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)ⓘ | |
| 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) 69.01614489 (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 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: 2025-08-07 Git hash: e62cedfc