MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1233
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 149694.48460000 (ANTIGONE) 155010.67130000 (BARON) 147870.62200000 (COUENNE) 153461.75500000 (GUROBI) 154969.44160000 (LINDO) 155010.53480000 (SCIP) 0.00000000 (SHOT) 150260.94680000 (XPRESS) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. 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ⓘ | Test Problem ex12.3.3 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Simultaneous Optimization for HEN Synthesis |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 52 |
| #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ⓘ | 40 |
| #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ⓘ | 3.3330e-01 |
| Maximal coefficientⓘ | 5.5000e+03 |
| Infeasibility of initial pointⓘ | 4400 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 65 21 0 44 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 53 41 12 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 221 193 28 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,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,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52
,objvar;
Positive Variables x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24;
Binary Variables b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52;
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.. -(300*x13/(0.5*x25*x26*(x25 + x26))**0.3333 + 300*x14/(0.5*x26*x27*(x26 +
x27))**0.3333 + 300*x15/(0.5*x28*x29*(x28 + x29))**0.3333 + 300*x16/(0.5*
x29*x30*(x29 + x30))**0.3333 + 300*x17/(0.5*x31*x32*(x31 + x32))**0.3333
+ 300*x18/(0.5*x32*x33*(x32 + x33))**0.3333 + 300*x19/(0.5*x34*x35*(x34
+ x35))**0.3333 + 300*x20/(0.5*x35*x36*(x35 + x36))**0.3333 + 300*x21/(35
*x37*(70 + x37))**0.33333 + 300*x22/(35*x38*(70 + x38))**0.33333 + 180*x23
/(15*x39*(30 + x39))**0.33333 + 180*x24/(90*x40*(180 + x40))**0.33333 + 80
*x23 + 80*x24 + 15*x21 + 15*x22) - 5500*b41 - 5500*b42 - 5500*b43
- 5500*b44 - 5500*b45 - 5500*b46 - 5500*b47 - 5500*b48 - 5500*b49
- 5500*b50 - 5500*b51 - 5500*b52 + objvar =E= 0;
e2.. x13 + x14 + x15 + x16 + x21 =E= 2800;
e3.. x17 + x18 + x19 + x20 + x22 =E= 4400;
e4.. x13 + x14 + x17 + x18 + x23 =E= 3600;
e5.. x15 + x16 + x19 + x20 + x24 =E= 1950;
e6.. 10*x1 - 10*x2 - x13 - x15 =E= 0;
e7.. 10*x2 - 10*x3 - x14 - x16 =E= 0;
e8.. 20*x4 - 20*x5 - x17 - x19 =E= 0;
e9.. 20*x5 - 20*x6 - x18 - x20 =E= 0;
e10.. 15*x7 - 15*x8 - x13 - x17 =E= 0;
e11.. 15*x8 - 15*x9 - x14 - x18 =E= 0;
e12.. 13*x10 - 13*x11 - x15 - x19 =E= 0;
e13.. 13*x11 - 13*x12 - x16 - x20 =E= 0;
e14.. x1 =E= 650;
e15.. x4 =E= 590;
e16.. x9 =E= 410;
e17.. x12 =E= 350;
e18.. - x1 + x2 =L= 0;
e19.. - x2 + x3 =L= 0;
e20.. - x4 + x5 =L= 0;
e21.. - x5 + x6 =L= 0;
e22.. - x7 + x8 =L= 0;
e23.. - x8 + x9 =L= 0;
e24.. - x10 + x11 =L= 0;
e25.. - x11 + x12 =L= 0;
e26.. - x3 =L= -370;
e27.. - x6 =L= -370;
e28.. x7 =L= 650;
e29.. x10 =L= 500;
e30.. 10*x3 - x21 =E= 3700;
e31.. 20*x6 - x22 =E= 7400;
e32.. 15*x7 + x23 =E= 9750;
e33.. 13*x10 + x24 =E= 6500;
e34.. x13 - 2800*b41 =L= 0;
e35.. x14 - 2800*b42 =L= 0;
e36.. x15 - 1950*b43 =L= 0;
e37.. x16 - 1950*b44 =L= 0;
e38.. x17 - 3600*b45 =L= 0;
e39.. x18 - 3600*b46 =L= 0;
e40.. x19 - 1950*b47 =L= 0;
e41.. x20 - 1950*b48 =L= 0;
e42.. x21 - 2800*b49 =L= 0;
e43.. x22 - 4400*b50 =L= 0;
e44.. x23 - 3600*b51 =L= 0;
e45.. x24 - 1950*b52 =L= 0;
e46.. - x1 + x7 + x25 + 280*b41 =L= 280;
e47.. - x2 + x8 + x26 + 130*b42 =L= 130;
e48.. - x1 + x10 + x28 + 280*b43 =L= 280;
e49.. - x2 + x11 + x29 + 150*b44 =L= 150;
e50.. - x4 + x7 + x31 + 280*b45 =L= 280;
e51.. - x5 + x8 + x32 + 130*b46 =L= 130;
e52.. - x4 + x10 + x34 + 280*b47 =L= 280;
e53.. - x5 + x11 + x35 + 150*b48 =L= 150;
e54.. - x2 + x8 + x26 + 280*b41 =L= 280;
e55.. - x3 + x9 + x27 + 130*b42 =L= 130;
e56.. - x2 + x11 + x29 + 280*b43 =L= 280;
e57.. - x3 + x12 + x30 + 150*b44 =L= 150;
e58.. - x5 + x8 + x32 + 280*b45 =L= 280;
e59.. - x6 + x9 + x33 + 130*b46 =L= 130;
e60.. - x5 + x11 + x35 + 280*b47 =L= 280;
e61.. - x6 + x12 + x36 + 150*b48 =L= 150;
e62.. - x3 + x37 =L= -320;
e63.. - x6 + x38 =L= -320;
e64.. x7 + x39 =L= 680;
e65.. x10 + x40 =L= 680;
* set non-default bounds
x1.lo = 370; x1.up = 650;
x2.lo = 370; x2.up = 650;
x3.lo = 370; x3.up = 650;
x4.lo = 370; x4.up = 590;
x5.lo = 370; x5.up = 590;
x6.lo = 370; x6.up = 590;
x7.lo = 410; x7.up = 650;
x8.lo = 410; x8.up = 650;
x9.lo = 410; x9.up = 650;
x10.lo = 350; x10.up = 500;
x11.lo = 350; x11.up = 500;
x12.lo = 350; x12.up = 500;
x25.lo = 10;
x26.lo = 10;
x27.lo = 10;
x28.lo = 10;
x29.lo = 10;
x30.lo = 10;
x31.lo = 10;
x32.lo = 10;
x33.lo = 10;
x34.lo = 10;
x35.lo = 10;
x36.lo = 10;
x37.lo = 10;
x38.lo = 10;
x39.lo = 10;
x40.lo = 10;
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: 2025-08-07 Git hash: e62cedfc