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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: ex1233

Formats ams gms mod nl osil
Primal Bounds
155010.67130000 p1 ( gdx sol )
(infeas: 5e-12)
Dual Bounds
143059.96680000 (ANTIGONE)
155010.67130000 (BARON)
147870.62200000 (COUENNE)
154969.44160000 (LINDO)
154825.76050000 (SCIP)
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 mul div 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
Infeasibility of initial point 4400
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2018-09-14 Git hash: ac5a5314
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