MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance tls4

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
12.40000000 p1 ( gdx sol )
(infeas: 0)
9.30000000 p2 ( gdx sol )
(infeas: 0)
8.30000000 p3 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
8.30000000 (ALPHAECP)
8.30000000 (ANTIGONE)
8.30000000 (BARON)
5.21403140 (BONMIN)
3.55376071 (COUENNE)
8.30000000 (LINDO)
8.30000000 (OCTERACT)
8.30000000 (SCIP)
8.30000000 (SHOT)
References Harjunkoski, Iiro, Westerlund, Tapio, Pörn, Ray, and Skrifvars, Hans, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP, European Journal of Operational Research, 105:3, 1998, 594-603.
Source MacMINLP model trimlon.mod with trimloss4.dat
Application Trim loss minimization problem
Added to library 01 May 2001
Problem type MINLP
#Variables 105
#Binary Variables 85
#Integer Variables 4
#Nonlinear Variables 20
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 4
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 25
#Nonlinear Nonzeros in Objective 0
#Constraints 64
#Linear Constraints 60
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 4
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 588
#Nonlinear Nonzeros in Jacobian 32
#Nonzeros in (Upper-Left) Hessian of Lagrangian 52
#Nonzeros in Diagonal of Hessian of Lagrangian 20
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 5
Maximal blocksize in Hessian of Lagrangian 5
Average blocksize in Hessian of Lagrangian 5.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-01
Maximal coefficient 1.8000e+03
Infeasibility of initial point 1700
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
*        106       17       85        4        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        614      582       32        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,i5,i6,i7,i8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
          ,b104,b105,objvar;

Binary Variables  b1,b2,b3,b4,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
          ,b104,b105;

Integer Variables  i5,i6,i7,i8;

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..  - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - b25 - 2*b26 - 3*b27 - 4*b28 - 5*b29
      - 6*b30 - 7*b31 - 8*b32 - b33 - 2*b34 - 3*b35 - 4*b36 - 5*b37 - 6*b38
      - 7*b39 - b40 - 2*b41 - 3*b42 - 4*b43 - b44 - 2*b45 + objvar =E= 0;

e2..    330*b46 + 660*b47 + 990*b48 + 1320*b49 + 360*b62 + 720*b63 + 1080*b64
      + 1440*b65 + 1800*b66 + 385*b82 + 770*b83 + 1155*b84 + 1540*b85 + 415*b98
      + 830*b99 =L= 1900;

e3..    330*b50 + 660*b51 + 990*b52 + 1320*b53 + 360*b67 + 720*b68 + 1080*b69
      + 1440*b70 + 1800*b71 + 385*b86 + 770*b87 + 1155*b88 + 1540*b89
      + 415*b100 + 830*b101 =L= 1900;

e4..    330*b54 + 660*b55 + 990*b56 + 1320*b57 + 360*b72 + 720*b73 + 1080*b74
      + 1440*b75 + 1800*b76 + 385*b90 + 770*b91 + 1155*b92 + 1540*b93
      + 415*b102 + 830*b103 =L= 1900;

e5..    330*b58 + 660*b59 + 990*b60 + 1320*b61 + 360*b77 + 720*b78 + 1080*b79
      + 1440*b80 + 1800*b81 + 385*b94 + 770*b95 + 1155*b96 + 1540*b97
      + 415*b104 + 830*b105 =L= 1900;

e6..  - 330*b46 - 660*b47 - 990*b48 - 1320*b49 - 360*b62 - 720*b63 - 1080*b64
      - 1440*b65 - 1800*b66 - 385*b82 - 770*b83 - 1155*b84 - 1540*b85 - 415*b98
      - 830*b99 =L= -1700;

e7..  - 330*b50 - 660*b51 - 990*b52 - 1320*b53 - 360*b67 - 720*b68 - 1080*b69
      - 1440*b70 - 1800*b71 - 385*b86 - 770*b87 - 1155*b88 - 1540*b89
      - 415*b100 - 830*b101 =L= -1700;

e8..  - 330*b54 - 660*b55 - 990*b56 - 1320*b57 - 360*b72 - 720*b73 - 1080*b74
      - 1440*b75 - 1800*b76 - 385*b90 - 770*b91 - 1155*b92 - 1540*b93
      - 415*b102 - 830*b103 =L= -1700;

e9..  - 330*b58 - 660*b59 - 990*b60 - 1320*b61 - 360*b77 - 720*b78 - 1080*b79
      - 1440*b80 - 1800*b81 - 385*b94 - 770*b95 - 1155*b96 - 1540*b97
      - 415*b104 - 830*b105 =L= -1700;

e10..    b46 + 2*b47 + 3*b48 + 4*b49 + b62 + 2*b63 + 3*b64 + 4*b65 + 5*b66
       + b82 + 2*b83 + 3*b84 + 4*b85 + b98 + 2*b99 =L= 5;

e11..    b50 + 2*b51 + 3*b52 + 4*b53 + b67 + 2*b68 + 3*b69 + 4*b70 + 5*b71
       + b86 + 2*b87 + 3*b88 + 4*b89 + b100 + 2*b101 =L= 5;

e12..    b54 + 2*b55 + 3*b56 + 4*b57 + b72 + 2*b73 + 3*b74 + 4*b75 + 5*b76
       + b90 + 2*b91 + 3*b92 + 4*b93 + b102 + 2*b103 =L= 5;

e13..    b58 + 2*b59 + 3*b60 + 4*b61 + b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81
       + b94 + 2*b95 + 3*b96 + 4*b97 + b104 + 2*b105 =L= 5;

e14..    b1 - b25 - 2*b26 - 3*b27 - 4*b28 - 5*b29 - 6*b30 - 7*b31 - 8*b32 =L= 0
      ;

e15..    b2 - b33 - 2*b34 - 3*b35 - 4*b36 - 5*b37 - 6*b38 - 7*b39 =L= 0;

e16..    b3 - b40 - 2*b41 - 3*b42 - 4*b43 =L= 0;

e17..    b4 - b44 - 2*b45 =L= 0;

e18..  - 8*b1 + b25 + 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32
       =L= 0;

e19..  - 7*b2 + b33 + 2*b34 + 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 =L= 0;

e20..  - 4*b3 + b40 + 2*b41 + 3*b42 + 4*b43 =L= 0;

e21..  - 2*b4 + b44 + 2*b45 =L= 0;

e22..    i5 - 3*b25 - 8*b26 - 15*b27 - 24*b28 - 35*b29 - 48*b30 - 63*b31
       - 80*b32 =E= 1;

e23..    i6 - 3*b33 - 8*b34 - 15*b35 - 24*b36 - 35*b37 - 48*b38 - 63*b39 =E= 1;

e24..    i7 - 3*b40 - 8*b41 - 15*b42 - 24*b43 =E= 1;

e25..    i8 - 3*b44 - 8*b45 =E= 1;

e26..    b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 =L= 1;

e27..    b33 + b34 + b35 + b36 + b37 + b38 + b39 =L= 1;

e28..    b40 + b41 + b42 + b43 =L= 1;

e29..    b44 + b45 =L= 1;

e30..    x9 - 3*b46 - 8*b47 - 15*b48 - 24*b49 =E= 1;

e31..    x10 - 3*b50 - 8*b51 - 15*b52 - 24*b53 =E= 1;

e32..    x11 - 3*b54 - 8*b55 - 15*b56 - 24*b57 =E= 1;

e33..    x12 - 3*b58 - 8*b59 - 15*b60 - 24*b61 =E= 1;

e34..    x13 - 3*b62 - 8*b63 - 15*b64 - 24*b65 - 35*b66 =E= 1;

e35..    x14 - 3*b67 - 8*b68 - 15*b69 - 24*b70 - 35*b71 =E= 1;

e36..    x15 - 3*b72 - 8*b73 - 15*b74 - 24*b75 - 35*b76 =E= 1;

e37..    x16 - 3*b77 - 8*b78 - 15*b79 - 24*b80 - 35*b81 =E= 1;

e38..    x17 - 3*b82 - 8*b83 - 15*b84 - 24*b85 =E= 1;

e39..    x18 - 3*b86 - 8*b87 - 15*b88 - 24*b89 =E= 1;

e40..    x19 - 3*b90 - 8*b91 - 15*b92 - 24*b93 =E= 1;

e41..    x20 - 3*b94 - 8*b95 - 15*b96 - 24*b97 =E= 1;

e42..    x21 - 3*b98 - 8*b99 =E= 1;

e43..    x22 - 3*b100 - 8*b101 =E= 1;

e44..    x23 - 3*b102 - 8*b103 =E= 1;

e45..    x24 - 3*b104 - 8*b105 =E= 1;

e46..    b46 + b47 + b48 + b49 =L= 1;

e47..    b50 + b51 + b52 + b53 =L= 1;

e48..    b54 + b55 + b56 + b57 =L= 1;

e49..    b58 + b59 + b60 + b61 =L= 1;

e50..    b62 + b63 + b64 + b65 + b66 =L= 1;

e51..    b67 + b68 + b69 + b70 + b71 =L= 1;

e52..    b72 + b73 + b74 + b75 + b76 =L= 1;

e53..    b77 + b78 + b79 + b80 + b81 =L= 1;

e54..    b82 + b83 + b84 + b85 =L= 1;

e55..    b86 + b87 + b88 + b89 =L= 1;

e56..    b90 + b91 + b92 + b93 =L= 1;

e57..    b94 + b95 + b96 + b97 =L= 1;

e58..    b98 + b99 =L= 1;

e59..    b100 + b101 =L= 1;

e60..    b102 + b103 =L= 1;

e61..    b104 + b105 =L= 1;

e62.. -(sqrt(i5*x9) + sqrt(i6*x10) + sqrt(i7*x11) + sqrt(i8*x12)) + b25 + 2*b26
       + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34 + 3*b35
       + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43 + b44
       + 2*b45 + b46 + 2*b47 + 3*b48 + 4*b49 + b50 + 2*b51 + 3*b52 + 4*b53
       + b54 + 2*b55 + 3*b56 + 4*b57 + b58 + 2*b59 + 3*b60 + 4*b61 =L= -12;

e63.. -(sqrt(i5*x13) + sqrt(i6*x14) + sqrt(i7*x15) + sqrt(i8*x16)) + b25
       + 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
       + 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
       + b44 + 2*b45 + b62 + 2*b63 + 3*b64 + 4*b65 + 5*b66 + b67 + 2*b68
       + 3*b69 + 4*b70 + 5*b71 + b72 + 2*b73 + 3*b74 + 4*b75 + 5*b76 + b77
       + 2*b78 + 3*b79 + 4*b80 + 5*b81 =L= -11;

e64.. -(sqrt(i5*x17) + sqrt(i6*x18) + sqrt(i7*x19) + sqrt(i8*x20)) + b25
       + 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
       + 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
       + b44 + 2*b45 + b82 + 2*b83 + 3*b84 + 4*b85 + b86 + 2*b87 + 3*b88
       + 4*b89 + b90 + 2*b91 + 3*b92 + 4*b93 + b94 + 2*b95 + 3*b96 + 4*b97
       =L= -16;

e65.. -(sqrt(i5*x21) + sqrt(i6*x22) + sqrt(i7*x23) + sqrt(i8*x24)) + b25
       + 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
       + 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
       + b44 + 2*b45 + b98 + 2*b99 + b100 + 2*b101 + b102 + 2*b103 + b104
       + 2*b105 =L= -15;

* set non-default bounds
i5.lo = 1; i5.up = 100;
i6.lo = 1; i6.up = 100;
i7.lo = 1; i7.up = 100;
i8.lo = 1; i8.up = 100;
x9.lo = 1;
x10.lo = 1;
x11.lo = 1;
x12.lo = 1;
x13.lo = 1;
x14.lo = 1;
x15.lo = 1;
x16.lo = 1;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 1;
x21.lo = 1;
x22.lo = 1;
x23.lo = 1;
x24.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;


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