MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex1252a

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	128893.74100000 p1 ( gdx sol ) (infeas: 1e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	128893.74100000 (ANTIGONE) 128893.74100000 (BARON) 128893.74100000 (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ⓘ	modified 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ⓘ	MINLP
#Variablesⓘ	24
#Binary Variablesⓘ	3
#Integer Variablesⓘ	6
#Nonlinear Variablesⓘ	21
#Nonlinear Binary Variablesⓘ	3
#Nonlinear Integer Variablesⓘ	6
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	12
#Nonlinear Nonzeros in Objectiveⓘ	12
#Constraintsⓘ	34
#Linear Constraintsⓘ	22
#Quadratic Constraintsⓘ	9
#Polynomial Constraintsⓘ	3
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	81
#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
*         35       14        0       21        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         25       16        3        6        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         94       58       36        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,i16,i17,i18,i19
          ,i20,i21,b22,b23,b24,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;

Binary Variables  b22,b23,b24;

Integer Variables  i16,i17,i18,i19,i20,i21;

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;


e1.. -((6329.03 + 1800*x1)*i16*i19*b22 + (2489.31 + 1800*x2)*i17*i20*b23 + (
     3270.27 + 1800*x3)*i18*i21*b24) + 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*i16 - x13 =E= 0;

e10.. 0.00285714285714286*x11*i17 - x14 =E= 0;

e11.. 0.00285714285714286*x12*i18 - x15 =E= 0;

e12.. 0.0025*x7*i19 - b22 =E= 0;

e13.. 0.0025*x8*i20 - b23 =E= 0;

e14.. 0.0025*x9*i21 - b24 =E= 0;

e15..    0.000338983050847458*x4 - b22 =L= 0;

e16..    0.000338983050847458*x5 - b23 =L= 0;

e17..    0.000338983050847458*x6 - b24 =L= 0;

e18..    0.0125*x1 - b22 =L= 0;

e19..    0.04*x2 - b23 =L= 0;

e20..    0.0222222222222222*x3 - b24 =L= 0;

e21..    0.0025*x7 - b22 =L= 0;

e22..    0.0025*x8 - b23 =L= 0;

e23..    0.0025*x9 - b24 =L= 0;

e24..    0.00285714285714286*x10 - b22 =L= 0;

e25..    0.00285714285714286*x11 - b23 =L= 0;

e26..    0.00285714285714286*x12 - b24 =L= 0;

e27..    x13 - b22 =L= 0;

e28..    x14 - b23 =L= 0;

e29..    x15 - b24 =L= 0;

e30..    i16 - 3*b22 =L= 0;

e31..    i17 - 3*b23 =L= 0;

e32..    i18 - 3*b24 =L= 0;

e33..    i19 - 3*b22 =L= 0;

e34..    i20 - 3*b23 =L= 0;

e35..    i21 - 3*b24 =L= 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;
i16.up = 3;
i17.up = 3;
i18.up = 3;
i19.up = 3;
i20.up = 3;
i21.up = 3;

* 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;
i16.l = 1;
i17.l = 1;
i18.l = 1;
i19.l = 1;
i20.l = 1;
i21.l = 1;
b22.l = 0.333333333333333;
b23.l = 0.333333333333333;
b24.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;