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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance syn05hfsg
Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. Equivalent perspective reformulation of syn05.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 837.73240090 (ALPHAECP) 837.73240170 (ANTIGONE) 837.73240170 (BARON) 837.73240090 (BONMIN) 837.73240090 (COUENNE) 837.73240100 (LINDO) 837.73240090 (SCIP) 1335.92639900 (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. Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019. |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 25 Sep 2019 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 42 |
| #Binary Variablesⓘ | 5 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 3 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 10 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 58 |
| #Linear Constraintsⓘ | 55 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 3 |
| Operands in Gen. Nonlin. Functionsⓘ | div log mul |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 127 |
| #Nonlinear Nonzeros in Jacobianⓘ | 9 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 18 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 3.0000e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 59 31 3 25 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 43 38 5 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 138 129 9 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,b39,b40,b41,b42,b43;
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;
Binary Variables b39,b40,b41,b42,b43;
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;
e1.. objvar - 5*x8 + 2*x13 - 200*x14 - 250*x15 - 300*x16 + 5*b39 + 8*b40
+ 6*b41 + 10*b42 + 6*b43 =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.. (x21/(0.001 + 0.999*b39) - log(1 + x17/(0.001 + 0.999*b39)))*(0.001 +
0.999*b39) =L= 0;
e7.. x18 =E= 0;
e8.. x22 =E= 0;
e9.. x3 - x17 - x18 =E= 0;
e10.. x5 - x21 - x22 =E= 0;
e11.. x17 - 10*b39 =L= 0;
e12.. x18 + 10*b39 =L= 10;
e13.. x21 - 2.39789527279837*b39 =L= 0;
e14.. x22 + 2.39789527279837*b39 =L= 2.39789527279837;
e15.. (x23/(0.001 + 0.999*b40) - 1.2*log(1 + x19/(0.001 + 0.999*b40)))*(0.001
+ 0.999*b40) =L= 0;
e16.. x20 =E= 0;
e17.. x24 =E= 0;
e18.. x4 - x19 - x20 =E= 0;
e19.. x6 - x23 - x24 =E= 0;
e20.. x19 - 10*b40 =L= 0;
e21.. x20 + 10*b40 =L= 10;
e22.. x23 - 2.87747432735804*b40 =L= 0;
e23.. x24 + 2.87747432735804*b40 =L= 2.87747432735804;
e24.. - 0.75*x25 + x33 =E= 0;
e25.. x26 =E= 0;
e26.. x34 =E= 0;
e27.. x10 - x25 - x26 =E= 0;
e28.. x14 - x33 - x34 =E= 0;
e29.. x25 - 2.87747432735804*b41 =L= 0;
e30.. x26 + 2.87747432735804*b41 =L= 2.87747432735804;
e31.. x33 - 2.15810574551853*b41 =L= 0;
e32.. x34 + 2.15810574551853*b41 =L= 2.15810574551853;
e33.. (x35/(0.001 + 0.999*b42) - 1.5*log(1 + x27/(0.001 + 0.999*b42)))*(0.001
+ 0.999*b42) =L= 0;
e34.. x28 =E= 0;
e35.. x36 =E= 0;
e36.. x11 - x27 - x28 =E= 0;
e37.. x15 - x35 - x36 =E= 0;
e38.. x27 - 2.87747432735804*b42 =L= 0;
e39.. x28 + 2.87747432735804*b42 =L= 2.87747432735804;
e40.. x35 - 2.03277599268042*b42 =L= 0;
e41.. x36 + 2.03277599268042*b42 =L= 2.03277599268042;
e42.. - x29 + x37 =E= 0;
e43.. - 0.5*x31 + x37 =E= 0;
e44.. x30 =E= 0;
e45.. x32 =E= 0;
e46.. x38 =E= 0;
e47.. x12 - x29 - x30 =E= 0;
e48.. x13 - x31 - x32 =E= 0;
e49.. x16 - x37 - x38 =E= 0;
e50.. x29 - 2.87747432735804*b43 =L= 0;
e51.. x30 + 2.87747432735804*b43 =L= 2.87747432735804;
e52.. x31 - 7*b43 =L= 0;
e53.. x32 + 7*b43 =L= 7;
e54.. x37 - 3.5*b43 =L= 0;
e55.. x38 + 3.5*b43 =L= 3.5;
e56.. b39 + b40 =E= 1;
e57.. b39 + b40 - b41 =G= 0;
e58.. b39 + b40 - b42 =G= 0;
e59.. b39 + b40 - b43 =G= 0;
* set non-default bounds
x2.up = 10;
x13.up = 7;
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