MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1252
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 128893.74100000 (ANTIGONE) 128893.74100000 (BARON) 128893.73460000 (COUENNE) 128893.74100000 (LINDO) 128893.74100000 (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. Westerlund, Tapio, Petterson, Frank, and Grossmann, I E, Optimization of Pump Configurations as a MINLP Problem, Computers and Chemical Engineering, 18:9, 1994, 845-858. |
| Sourceⓘ | Test Problem ex12.5.2 of Chapter 12 of Floudas e.a. handbook |
| Applicationⓘ | Pump configuration problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 39 |
| #Binary Variablesⓘ | 15 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 21 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | polynomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 12 |
| #Constraintsⓘ | 43 |
| #Linear Constraintsⓘ | 31 |
| #Quadratic Constraintsⓘ | 9 |
| #Polynomial Constraintsⓘ | 3 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 105 |
| #Nonlinear Nonzeros in Jacobianⓘ | 24 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 60 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 7 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 7.8644e-08 |
| Maximal coefficientⓘ | 6.3290e+03 |
| Infeasibility of initial pointⓘ | 1560 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 44 23 0 21 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 40 25 15 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 118 82 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,b19
,b20,b21,b22,b23,b24,x25,x26,x27,b28,b29,b30,b31,b32,b33,x34,x35,x36
,b37,b38,b39,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,x25,x26,x27,x34,x35,x36;
Binary Variables b19,b20,b21,b22,b23,b24,b28,b29,b30,b31,b32,b33,b37,b38,b39;
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;
e1.. -((6329.03 + 1800*x1)*x16*x25*x34 + (2489.31 + 1800*x2)*x17*x26*x35 + (
3270.27 + 1800*x3)*x18*x27*x36) + objvar =E= 0;
e2.. (-19.9*POWER(0.000338983050847458*x4,3)) - 0.161*sqr(0.000338983050847458*
x4)*x10 + 1.90169491525424e-7*sqr(x10)*x4 + x1 =E= 0;
e3.. (-1.21*POWER(0.000338983050847458*x5,3)) - 0.0644*sqr(0.000338983050847458
*x5)*x11 + 1.91186440677966e-7*sqr(x11)*x5 + x2 =E= 0;
e4.. (-6.52*POWER(0.000338983050847458*x6,3)) - 0.102*sqr(0.000338983050847458*
x6)*x12 + 7.86440677966102e-8*sqr(x12)*x6 + x3 =E= 0;
e5.. (-0.00023593220338983*x4*x10) - 629*sqr(0.000338983050847458*x4) + 0.0116*
sqr(x10) + x7 =E= 0;
e6.. (-0.001*x5*x11) - 215*sqr(0.000338983050847458*x5) + 0.115*sqr(x11) + x8
=E= 0;
e7.. (-0.000179661016949153*x6*x12) - 361*sqr(0.000338983050847458*x6) +
0.00946*sqr(x12) + x9 =E= 0;
e8.. x13 + x14 + x15 =E= 1;
e9.. 0.00285714285714286*x10*x16 - x13 =E= 0;
e10.. 0.00285714285714286*x11*x17 - x14 =E= 0;
e11.. 0.00285714285714286*x12*x18 - x15 =E= 0;
e12.. 0.0025*x7*x25 - x34 =E= 0;
e13.. 0.0025*x8*x26 - x35 =E= 0;
e14.. 0.0025*x9*x27 - x36 =E= 0;
e15.. 0.000338983050847458*x4 - x34 =L= 0;
e16.. 0.000338983050847458*x5 - x35 =L= 0;
e17.. 0.000338983050847458*x6 - x36 =L= 0;
e18.. 0.0125*x1 - x34 =L= 0;
e19.. 0.04*x2 - x35 =L= 0;
e20.. 0.0222222222222222*x3 - x36 =L= 0;
e21.. 0.0025*x7 - x34 =L= 0;
e22.. 0.0025*x8 - x35 =L= 0;
e23.. 0.0025*x9 - x36 =L= 0;
e24.. 0.00285714285714286*x10 - x34 =L= 0;
e25.. 0.00285714285714286*x11 - x35 =L= 0;
e26.. 0.00285714285714286*x12 - x36 =L= 0;
e27.. x13 - x34 =L= 0;
e28.. x14 - x35 =L= 0;
e29.. x15 - x36 =L= 0;
e30.. x16 - 3*x34 =L= 0;
e31.. x17 - 3*x35 =L= 0;
e32.. x18 - 3*x36 =L= 0;
e33.. x25 - 3*x34 =L= 0;
e34.. x26 - 3*x35 =L= 0;
e35.. x27 - 3*x36 =L= 0;
e36.. x16 - b19 - 2*b20 =E= 0;
e37.. x17 - b21 - 2*b22 =E= 0;
e38.. x18 - b23 - 2*b24 =E= 0;
e39.. x25 - b28 - 2*b29 =E= 0;
e40.. x26 - b30 - 2*b31 =E= 0;
e41.. x27 - b32 - 2*b33 =E= 0;
e42.. x34 - b37 =E= 0;
e43.. x35 - b38 =E= 0;
e44.. x36 - b39 =E= 0;
* set non-default bounds
x1.up = 80;
x2.up = 25;
x3.up = 45;
x4.up = 2950;
x5.up = 2950;
x6.up = 2950;
x7.up = 400;
x8.up = 400;
x9.up = 400;
x10.up = 350;
x11.up = 350;
x12.up = 350;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 3;
x17.up = 3;
x18.up = 3;
x25.up = 3;
x26.up = 3;
x27.up = 3;
x34.up = 1;
x35.up = 1;
x36.up = 1;
* set non-default levels
x4.l = 983.333333333333;
x5.l = 983.333333333333;
x6.l = 983.333333333333;
x7.l = 133.333333333333;
x8.l = 133.333333333333;
x9.l = 133.333333333333;
x10.l = 116.666666666667;
x11.l = 116.666666666667;
x12.l = 116.666666666667;
x13.l = 0.333333333333333;
x14.l = 0.333333333333333;
x15.l = 0.333333333333333;
x16.l = 1;
x17.l = 1;
x18.l = 1;
x25.l = 1;
x26.l = 1;
x27.l = 1;
x34.l = 0.333333333333333;
x35.l = 0.333333333333333;
x36.l = 0.333333333333333;
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: 2024-08-26 Git hash: 6cc1607f