + 5*b124 + 5*b125 + 6*b126 + 2*b127 + 6*b128 + 3*b129
      + 5*b130 + 9*b131 =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 - x47 =E= 0;

e13..    x47 - x48 - x49 =E= 0;

e14..  - x50 - x51 + x52 =E= 0;

e15..    x52 - x53 - x54 =E= 0;

e16..    x54 - x55 - x56 - x57 =E= 0;

e17..    x59 - x62 - x63 =E= 0;

e18..    x61 - x64 - x65 - x66 =E= 0;

e19..    x69 - x73 - x74 =E= 0;

e20..  - x70 - x76 + x77 =E= 0;

e21..    x71 - x78 - x79 =E= 0;

e22..    x72 - x80 - x81 - x82 =E= 0;

e23.. -log(1 + x3) + x5 + b92 =L= 1;

e24..    x3 - 40*b92 =L= 0;

e25..    x5 - 3.71357206670431*b92 =L= 0;

e26.. -1.2*log(1 + x4) + x6 + b93 =L= 1;

e27..    x4 - 40*b93 =L= 0;

e28..    x6 - 4.45628648004517*b93 =L= 0;

e29..  - 0.75*x10 + x14 + b94 =L= 1;

e30..  - 0.75*x10 + x14 - b94 =G= -1;

e31..    x10 - 4.45628648004517*b94 =L= 0;

e32..    x14 - 3.34221486003388*b94 =L= 0;

e33.. -1.5*log(1 + x11) + x15 + b95 =L= 1;

e34..    x11 - 4.45628648004517*b95 =L= 0;

e35..    x15 - 2.54515263975353*b95 =L= 0;

e36..  - x12 + x16 + b96 =L= 1;

e37..  - x12 + x16 - b96 =G= -1;

e38..  - 0.5*x13 + x16 + b96 =L= 1;

e39..  - 0.5*x13 + x16 - b96 =G= -1;

e40..    x12 - 4.45628648004517*b96 =L= 0;

e41..    x13 - 30*b96 =L= 0;

e42..    x16 - 15*b96 =L= 0;

e43.. -1.25*log(1 + x17) + x22 + b97 =L= 1;

e44..    x17 - 3.34221486003388*b97 =L= 0;

e45..    x22 - 1.83548069293539*b97 =L= 0;

e46.. -0.9*log(1 + x18) + x23 + b98 =L= 1;

e47..    x18 - 3.34221486003388*b98 =L= 0;

e48..    x23 - 1.32154609891348*b98 =L= 0;

e49.. -log(1 + x15) + x24 + b99 =L= 1;

e50..    x15 - 2.54515263975353*b99 =L= 0;

e51..    x24 - 1.26558121681553*b99 =L= 0;

e52..  - 0.9*x19 + x25 + b100 =L= 1;

e53..  - 0.9*x19 + x25 - b100 =G= -1;

e54..    x19 - 15*b100 =L= 0;

e55..    x25 - 13.5*b100 =L= 0;

e56..  - 0.6*x20 + x26 + b101 =L= 1;

e57..  - 0.6*x20 + x26 - b101 =G= -1;

e58..    x20 - 15*b101 =L= 0;

e59..    x26 - 9*b101 =L= 0;

e60.. -1.1*log(1 + x21) + x27 + b102 =L= 1;

e61..    x21 - 15*b102 =L= 0;

e62..    x27 - 3.04984759446376*b102 =L= 0;

e63..  - 0.9*x22 + x38 + b103 =L= 1;

e64..  - 0.9*x22 + x38 - b103 =G= -1;

e65..  - x30 + x38 + b103 =L= 1;

e66..  - x30 + x38 - b103 =G= -1;

e67..    x22 - 1.83548069293539*b103 =L= 0;

e68..    x30 - 20*b103 =L= 0;

e69..    x38 - 20*b103 =L= 0;

e70.. -log(1 + x23) + x39 + b104 =L= 1;

e71..    x23 - 1.32154609891348*b104 =L= 0;

e72..    x39 - 0.842233385663186*b104 =L= 0;

e73.. -0.7*log(1 + x28) + x40 + b105 =L= 1;

e74..    x28 - 1.26558121681553*b105 =L= 0;

e75..    x40 - 0.572481933717686*b105 =L= 0;

e76.. -0.65*log(1 + x29) + x41 + b106 =L= 1;

e77.. -0.65*log(1 + x32) + x41 + b106 =L= 1;

e78..    x29 - 1.26558121681553*b106 =L= 0;

e79..    x32 - 33.5*b106 =L= 0;

e80..    x41 - 2.30162356062425*b106 =L= 0;

e81..  - x33 + x42 + b107 =L= 1;

e82..  - x33 + x42 - b107 =G= -1;

e83..    x33 - 9*b107 =L= 0;

e84..    x42 - 9*b107 =L= 0;

e85..  - x34 + x43 + b108 =L= 1;

e86..  - x34 + x43 - b108 =G= -1;

e87..    x34 - 9*b108 =L= 0;

e88..    x43 - 9*b108 =L= 0;

e89.. -0.75*log(1 + x35) + x44 + b109 =L= 1;

e90..    x35 - 3.04984759446376*b109 =L= 0;

e91..    x44 - 1.04900943706034*b109 =L= 0;

e92.. -0.8*log(1 + x36) + x45 + b110 =L= 1;

e93..    x36 - 3.04984759446376*b110 =L= 0;

e94..    x45 - 1.11894339953103*b110 =L= 0;

e95.. -0.85*log(1 + x37) + x46 + b111 =L= 1;

e96..    x37 - 3.04984759446376*b111 =L= 0;

e97..    x46 - 1.18887736200171*b111 =L= 0;

e98.. -log(1 + x48) + x50 + b112 =L= 1;

e99..    x48 - 1.18887736200171*b112 =L= 0;

e100..    x50 - 0.78338879230327*b112 =L= 0;

e101.. -1.2*log(1 + x49) + x51 + b113 =L= 1;

e102..    x49 - 1.18887736200171*b113 =L= 0;

e103..    x51 - 0.940066550763924*b113 =L= 0;

e104..  - 0.75*x55 + x59 + b114 =L= 1;

e105..  - 0.75*x55 + x59 - b114 =G= -1;

e106..    x55 - 0.940066550763924*b114 =L= 0;

e107..    x59 - 0.705049913072943*b114 =L= 0;

e108.. -1.5*log(1 + x56) + x60 + b115 =L= 1;

e109..    x56 - 0.940066550763924*b115 =L= 0;

e110..    x60 - 0.994083415506506*b115 =L= 0;

e111..  - x57 + x61 + b116 =L= 1;

e112..  - x57 + x61 - b116 =G= -1;

e113..  - 0.5*x58 + x61 + b116 =L= 1;

e114..  - 0.5*x58 + x61 - b116 =G= -1;

e115..    x57 - 0.940066550763924*b116 =L= 0;

e116..    x58 - 30*b116 =L= 0;

e117..    x61 - 15*b116 =L= 0;

e118.. -1.25*log(1 + x62) + x67 + b117 =L= 1;

e119..    x62 - 0.705049913072943*b117 =L= 0;

e120..    x67 - 0.666992981045719*b117 =L= 0;

e121.. -0.9*log(1 + x63) + x68 + b118 =L= 1;

e122..    x63 - 0.705049913072943*b118 =L= 0;

e123..    x68 - 0.480234946352917*b118 =L= 0;

e124.. -log(1 + x60) + x69 + b119 =L= 1;

e125..    x60 - 0.994083415506506*b119 =L= 0;

e126..    x69 - 0.690184503917672*b119 =L= 0;

e127..  - 0.9*x64 + x70 + b120 =L= 1;

e128..  - 0.9*x64 + x70 - b120 =G= -1;

e129..    x64 - 15*b120 =L= 0;

e130..    x70 - 13.5*b120 =L= 0;

e131..  - 0.6*x65 + x71 + b121 =L= 1;

e132..  - 0.6*x65 + x71 - b121 =G= -1;

e133..    x65 - 15*b121 =L= 0;

e134..    x71 - 9*b121 =L= 0;

e135.. -1.1*log(1 + x66) + x72 + b122 =L= 1;

e136..    x66 - 15*b122 =L= 0;

e137..    x72 - 3.04984759446376*b122 =L= 0;

e138..  - 0.9*x67 + x83 + b123 =L= 1;

e139..  - 0.9*x67 + x83 - b123 =G= -1;

e140..  - x75 + x83 + b123 =L= 1;

e141..  - x75 + x83 - b123 =G= -1;

e142..    x67 - 0.666992981045719*b123 =L= 0;

e143..    x75 - 25*b123 =L= 0;

e144..    x83 - 25*b123 =L= 0;

e145.. -log(1 + x68) + x84 + b124 =L= 1;

e146..    x68 - 0.480234946352917*b124 =L= 0;

e147..    x84 - 0.392200822712722*b124 =L= 0;

e148.. -0.7*log(1 + x73) + x85 + b125 =L= 1;

e149..    x73 - 0.690184503917672*b125 =L= 0;

e150..    x85 - 0.367386387824208*b125 =L= 0;

e151.. -0.65*log(1 + x74) + x86 + b126 =L= 1;

e152.. -0.65*log(1 + x77) + x86 + b126 =L= 1;

e153..    x74 - 0.690184503917672*b126 =L= 0;

e154..    x77 - 38.5*b126 =L= 0;

e155..    x86 - 2.3895954367396*b126 =L= 0;

e156..  - x78 + x87 + b127 =L= 1;

e157..  - x78 + x87 - b127 =G= -1;

e158..    x78 - 9*b127 =L= 0;

e159..    x87 - 9*b127 =L= 0;

e160..  - x79 + x88 + b128 =L= 1;

e161..  - x79 + x88 - b128 =G= -1;

e162..    x79 - 9*b128 =L= 0;

e163..    x88 - 9*b128 =L= 0;

e164.. -0.75*log(1 + x80) + x89 + b129 =L= 1;

e165..    x80 - 3.04984759446376*b129 =L= 0;

e166..    x89 - 1.04900943706034*b129 =L= 0;

e167.. -0.8*log(1 + x81) + x90 + b130 =L= 1;

e168..    x81 - 3.04984759446376*b130 =L= 0;

e169..    x90 - 1.11894339953103*b130 =L= 0;

e170.. -0.85*log(1 + x82) + x91 + b131 =L= 1;

e171..    x82 - 3.04984759446376*b131 =L= 0;

e172..    x91 - 1.18887736200171*b131 =L= 0;

e173..    b92 + b93 =E= 1;

e174..  - b94 + b97 + b98 =G= 0;

e175..  - b97 + b103 =G= 0;

e176..  - b98 + b104 =G= 0;

e177..  - b95 + b99 =G= 0;

e178..  - b99 + b105 + b106 =G= 0;

e179..  - b96 + b100 + b101 + b102 =G= 0;

e180..  - b100 + b106 =G= 0;

e181..  - b101 + b107 + b108 =G= 0;

e182..  - b102 + b109 + b110 + b111 =G= 0;

e183..    b94 - b97 =G= 0;

e184..    b94 - b98 =G= 0;

e185..    b95 - b99 =G= 0;

e186..    b96 - b100 =G= 0;

e187..    b96 - b101 =G= 0;

e188..    b96 - b102 =G= 0;

e189..    b97 - b103 =G= 0;

e190..    b98 - b104 =G= 0;

e191..    b99 - b105 =G= 0;

e192..    b99 - b106 =G= 0;

e193..    b101 - b107 =G= 0;

e194..    b101 - b108 =G= 0;

e195..    b102 - b109 =G= 0;

e196..    b102 - b110 =G= 0;

e197..    b102 - b111 =G= 0;

e198..  - b111 + b112 + b113 =G= 0;

e199..  - b114 + b117 + b118 =G= 0;

e200..  - b117 + b123 =G= 0;

e201..  - b118 + b124 =G= 0;

e202..  - b115 + b119 =G= 0;

e203..  - b119 + b125 + b126 =G= 0;

e204..  - b116 + b120 + b121 + b122 =G= 0;

e205..  - b120 + b126 =G= 0;

e206..  - b121 + b127 + b128 =G= 0;

e207..  - b122 + b129 + b130 + b131 =G= 0;

e208..    b114 - b117 =G= 0;

e209..    b114 - b118 =G= 0;

e210..    b117 - b123 =G= 0;

e211..    b118 - b124 =G= 0;

e212..    b115 - b119 =G= 0;

e213..    b119 - b125 =G= 0;

e214..    b119 - b126 =G= 0;

e215..    b116 - b120 =G= 0;

e216..    b116 - b121 =G= 0;

e217..    b116 - b122 =G= 0;

e218..    b121 - b127 =G= 0;

e219..    b121 - b128 =G= 0;

e220..    b122 - b129 =G= 0;

e221..    b122 - b130 =G= 0;

e222..    b122 - b131 =G= 0;

e223..    b92 + b93 - b94 =G= 0;

e224..    b92 + b93 - b95 =G= 0;

e225..    b92 + b93 - b96 =G= 0;

e226..    b111 - b112 =G= 0;

e227..    b111 - b113 =G= 0;

* set non-default bounds
x2.up = 40;
x13.up = 30;
x30.up = 20;
x31.up = 20;
x58.up = 30;
x75.up = 25;
x76.up = 25;

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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0