MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance heatexch_spec2
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 634977.82770000 (ANTIGONE) 634978.00000000 (BARON) 627798.51140000 (COUENNE) 634973.22300000 (LINDO) 634977.72360000 (SCIP) 6.32995381 (SHOT) |
| Referencesⓘ | Escobar, Marcelo and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for Optimal Simultaneous Synthesis of Heat Exchangers Network, 2010. |
| Sourceⓘ | Specilized_Model_Case2_NLP_Improvement.gms from minlp.org model 93 |
| Applicationⓘ | Heat Exchanger Network |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 76 |
| #Binary Variablesⓘ | 16 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 42 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 58 |
| #Nonlinear Nonzeros in Objectiveⓘ | 42 |
| #Constraintsⓘ | 90 |
| #Linear Constraintsⓘ | 90 |
| #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ⓘ | 242 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 114 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 42 |
| #Blocks in Hessian of Lagrangianⓘ | 16 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 5 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.625 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-06 |
| Maximal coefficientⓘ | 6.6600e+03 |
| Infeasibility of initial pointⓘ | 6660 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 91 31 18 42 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 77 61 16 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 301 259 42 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,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,x72,x73,x74,x75,x76,objvar;
Positive Variables x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48
,x49,x50,x51,x52,x53,x54,x55;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16;
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;
e1.. 6*x17 - 6*x18 - x35 =E= 0;
e2.. 6*x18 - 6*x19 - x36 =E= 0;
e3.. 4*x20 - 4*x21 - x38 =E= 0;
e4.. 4*x21 - 4*x22 - x39 =E= 0;
e5.. 6*x23 - 6*x24 - x41 =E= 0;
e6.. 6*x24 - 6*x25 - x42 =E= 0;
e7.. 20*x26 - 20*x27 - x44 =E= 0;
e8.. 20*x27 - 20*x28 - x45 =E= 0;
e9.. 12*x29 - 12*x30 - x47 =E= 0;
e10.. 12*x30 - 12*x31 - x48 =E= 0;
e11.. 18*x32 - 18*x33 - x35 - x38 - x41 - x44 - x47 =E= 0;
e12.. 18*x33 - 18*x34 - x36 - x39 - x42 - x45 - x48 =E= 0;
e13.. 6*x19 - x50 =E= 1920;
e14.. 4*x22 - x51 =E= 1520;
e15.. 6*x25 - x52 =E= 2160;
e16.. 20*x28 - x53 =E= 7200;
e17.. 12*x31 - x54 =E= 3840;
e18.. - x35 - x36 - x50 =E= -1080;
e19.. - x38 - x39 - x51 =E= -400;
e20.. - x41 - x42 - x52 =E= -600;
e21.. - x44 - x45 - x53 =E= -400;
e22.. - x47 - x48 - x54 =E= -720;
e23.. - 18*x32 - x55 =E= -11880;
e24.. - x35 - x36 - x38 - x39 - x41 - x42 - x44 - x45 - x47 - x48 - x55
=E= -6660;
e25.. x17 - x18 =G= 0;
e26.. x18 - x19 =G= 0;
e27.. x20 - x21 =G= 0;
e28.. x21 - x22 =G= 0;
e29.. x23 - x24 =G= 0;
e30.. x24 - x25 =G= 0;
e31.. x26 - x27 =G= 0;
e32.. x27 - x28 =G= 0;
e33.. x29 - x30 =G= 0;
e34.. x30 - x31 =G= 0;
e35.. x32 - x33 =G= 0;
e36.. x33 - x34 =G= 0;
e37.. x19 =G= 320;
e38.. x22 =G= 380;
e39.. x25 =G= 360;
e40.. x28 =G= 360;
e41.. x31 =G= 320;
e42.. - x32 =G= -660;
e43.. - x17 =E= -500;
e44.. - x20 =E= -480;
e45.. - x23 =E= -460;
e46.. - x26 =E= -380;
e47.. - x29 =E= -380;
e48.. - x34 =E= -290;
e49.. - 1080*b1 + x35 =L= 0;
e50.. - 1080*b2 + x36 =L= 0;
e51.. - 400*b3 + x38 =L= 0;
e52.. - 400*b4 + x39 =L= 0;
e53.. - 600*b5 + x41 =L= 0;
e54.. - 600*b6 + x42 =L= 0;
e55.. - 400*b7 + x44 =L= 0;
e56.. - 400*b8 + x45 =L= 0;
e57.. - 720*b9 + x47 =L= 0;
e58.. - 720*b10 + x48 =L= 0;
e59.. - 6660*b16 + x55 =L= 0;
e60.. - 1080*b11 + x50 =L= 0;
e61.. - 400*b12 + x51 =L= 0;
e62.. - 600*b13 + x52 =L= 0;
e63.. - 400*b14 + x53 =L= 0;
e64.. - 720*b15 + x54 =L= 0;
e65.. 340*b1 - x17 + x32 + x56 =L= 340;
e66.. 340*b2 - x18 + x33 + x57 =L= 340;
e67.. 280*b3 - x20 + x32 + x59 =L= 280;
e68.. 280*b4 - x21 + x33 + x60 =L= 280;
e69.. 300*b5 - x23 + x32 + x62 =L= 300;
e70.. 300*b6 - x24 + x33 + x63 =L= 300;
e71.. 300*b7 - x26 + x32 + x65 =L= 300;
e72.. 300*b8 - x27 + x33 + x66 =L= 300;
e73.. 340*b9 - x29 + x32 + x68 =L= 340;
e74.. 340*b10 - x30 + x33 + x69 =L= 340;
e75.. 340*b1 - x18 + x33 + x57 =L= 340;
e76.. 340*b2 - x19 + x34 + x58 =L= 340;
e77.. 280*b3 - x21 + x33 + x60 =L= 280;
e78.. 280*b4 - x22 + x34 + x61 =L= 280;
e79.. 300*b5 - x24 + x33 + x63 =L= 300;
e80.. 300*b6 - x25 + x34 + x64 =L= 300;
e81.. 300*b7 - x27 + x33 + x66 =L= 300;
e82.. 300*b8 - x28 + x34 + x67 =L= 300;
e83.. 340*b9 - x30 + x33 + x69 =L= 340;
e84.. 340*b10 - x31 + x34 + x70 =L= 340;
e85.. - x19 + x71 =L= -320;
e86.. - x22 + x72 =L= -320;
e87.. - x25 + x73 =L= -320;
e88.. - x28 + x74 =L= -320;
e89.. - x31 + x75 =L= -320;
e90.. x32 + x76 =L= 700;
e91.. -(1200*((1e-6 + x35/(1e-6 + (1e-6 + 0.5*x56*x57*(x56 + x57))**0.33333))**
0.6 + (1e-6 + x36/(1e-6 + (1e-6 + 0.5*x57*x58*(x57 + x58))**0.33333))**
0.6 + (1e-6 + 99.9853968566039*x37)**0.6 + (1e-6 + x38/(1e-6 + (1e-6 +
0.5*x59*x60*(x59 + x60))**0.33333))**0.6 + (1e-6 + x39/(1e-6 + (1e-6 +
0.5*x60*x61*(x60 + x61))**0.33333))**0.6 + (1e-6 + 99.9853968566039*x40)
**0.6 + (1e-6 + x41/(1e-6 + (1e-6 + 0.5*x62*x63*(x62 + x63))**0.33333))**
0.6 + (1e-6 + x42/(1e-6 + (1e-6 + 0.5*x63*x64*(x63 + x64))**0.33333))**
0.6 + (1e-6 + 99.9853968566039*x43)**0.6 + (1e-6 + x44/(1e-6 + (1e-6 +
0.5*x65*x66*(x65 + x66))**0.33333))**0.6 + (1e-6 + x45/(1e-6 + (1e-6 +
0.5*x66*x67*(x66 + x67))**0.33333))**0.6 + (1e-6 + 99.9853968566039*x46)
**0.6 + (1e-6 + x47/(1e-6 + (1e-6 + 0.5*x68*x69*(x68 + x69))**0.33333))**
0.6 + (1e-6 + x48/(1e-6 + (1e-6 + 0.5*x69*x70*(x69 + x70))**0.33333))**
0.6 + (1e-6 + 99.9853968566039*x49)**0.6) + 1200*(1e-6 + x55/(1e-6 + 40*
x76*(20 + 0.5*x76))**0.33333)**0.6 + 140*x55 + 1200*((1e-6 + x50/(1e-6 +
10*x71*(20 + x71))**0.33333)**0.6 + (1e-6 + x51/(1e-6 + 40*x72*(80 + x72)
)**0.33333)**0.6 + (1e-6 + x52/(1e-6 + 30*x73*(60 + x73))**0.33333)**0.6
+ (1e-6 + x53/(1e-6 + 30*x74*(60 + x74))**0.33333)**0.6 + (1e-6 + x54/(
1e-6 + 10*x75*(20 + x75))**0.33333)**0.6) + 10*x50 + 10*x51 + 10*x52 + 10
*x53 + 10*x54) - 5500*b1 - 5500*b2 - 5500*b3 - 5500*b4 - 5500*b5
- 5500*b6 - 5500*b7 - 5500*b8 - 5500*b9 - 5500*b10 - 5500*b11 - 5500*b12
- 5500*b13 - 5500*b14 - 5500*b15 - 5500*b16 + objvar =E= 0;
* set non-default bounds
x17.lo = 320; x17.up = 500;
x18.lo = 320; x18.up = 500;
x19.lo = 320; x19.up = 500;
x20.lo = 380; x20.up = 480;
x21.lo = 380; x21.up = 480;
x22.lo = 380; x22.up = 480;
x23.lo = 360; x23.up = 460;
x24.lo = 360; x24.up = 460;
x25.lo = 360; x25.up = 460;
x26.lo = 360; x26.up = 380;
x27.lo = 360; x27.up = 380;
x28.lo = 360; x28.up = 380;
x29.lo = 320; x29.up = 380;
x30.lo = 320; x30.up = 380;
x31.lo = 320; x31.up = 380;
x32.lo = 290; x32.up = 660;
x33.lo = 290; x33.up = 660;
x34.lo = 290; x34.up = 660;
x56.lo = 10;
x57.lo = 10;
x58.lo = 10;
x59.lo = 10;
x60.lo = 10;
x61.lo = 10;
x62.lo = 10;
x63.lo = 10;
x64.lo = 10;
x65.lo = 10;
x66.lo = 10;
x67.lo = 10;
x68.lo = 10;
x69.lo = 10;
x70.lo = 10;
x71.lo = 10;
x72.lo = 10;
x73.lo = 10;
x74.lo = 10;
x75.lo = 10;
x76.lo = 10;
* set non-default levels
x17.l = 500;
x18.l = 500;
x19.l = 500;
x20.l = 480;
x21.l = 480;
x22.l = 480;
x23.l = 460;
x24.l = 460;
x25.l = 460;
x26.l = 380;
x27.l = 380;
x28.l = 380;
x29.l = 380;
x30.l = 380;
x31.l = 380;
x35.l = 1080;
x36.l = 1080;
x38.l = 400;
x39.l = 400;
x41.l = 600;
x42.l = 600;
x44.l = 400;
x45.l = 400;
x47.l = 720;
x48.l = 720;
x56.l = 210;
x57.l = 210;
x58.l = 210;
x59.l = 190;
x60.l = 190;
x61.l = 190;
x62.l = 170;
x63.l = 170;
x64.l = 170;
x65.l = 90;
x66.l = 90;
x67.l = 90;
x68.l = 90;
x69.l = 90;
x70.l = 90;
x71.l = 180;
x72.l = 160;
x73.l = 140;
x74.l = 60;
x75.l = 60;
x76.l = 410;
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