MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance syn20m
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ⓘ | 924.82784000 (ALPHAECP) 924.26361410 (ANTIGONE) 924.26331180 (BARON) 924.26331050 (BONMIN) 924.26341520 (COUENNE) 924.26331050 (LINDO) 924.26375390 (SCIP) 924.27069040 (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ⓘ | Syn20M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 65 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 14 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 30 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 113 |
| #Linear Constraintsⓘ | 99 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 14 |
| Operands in Gen. Nonlin. Functionsⓘ | log |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 281 |
| #Nonlinear Nonzeros in Jacobianⓘ | 14 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 14 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 14 |
| #Blocks in Hessian of Lagrangianⓘ | 14 |
| 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ⓘ | 7.0000e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 114 12 36 66 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 66 46 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 312 298 14 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,b47,b48,b49,b50,b51,b52
,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66;
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;
Binary Variables b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61
,b62,b63,b64,b65,b66;
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;
e1.. objvar - 5*x8 - 200*x38 - 250*x39 - 200*x40 - 700*x41 - 400*x42
- 500*x43 - 400*x44 - 600*x45 - 700*x46 + 5*b47 + 8*b48 + 6*b49 + 10*b50
+ 6*b51 + 7*b52 + 4*b53 + 5*b54 + 2*b55 + 4*b56 + 3*b57 + 7*b58 + 3*b59
+ 2*b60 + 4*b61 + 2*b62 + 3*b63 + 5*b64 + 2*b65 + 8*b66 =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.. -log(1 + x3) + x5 + b47 =L= 1;
e13.. x3 - 10*b47 =L= 0;
e14.. x5 - 2.39789527279837*b47 =L= 0;
e15.. -1.2*log(1 + x4) + x6 + b48 =L= 1;
e16.. x4 - 10*b48 =L= 0;
e17.. x6 - 2.87747432735804*b48 =L= 0;
e18.. - 0.75*x10 + x14 + b49 =L= 1;
e19.. - 0.75*x10 + x14 - b49 =G= -1;
e20.. x10 - 2.87747432735804*b49 =L= 0;
e21.. x14 - 2.15810574551853*b49 =L= 0;
e22.. -1.5*log(1 + x11) + x15 + b50 =L= 1;
e23.. x11 - 2.87747432735804*b50 =L= 0;
e24.. x15 - 2.03277599268042*b50 =L= 0;
e25.. - x12 + x16 + b51 =L= 1;
e26.. - x12 + x16 - b51 =G= -1;
e27.. - 0.5*x13 + x16 + b51 =L= 1;
e28.. - 0.5*x13 + x16 - b51 =G= -1;
e29.. x12 - 2.87747432735804*b51 =L= 0;
e30.. x13 - 7*b51 =L= 0;
e31.. x16 - 3.5*b51 =L= 0;
e32.. -1.25*log(1 + x17) + x22 + b52 =L= 1;
e33.. x17 - 2.15810574551853*b52 =L= 0;
e34.. x22 - 1.43746550029693*b52 =L= 0;
e35.. -0.9*log(1 + x18) + x23 + b53 =L= 1;
e36.. x18 - 2.15810574551853*b53 =L= 0;
e37.. x23 - 1.03497516021379*b53 =L= 0;
e38.. -log(1 + x15) + x24 + b54 =L= 1;
e39.. x15 - 2.03277599268042*b54 =L= 0;
e40.. x24 - 1.10947836929589*b54 =L= 0;
e41.. - 0.9*x19 + x25 + b55 =L= 1;
e42.. - 0.9*x19 + x25 - b55 =G= -1;
e43.. x19 - 3.5*b55 =L= 0;
e44.. x25 - 3.15*b55 =L= 0;
e45.. - 0.6*x20 + x26 + b56 =L= 1;
e46.. - 0.6*x20 + x26 - b56 =G= -1;
e47.. x20 - 3.5*b56 =L= 0;
e48.. x26 - 2.1*b56 =L= 0;
e49.. -1.1*log(1 + x21) + x27 + b57 =L= 1;
e50.. x21 - 3.5*b57 =L= 0;
e51.. x27 - 1.6544851364539*b57 =L= 0;
e52.. - 0.9*x22 + x38 + b58 =L= 1;
e53.. - 0.9*x22 + x38 - b58 =G= -1;
e54.. - x30 + x38 + b58 =L= 1;
e55.. - x30 + x38 - b58 =G= -1;
e56.. x22 - 1.43746550029693*b58 =L= 0;
e57.. x30 - 5*b58 =L= 0;
e58.. x38 - 5*b58 =L= 0;
e59.. -log(1 + x23) + x39 + b59 =L= 1;
e60.. x23 - 1.03497516021379*b59 =L= 0;
e61.. x39 - 0.710483612536911*b59 =L= 0;
e62.. -0.7*log(1 + x28) + x40 + b60 =L= 1;
e63.. x28 - 1.10947836929589*b60 =L= 0;
e64.. x40 - 0.522508489006913*b60 =L= 0;
e65.. -0.65*log(1 + x29) + x41 + b61 =L= 1;
e66.. -0.65*log(1 + x32) + x41 + b61 =L= 1;
e67.. x29 - 1.10947836929589*b61 =L= 0;
e68.. x32 - 8.15*b61 =L= 0;
e69.. x41 - 1.43894002153683*b61 =L= 0;
e70.. - x33 + x42 + b62 =L= 1;
e71.. - x33 + x42 - b62 =G= -1;
e72.. x33 - 2.1*b62 =L= 0;
e73.. x42 - 2.1*b62 =L= 0;
e74.. - x34 + x43 + b63 =L= 1;
e75.. - x34 + x43 - b63 =G= -1;
e76.. x34 - 2.1*b63 =L= 0;
e77.. x43 - 2.1*b63 =L= 0;
e78.. -0.75*log(1 + x35) + x44 + b64 =L= 1;
e79.. x35 - 1.6544851364539*b64 =L= 0;
e80.. x44 - 0.732188035236726*b64 =L= 0;
e81.. -0.8*log(1 + x36) + x45 + b65 =L= 1;
e82.. x36 - 1.6544851364539*b65 =L= 0;
e83.. x45 - 0.781000570919175*b65 =L= 0;
e84.. -0.85*log(1 + x37) + x46 + b66 =L= 1;
e85.. x37 - 1.6544851364539*b66 =L= 0;
e86.. x46 - 0.829813106601623*b66 =L= 0;
e87.. b47 + b48 =E= 1;
e88.. - b49 + b52 + b53 =G= 0;
e89.. - b52 + b58 =G= 0;
e90.. - b53 + b59 =G= 0;
e91.. - b50 + b54 =G= 0;
e92.. - b54 + b60 + b61 =G= 0;
e93.. - b51 + b55 + b56 + b57 =G= 0;
e94.. - b55 + b61 =G= 0;
e95.. - b56 + b62 + b63 =G= 0;
e96.. - b57 + b64 + b65 + b66 =G= 0;
e97.. b47 + b48 - b49 =G= 0;
e98.. b47 + b48 - b50 =G= 0;
e99.. b47 + b48 - b51 =G= 0;
e100.. b49 - b52 =G= 0;
e101.. b49 - b53 =G= 0;
e102.. b50 - b54 =G= 0;
e103.. b51 - b55 =G= 0;
e104.. b51 - b56 =G= 0;
e105.. b51 - b57 =G= 0;
e106.. b52 - b58 =G= 0;
e107.. b53 - b59 =G= 0;
e108.. b54 - b60 =G= 0;
e109.. b54 - b61 =G= 0;
e110.. b56 - b62 =G= 0;
e111.. b56 - b63 =G= 0;
e112.. b57 - b64 =G= 0;
e113.. b57 - b65 =G= 0;
e114.. b57 - b66 =G= 0;
* set non-default bounds
x2.up = 10;
x13.up = 7;
x30.up = 5;
x31.up = 5;
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