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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance syn30m
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ⓘ | 138.15960250 (ALPHAECP) 138.16010180 (ANTIGONE) 138.15961290 (BARON) 138.15960250 (BONMIN) 138.15961130 (COUENNE) 138.15960820 (LINDO) 138.15978010 (SCIP) 139.67096280 (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ⓘ | Syn30M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 100 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 20 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 51 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 167 |
| #Linear Constraintsⓘ | 147 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 20 |
| Operands in Gen. Nonlin. Functionsⓘ | log |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 415 |
| #Nonlinear Nonzeros in Jacobianⓘ | 20 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 20 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #Blocks in Hessian of Lagrangianⓘ | 20 |
| 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ⓘ | 4.8023e-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
* 168 19 51 98 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 101 71 30 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 467 447 20 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,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;
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;
Binary Variables 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;
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 - 80*x66
- 285*x67 - 290*x68 - 280*x69 - 290*x70 - 350*x71 + 5*b72 + 8*b73 + 6*b74
+ 10*b75 + 6*b76 + 7*b77 + 4*b78 + 5*b79 + 2*b80 + 4*b81 + 3*b82 + 7*b83
+ 3*b84 + 2*b85 + 4*b86 + 2*b87 + 3*b88 + 5*b89 + 2*b90 + b91 + 2*b92
+ 9*b93 + 5*b94 + 2*b95 + 10*b96 + 4*b97 + 7*b98 + 4*b99 + 2*b100
+ 8*b101 =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.. -log(1 + x3) + x5 + b72 =L= 1;
e20.. x3 - 40*b72 =L= 0;
e21.. x5 - 3.71357206670431*b72 =L= 0;
e22.. -1.2*log(1 + x4) + x6 + b73 =L= 1;
e23.. x4 - 40*b73 =L= 0;
e24.. x6 - 4.45628648004517*b73 =L= 0;
e25.. - 0.75*x10 + x14 + b74 =L= 1;
e26.. - 0.75*x10 + x14 - b74 =G= -1;
e27.. x10 - 4.45628648004517*b74 =L= 0;
e28.. x14 - 3.34221486003388*b74 =L= 0;
e29.. -1.5*log(1 + x11) + x15 + b75 =L= 1;
e30.. x11 - 4.45628648004517*b75 =L= 0;
e31.. x15 - 2.54515263975353*b75 =L= 0;
e32.. - x12 + x16 + b76 =L= 1;
e33.. - x12 + x16 - b76 =G= -1;
e34.. - 0.5*x13 + x16 + b76 =L= 1;
e35.. - 0.5*x13 + x16 - b76 =G= -1;
e36.. x12 - 4.45628648004517*b76 =L= 0;
e37.. x13 - 30*b76 =L= 0;
e38.. x16 - 15*b76 =L= 0;
e39.. -1.25*log(1 + x17) + x22 + b77 =L= 1;
e40.. x17 - 3.34221486003388*b77 =L= 0;
e41.. x22 - 1.83548069293539*b77 =L= 0;
e42.. -0.9*log(1 + x18) + x23 + b78 =L= 1;
e43.. x18 - 3.34221486003388*b78 =L= 0;
e44.. x23 - 1.32154609891348*b78 =L= 0;
e45.. -log(1 + x15) + x24 + b79 =L= 1;
e46.. x15 - 2.54515263975353*b79 =L= 0;
e47.. x24 - 1.26558121681553*b79 =L= 0;
e48.. - 0.9*x19 + x25 + b80 =L= 1;
e49.. - 0.9*x19 + x25 - b80 =G= -1;
e50.. x19 - 15*b80 =L= 0;
e51.. x25 - 13.5*b80 =L= 0;
e52.. - 0.6*x20 + x26 + b81 =L= 1;
e53.. - 0.6*x20 + x26 - b81 =G= -1;
e54.. x20 - 15*b81 =L= 0;
e55.. x26 - 9*b81 =L= 0;
e56.. -1.1*log(1 + x21) + x27 + b82 =L= 1;
e57.. x21 - 15*b82 =L= 0;
e58.. x27 - 3.04984759446376*b82 =L= 0;
e59.. - 0.9*x22 + x38 + b83 =L= 1;
e60.. - 0.9*x22 + x38 - b83 =G= -1;
e61.. - x30 + x38 + b83 =L= 1;
e62.. - x30 + x38 - b83 =G= -1;
e63.. x22 - 1.83548069293539*b83 =L= 0;
e64.. x30 - 20*b83 =L= 0;
e65.. x38 - 20*b83 =L= 0;
e66.. -log(1 + x23) + x39 + b84 =L= 1;
e67.. x23 - 1.32154609891348*b84 =L= 0;
e68.. x39 - 0.842233385663186*b84 =L= 0;
e69.. -0.7*log(1 + x28) + x40 + b85 =L= 1;
e70.. x28 - 1.26558121681553*b85 =L= 0;
e71.. x40 - 0.572481933717686*b85 =L= 0;
e72.. -0.65*log(1 + x29) + x41 + b86 =L= 1;
e73.. -0.65*log(1 + x32) + x41 + b86 =L= 1;
e74.. x29 - 1.26558121681553*b86 =L= 0;
e75.. x32 - 33.5*b86 =L= 0;
e76.. x41 - 2.30162356062425*b86 =L= 0;
e77.. - x33 + x42 + b87 =L= 1;
e78.. - x33 + x42 - b87 =G= -1;
e79.. x33 - 9*b87 =L= 0;
e80.. x42 - 9*b87 =L= 0;
e81.. - x34 + x43 + b88 =L= 1;
e82.. - x34 + x43 - b88 =G= -1;
e83.. x34 - 9*b88 =L= 0;
e84.. x43 - 9*b88 =L= 0;
e85.. -0.75*log(1 + x35) + x44 + b89 =L= 1;
e86.. x35 - 3.04984759446376*b89 =L= 0;
e87.. x44 - 1.04900943706034*b89 =L= 0;
e88.. -0.8*log(1 + x36) + x45 + b90 =L= 1;
e89.. x36 - 3.04984759446376*b90 =L= 0;
e90.. x45 - 1.11894339953103*b90 =L= 0;
e91.. -0.85*log(1 + x37) + x46 + b91 =L= 1;
e92.. x37 - 3.04984759446376*b91 =L= 0;
e93.. x46 - 1.18887736200171*b91 =L= 0;
e94.. -log(1 + x48) + x50 + b92 =L= 1;
e95.. x48 - 1.18887736200171*b92 =L= 0;
e96.. x50 - 0.78338879230327*b92 =L= 0;
e97.. -1.2*log(1 + x49) + x51 + b93 =L= 1;
e98.. x49 - 1.18887736200171*b93 =L= 0;
e99.. x51 - 0.940066550763924*b93 =L= 0;
e100.. - 0.75*x55 + x59 + b94 =L= 1;
e101.. - 0.75*x55 + x59 - b94 =G= -1;
e102.. x55 - 0.940066550763924*b94 =L= 0;
e103.. x59 - 0.705049913072943*b94 =L= 0;
e104.. -1.5*log(1 + x56) + x60 + b95 =L= 1;
e105.. x56 - 0.940066550763924*b95 =L= 0;
e106.. x60 - 0.994083415506506*b95 =L= 0;
e107.. - x57 + x61 + b96 =L= 1;
e108.. - x57 + x61 - b96 =G= -1;
e109.. - 0.5*x58 + x61 + b96 =L= 1;
e110.. - 0.5*x58 + x61 - b96 =G= -1;
e111.. x57 - 0.940066550763924*b96 =L= 0;
e112.. x58 - 30*b96 =L= 0;
e113.. x61 - 15*b96 =L= 0;
e114.. -1.25*log(1 + x62) + x67 + b97 =L= 1;
e115.. x62 - 0.705049913072943*b97 =L= 0;
e116.. x67 - 0.666992981045719*b97 =L= 0;
e117.. -0.9*log(1 + x63) + x68 + b98 =L= 1;
e118.. x63 - 0.705049913072943*b98 =L= 0;
e119.. x68 - 0.480234946352917*b98 =L= 0;
e120.. -log(1 + x60) + x69 + b99 =L= 1;
e121.. x60 - 0.994083415506506*b99 =L= 0;
e122.. x69 - 0.690184503917672*b99 =L= 0;
e123.. - 0.9*x64 + x70 + b100 =L= 1;
e124.. - 0.9*x64 + x70 - b100 =G= -1;
e125.. x64 - 15*b100 =L= 0;
e126.. x70 - 13.5*b100 =L= 0;
e127.. - 0.6*x65 + x71 + b101 =L= 1;
e128.. - 0.6*x65 + x71 - b101 =G= -1;
e129.. x65 - 15*b101 =L= 0;
e130.. x71 - 9*b101 =L= 0;
e131.. b72 + b73 =E= 1;
e132.. - b74 + b77 + b78 =G= 0;
e133.. - b77 + b83 =G= 0;
e134.. - b78 + b84 =G= 0;
e135.. - b75 + b79 =G= 0;
e136.. - b79 + b85 + b86 =G= 0;
e137.. - b76 + b80 + b81 + b82 =G= 0;
e138.. - b80 + b86 =G= 0;
e139.. - b81 + b87 + b88 =G= 0;
e140.. - b82 + b89 + b90 + b91 =G= 0;
e141.. b72 + b73 - b74 =G= 0;
e142.. b72 + b73 - b75 =G= 0;
e143.. b72 + b73 - b76 =G= 0;
e144.. b74 - b77 =G= 0;
e145.. b74 - b78 =G= 0;
e146.. b75 - b79 =G= 0;
e147.. b76 - b80 =G= 0;
e148.. b76 - b81 =G= 0;
e149.. b76 - b82 =G= 0;
e150.. b77 - b83 =G= 0;
e151.. b78 - b84 =G= 0;
e152.. b79 - b85 =G= 0;
e153.. b79 - b86 =G= 0;
e154.. b81 - b87 =G= 0;
e155.. b81 - b88 =G= 0;
e156.. b82 - b89 =G= 0;
e157.. b82 - b90 =G= 0;
e158.. b82 - b91 =G= 0;
e159.. - b91 + b92 + b93 =G= 0;
e160.. - b94 + b97 + b98 =G= 0;
e161.. - b95 + b99 =G= 0;
e162.. b91 - b92 =G= 0;
e163.. b91 - b93 =G= 0;
e164.. b94 - b97 =G= 0;
e165.. b94 - b98 =G= 0;
e166.. b95 - b99 =G= 0;
e167.. b96 - b100 =G= 0;
e168.. b96 - b101 =G= 0;
* set non-default bounds
x2.up = 40;
x13.up = 30;
x30.up = 20;
x31.up = 20;
x58.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: 2024-04-02 Git hash: 1dd5fb9b