MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance synheat
This MINLPLib instance is generated from a GAMS model library model before GAMS 51.1.0. A bugfix to synheat from GAMS 51.1.0 has not been applied here. It would have no effect on the optimal value either.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 131503.1595 (ANTIGONE) 154997.3349 (BARON) 145371.5918 (COUENNE) 154993.8736 (GUROBI) 154961.2314 (LINDO) 154402.3342 (SCIP) 0. (SHOT) 151108.4843 (XPRESS) |
| Referencesⓘ | Yee, Terrence F and Grossmann, I E, Simultaneous Optimization of Models for Heat Integration - II. Heat Exchanger Network Synthesis, Computers and Chemical Engineering, 14:10, 1990, 1165-1184. |
| Sourceⓘ | GAMS Model Library model synheat |
| Applicationⓘ | Simultaneous Optimization for HEN Synthesis |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 56 |
| #Binary Variablesⓘ | 12 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 28 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 44 |
| #Nonlinear Nonzeros in Objectiveⓘ | 28 |
| #Constraintsⓘ | 64 |
| #Linear Constraintsⓘ | 64 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul vcpower |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 180 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 72 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 16 |
| #Blocks in Hessian of Lagrangianⓘ | 8 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 5 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-06 |
| Maximal coefficientⓘ | 2.9996e+04 |
| Infeasibility of initial pointⓘ | 9200 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 65 21 12 32 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 57 45 12 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 225 197 28 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,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,objvar;
Positive Variables x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38
,x39,x40;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12;
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;
e1.. 10*x13 - 10*x14 - x25 - x28 =E= 0;
e2.. 10*x14 - 10*x15 - x26 - x29 =E= 0;
e3.. 20*x16 - 20*x17 - x31 - x34 =E= 0;
e4.. 20*x17 - 20*x18 - x32 - x35 =E= 0;
e5.. 10*x15 - x37 =E= 3700;
e6.. 20*x18 - x38 =E= 7400;
e7.. - x25 - x26 - x28 - x29 - x37 =E= -2800;
e8.. - x31 - x32 - x34 - x35 - x38 =E= -4400;
e9.. 15*x19 - 15*x20 - x25 - x31 =E= 0;
e10.. 15*x20 - 15*x21 - x26 - x32 =E= 0;
e11.. 13*x22 - 13*x23 - x28 - x34 =E= 0;
e12.. 13*x23 - 13*x24 - x29 - x35 =E= 0;
e13.. - 15*x19 - x39 =E= -9750;
e14.. - 13*x22 - x40 =E= -6500;
e15.. - x25 - x26 - x31 - x32 - x39 =E= -3600;
e16.. - x28 - x29 - x34 - x35 - x40 =E= -1950;
e17.. x13 - x14 =G= 0;
e18.. x14 - x15 =G= 0;
e19.. x16 - x17 =G= 0;
e20.. x17 - x18 =G= 0;
e21.. x19 - x20 =G= 0;
e22.. x20 - x21 =G= 0;
e23.. x22 - x23 =G= 0;
e24.. x23 - x24 =G= 0;
e25.. x15 =G= 370;
e26.. x18 =G= 370;
e27.. - x19 =G= -650;
e28.. - x22 =G= -500;
e29.. - x13 =E= -650;
e30.. - x16 =E= -590;
e31.. - x21 =E= -410;
e32.. - x24 =E= -350;
e33.. - 2800*b1 + x25 =L= 0;
e34.. - 2800*b2 + x26 =L= 0;
e35.. - 1950*b3 + x28 =L= 0;
e36.. - 1950*b4 + x29 =L= 0;
e37.. - 3600*b5 + x31 =L= 0;
e38.. - 3600*b6 + x32 =L= 0;
e39.. - 1950*b7 + x34 =L= 0;
e40.. - 1950*b8 + x35 =L= 0;
e41.. - 3600*b11 + x39 =L= 0;
e42.. - 1950*b12 + x40 =L= 0;
e43.. - 2800*b9 + x37 =L= 0;
e44.. - 4400*b10 + x38 =L= 0;
e45.. 280*b1 - x13 + x19 + x41 =L= 280;
e46.. 280*b2 - x14 + x20 + x42 =L= 280;
e47.. 130*b3 - x13 + x22 + x44 =L= 130;
e48.. 130*b4 - x14 + x23 + x45 =L= 130;
e49.. 280*b5 - x16 + x19 + x47 =L= 280;
e50.. 280*b6 - x17 + x20 + x48 =L= 280;
e51.. 130*b7 - x16 + x22 + x50 =L= 130;
e52.. 130*b8 - x17 + x23 + x51 =L= 130;
e53.. 280*b1 - x14 + x20 + x42 =L= 280;
e54.. 280*b2 - x15 + x21 + x43 =L= 280;
e55.. 130*b3 - x14 + x23 + x45 =L= 130;
e56.. 130*b4 - x15 + x24 + x46 =L= 130;
e57.. 280*b5 - x17 + x20 + x48 =L= 280;
e58.. 280*b6 - x18 + x21 + x49 =L= 280;
e59.. 130*b7 - x17 + x23 + x51 =L= 130;
e60.. 130*b8 - x18 + x24 + x52 =L= 130;
e61.. - x15 + x53 =L= -320;
e62.. - x18 + x54 =L= -320;
e63.. x19 + x55 =L= 680;
e64.. x22 + x56 =L= 680;
e65.. -(150*(2*x25/(1e-6 + (1e-6 + 0.5*x41*x42*(x41 + x42))**0.33333) + 2*x26/(
1e-6 + (1e-6 + 0.5*x42*x43*(x42 + x43))**0.33333) + 2*x28/(1e-6 + (1e-6
+ 0.5*x44*x45*(x44 + x45))**0.33333) + 2*x29/(1e-6 + (1e-6 + 0.5*x45*x46
*(x45 + x46))**0.33333) + 2*x31/(1e-6 + (1e-6 + 0.5*x47*x48*(x47 + x48))
**0.33333) + 2*x32/(1e-6 + (1e-6 + 0.5*x48*x49*(x48 + x49))**0.33333) + 2
*x34/(1e-6 + (1e-6 + 0.5*x50*x51*(x50 + x51))**0.33333) + 2*x35/(1e-6 + (
1e-6 + 0.5*x51*x52*(x51 + x52))**0.33333)) + 150*(1.2*x39/(1e-6 + 30*x55*
(15 + 0.5*x55))**0.33333 + 1.2*x40/(1e-6 + 180*x56*(90 + 0.5*x56))**
0.33333) + 150*(2*x37/(1e-6 + 35*x53*(70 + x53))**0.33333 + 2*x38/(1e-6
+ 35*x54*(70 + x54))**0.33333) + 80*x39 + 80*x40 + 15*x37 + 15*x38)
- 5500*b1 - 5500*b2 - 5500*b3 - 5500*b4 - 5500*b5 - 5500*b6 - 5500*b7
- 5500*b8 - 5500*b9 - 5500*b10 - 5500*b11 - 5500*b12
- 29995.6190569812*x27 - 29995.6190569812*x30 - 29995.6190569812*x33
- 29995.6190569812*x36 + objvar =E= 0.0024;
* set non-default bounds
x13.lo = 370; x13.up = 650;
x14.lo = 370; x14.up = 650;
x15.lo = 370; x15.up = 650;
x16.lo = 370; x16.up = 590;
x17.lo = 370; x17.up = 590;
x18.lo = 370; x18.up = 590;
x19.lo = 410; x19.up = 650;
x20.lo = 410; x20.up = 650;
x21.lo = 410; x21.up = 650;
x22.lo = 350; x22.up = 500;
x23.lo = 350; x23.up = 500;
x24.lo = 350; x24.up = 500;
x41.lo = 10;
x42.lo = 10;
x43.lo = 10;
x44.lo = 10;
x45.lo = 10;
x46.lo = 10;
x47.lo = 10;
x48.lo = 10;
x49.lo = 10;
x50.lo = 10;
x51.lo = 10;
x52.lo = 10;
x53.lo = 10;
x54.lo = 10;
x55.lo = 10;
x56.lo = 10;
* set non-default levels
x25.l = 2800;
x26.l = 2800;
x28.l = 1950;
x29.l = 1950;
x31.l = 3600;
x32.l = 3600;
x34.l = 1950;
x35.l = 1950;
x41.l = 240;
x42.l = 240;
x43.l = 240;
x44.l = 300;
x45.l = 300;
x46.l = 300;
x47.l = 180;
x48.l = 180;
x49.l = 180;
x50.l = 240;
x51.l = 240;
x52.l = 240;
x53.l = 330;
x54.l = 270;
x55.l = 270;
x56.l = 330;
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% minimizing objvar;
Last updated: 2026-09-14 Git hash: 9472b011