MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1243
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 83402.50633000 (ANTIGONE) 83402.50633000 (BARON) 83402.50638000 (COUENNE) 83402.50641000 (LINDO) 83402.50641000 (SCIP) 0.00000000 (SHOT) |
| 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. Zamora, Juan and Grossmann, I E, A Global MINLP Optimization Algorithm for the Synthesis of Heat Exchanger Networks with No Stream Splits, Computers and Chemical Engineering, 22:3, 1998, 367-384. |
| Sourceⓘ | Test Problem ex12.4.3 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Simultaneous Optimization for HEN Synthesis |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 68 |
| #Binary Variablesⓘ | 16 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 36 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 52 |
| #Nonlinear Nonzeros in Objectiveⓘ | 36 |
| #Constraintsⓘ | 96 |
| #Linear Constraintsⓘ | 96 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 276 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 100 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #Blocks in Hessian of Lagrangianⓘ | 8 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 4.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 6.2500e+03 |
| Infeasibility of initial pointⓘ | 3300 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 97 25 0 72 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 69 53 16 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 329 293 36 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,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,objvar;
Positive Variables x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30
,x31,x32;
Binary Variables b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67
,b68;
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;
e1.. -(208.15*x17/(x33 + x34) + 208.15*x18/(x34 + x35) + 208.15*x19/(x35 + x36)
+ 208.15*x20/(x37 + x38) + 208.15*x21/(x38 + x39) + 208.15*x22/(x39 + x40
) + 208.15*x23/(x41 + x42) + 208.15*x24/(x42 + x43) + 208.15*x25/(x43 +
x44) + 208.15*x26/(x45 + x46) + 208.15*x27/(x46 + x47) + 208.15*x28/(x47
+ x48) + 208.15*x29/(40 + x49) + 208.15*x30/(10 + x50) + 166.516666666667
*x31/(42 + x51) + 166.516666666667*x32/(37 + x52) + 80*x31 + 80*x32 + 20*
x29 + 20*x30) - 6250*b53 - 6250*b54 - 6250*b55 - 6250*b56 - 6250*b57
- 6250*b58 - 6250*b59 - 6250*b60 - 6250*b61 - 6250*b62 - 6250*b63
- 6250*b64 - 6250*b65 - 6250*b66 - 6250*b67 - 6250*b68 + objvar =E= 0;
e2.. x17 + x18 + x19 + x20 + x21 + x22 + x29 =E= 3300;
e3.. x23 + x24 + x25 + x26 + x27 + x28 + x30 =E= 1800;
e4.. x17 + x18 + x19 + x23 + x24 + x25 + x31 =E= 2300;
e5.. x20 + x21 + x22 + x26 + x27 + x28 + x32 =E= 2400;
e6.. 30*x1 - 30*x2 - x17 - x20 =E= 0;
e7.. 30*x2 - 30*x3 - x18 - x21 =E= 0;
e8.. 30*x3 - 30*x4 - x19 - x22 =E= 0;
e9.. 15*x5 - 15*x6 - x23 - x26 =E= 0;
e10.. 15*x6 - 15*x7 - x24 - x27 =E= 0;
e11.. 15*x7 - 15*x8 - x25 - x28 =E= 0;
e12.. 20*x9 - 20*x10 - x17 - x23 =E= 0;
e13.. 20*x10 - 20*x11 - x18 - x24 =E= 0;
e14.. 20*x11 - 20*x12 - x19 - x25 =E= 0;
e15.. 40*x13 - 40*x14 - x20 - x26 =E= 0;
e16.. 40*x14 - 40*x15 - x21 - x27 =E= 0;
e17.. 40*x15 - 40*x16 - x22 - x28 =E= 0;
e18.. x1 =E= 443;
e19.. x5 =E= 423;
e20.. x11 =E= 293;
e21.. x15 =E= 353;
e22.. - x1 + x2 =L= 0;
e23.. - x2 + x3 =L= 0;
e24.. - x3 + x4 =L= 0;
e25.. - x5 + x6 =L= 0;
e26.. - x6 + x7 =L= 0;
e27.. - x7 + x8 =L= 0;
e28.. - x9 + x10 =L= 0;
e29.. - x10 + x11 =L= 0;
e30.. - x11 + x12 =L= 0;
e31.. - x13 + x14 =L= 0;
e32.. - x14 + x15 =L= 0;
e33.. - x15 + x16 =L= 0;
e34.. - x3 =L= -333;
e35.. - x7 =L= -303;
e36.. x9 =L= 408;
e37.. x13 =L= 413;
e38.. 30*x3 - x29 =E= 9990;
e39.. 15*x7 - x30 =E= 4545;
e40.. 20*x9 + x31 =E= 8160;
e41.. 40*x13 + x32 =E= 16520;
e42.. x17 - 2300*b53 =L= 0;
e43.. x18 - 2300*b54 =L= 0;
e44.. x19 - 2300*b55 =L= 0;
e45.. x20 - 2400*b56 =L= 0;
e46.. x21 - 2400*b57 =L= 0;
e47.. x22 - 2400*b58 =L= 0;
e48.. x23 - 1800*b59 =L= 0;
e49.. x24 - 1800*b60 =L= 0;
e50.. x25 - 1800*b61 =L= 0;
e51.. x26 - 1800*b62 =L= 0;
e52.. x27 - 1800*b63 =L= 0;
e53.. x28 - 1800*b64 =L= 0;
e54.. x29 - 3300*b65 =L= 0;
e55.. x30 - 1800*b66 =L= 0;
e56.. x31 - 2300*b67 =L= 0;
e57.. x32 - 2400*b68 =L= 0;
e58.. - x1 + x9 + x33 + 150*b53 =L= 150;
e59.. - x2 + x10 + x34 + 150*b54 =L= 150;
e60.. - x3 + x11 + x35 + 150*b55 =L= 150;
e61.. - x1 + x13 + x37 + 90*b56 =L= 90;
e62.. - x2 + x14 + x38 + 90*b57 =L= 90;
e63.. - x3 + x15 + x39 + 90*b58 =L= 90;
e64.. - x5 + x9 + x41 + 130*b59 =L= 130;
e65.. - x6 + x10 + x42 + 130*b60 =L= 130;
e66.. - x7 + x11 + x43 + 130*b61 =L= 130;
e67.. - x5 + x13 + x45 + 70*b62 =L= 70;
e68.. - x6 + x14 + x46 + 70*b63 =L= 70;
e69.. - x7 + x15 + x47 + 70*b64 =L= 70;
e70.. - x2 + x10 + x34 + 150*b53 =L= 150;
e71.. - x3 + x11 + x35 + 150*b54 =L= 150;
e72.. - x4 + x12 + x36 + 150*b55 =L= 150;
e73.. - x2 + x14 + x38 + 90*b56 =L= 90;
e74.. - x3 + x15 + x39 + 90*b57 =L= 90;
e75.. - x4 + x16 + x40 + 90*b58 =L= 90;
e76.. - x6 + x10 + x42 + 130*b59 =L= 130;
e77.. - x7 + x11 + x43 + 130*b60 =L= 130;
e78.. - x8 + x12 + x44 + 130*b61 =L= 130;
e79.. - x6 + x14 + x46 + 70*b62 =L= 70;
e80.. - x7 + x15 + x47 + 70*b63 =L= 70;
e81.. - x8 + x16 + x48 + 70*b64 =L= 70;
e82.. - x3 + x49 =L= -313;
e83.. - x7 + x50 =L= -313;
e84.. x9 + x51 =L= 450;
e85.. x13 + x52 =L= 450;
e86.. b53 + b59 =L= 1;
e87.. b54 + b60 =L= 1;
e88.. b55 + b61 =L= 1;
e89.. b56 + b62 =L= 1;
e90.. b57 + b63 =L= 1;
e91.. b58 + b64 =L= 1;
e92.. b53 + b56 =L= 1;
e93.. b54 + b57 =L= 1;
e94.. b55 + b58 =L= 1;
e95.. b59 + b62 =L= 1;
e96.. b60 + b63 =L= 1;
e97.. b61 + b64 =L= 1;
* set non-default bounds
x1.lo = 333; x1.up = 443;
x2.lo = 333; x2.up = 443;
x3.lo = 333; x3.up = 443;
x4.lo = 333; x4.up = 443;
x5.lo = 303; x5.up = 423;
x6.lo = 303; x6.up = 423;
x7.lo = 303; x7.up = 423;
x8.lo = 303; x8.up = 423;
x9.lo = 293; x9.up = 408;
x10.lo = 293; x10.up = 408;
x11.lo = 293; x11.up = 408;
x12.lo = 293; x12.up = 408;
x13.lo = 353; x13.up = 413;
x14.lo = 353; x14.up = 413;
x15.lo = 353; x15.up = 413;
x16.lo = 353; x16.up = 413;
x33.lo = 1;
x34.lo = 1;
x35.lo = 1;
x36.lo = 1;
x37.lo = 1;
x38.lo = 1;
x39.lo = 1;
x40.lo = 1;
x41.lo = 1;
x42.lo = 1;
x43.lo = 1;
x44.lo = 1;
x45.lo = 1;
x46.lo = 1;
x47.lo = 1;
x48.lo = 1;
x49.lo = 1;
x50.lo = 1;
x51.lo = 1;
x52.lo = 1;
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