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Instance syn05m02m

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
3032.73538600 p1 ( gdx sol )
(infeas: 3e-11)
Other points (infeas > 1e-08)  
Dual Bounds
3032.87700000 (ALPHAECP)
3032.73579200 (ANTIGONE)
3032.73542300 (BARON)
3032.73540000 (BONMIN)
3032.73538600 (COUENNE)
3032.73538600 (LINDO)
3032.73546900 (SCIP)
3032.73590200 (SHOT)
References Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339.
Türkay, Metin and Grossmann, I E, Logic-based MINLP Algorithms for optimal synthesis of process networks, Computers and Chemical Engineering, 20:8, 1996, 959-978.
Source Syn05M02M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 60
#Binary Variables 20
#Integer Variables 0
#Nonlinear Variables 6
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 22
#Nonlinear Nonzeros in Objective 0
#Constraints 101
#Linear Constraints 95
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 6
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 241
#Nonlinear Nonzeros in Jacobian 6
#Nonzeros in (Upper-Left) Hessian of Lagrangian 6
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 6
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.0000e-01
Maximal coefficient 4.0500e+02
Infeasibility of initial point 1
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
*        102       11       22       69        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         61       41       20        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        264      258        6        0
*
*  Solve m using MINLP maximizing objvar;


Variables  objvar,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,b32,b33,b34,b35
          ,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61;

Positive Variables  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;

Binary Variables  b32,b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46
          ,b47,b48,b49,b50,b51;

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,e98,e99,e100,e101,e102;


e1..    objvar + x2 + x3 - 5*x14 - 10*x15 + 2*x24 + x25 - 80*x26 - 90*x27
      - 285*x28 - 390*x29 - 290*x30 - 405*x31 + 5*b42 + 4*b43 + 8*b44 + 7*b45
      + 6*b46 + 9*b47 + 10*b48 + 9*b49 + 6*b50 + 10*b51 =E= 0;

e2..    x2 - x4 - x6 =E= 0;

e3..    x3 - x5 - x7 =E= 0;

e4..  - x8 - x10 + x12 =E= 0;

e5..  - x9 - x11 + x13 =E= 0;

e6..    x12 - x14 - x16 =E= 0;

e7..    x13 - x15 - x17 =E= 0;

e8..    x16 - x18 - x20 - x22 =E= 0;

e9..    x17 - x19 - x21 - x23 =E= 0;

e10.. -log(1 + x4) + x8 + b32 =L= 1;

e11.. -log(1 + x5) + x9 + b33 =L= 1;

e12..    x4 - 40*b32 =L= 0;

e13..    x5 - 40*b33 =L= 0;

e14..    x8 - 3.71357206670431*b32 =L= 0;

e15..    x9 - 3.71357206670431*b33 =L= 0;

e16.. -1.2*log(1 + x6) + x10 + b34 =L= 1;

e17.. -1.2*log(1 + x7) + x11 + b35 =L= 1;

e18..    x6 - 40*b34 =L= 0;

e19..    x7 - 40*b35 =L= 0;

e20..    x10 - 4.45628648004517*b34 =L= 0;

e21..    x11 - 4.45628648004517*b35 =L= 0;

e22..  - 0.75*x18 + x26 + b36 =L= 1;

e23..  - 0.75*x19 + x27 + b37 =L= 1;

e24..  - 0.75*x18 + x26 - b36 =G= -1;

e25..  - 0.75*x19 + x27 - b37 =G= -1;

e26..    x18 - 4.45628648004517*b36 =L= 0;

e27..    x19 - 4.45628648004517*b37 =L= 0;

e28..    x26 - 3.34221486003388*b36 =L= 0;

e29..    x27 - 3.34221486003388*b37 =L= 0;

e30.. -1.5*log(1 + x20) + x28 + b38 =L= 1;

e31.. -1.5*log(1 + x21) + x29 + b39 =L= 1;

e32..    x20 - 4.45628648004517*b38 =L= 0;

e33..    x21 - 4.45628648004517*b39 =L= 0;

e34..    x28 - 2.54515263975353*b38 =L= 0;

e35..    x29 - 2.54515263975353*b39 =L= 0;

e36..  - x22 + x30 + b40 =L= 1;

e37..  - x23 + x31 + b41 =L= 1;

e38..  - x22 + x30 - b40 =G= -1;

e39..  - x23 + x31 - b41 =G= -1;

e40..  - 0.5*x24 + x30 + b40 =L= 1;

e41..  - 0.5*x25 + x31 + b41 =L= 1;

e42..  - 0.5*x24 + x30 - b40 =G= -1;

e43..  - 0.5*x25 + x31 - b41 =G= -1;

e44..    x22 - 4.45628648004517*b40 =L= 0;

e45..    x23 - 4.45628648004517*b41 =L= 0;

e46..    x24 - 30*b40 =L= 0;

e47..    x25 - 30*b41 =L= 0;

e48..    x30 - 15*b40 =L= 0;

e49..    x31 - 15*b41 =L= 0;

e50..    5*b42 + x52 =L= 0;

e51..    4*b43 + x53 =L= 0;

e52..    8*b44 + x54 =L= 0;

e53..    7*b45 + x55 =L= 0;

e54..    6*b46 + x56 =L= 0;

e55..    9*b47 + x57 =L= 0;

e56..    10*b48 + x58 =L= 0;

e57..    9*b49 + x59 =L= 0;

e58..    6*b50 + x60 =L= 0;

e59..    10*b51 + x61 =L= 0;

e60..    5*b42 + x52 =G= 0;

e61..    4*b43 + x53 =G= 0;

e62..    8*b44 + x54 =G= 0;

e63..    7*b45 + x55 =G= 0;

e64..    6*b46 + x56 =G= 0;

e65..    9*b47 + x57 =G= 0;

e66..    10*b48 + x58 =G= 0;

e67..    9*b49 + x59 =G= 0;

e68..    6*b50 + x60 =G= 0;

e69..    10*b51 + x61 =G= 0;

e70..    b32 - b33 =L= 0;

e71..    b34 - b35 =L= 0;

e72..    b36 - b37 =L= 0;

e73..    b38 - b39 =L= 0;

e74..    b40 - b41 =L= 0;

e75..    b42 + b43 =L= 1;

e76..    b42 + b43 =L= 1;

e77..    b44 + b45 =L= 1;

e78..    b44 + b45 =L= 1;

e79..    b46 + b47 =L= 1;

e80..    b46 + b47 =L= 1;

e81..    b48 + b49 =L= 1;

e82..    b48 + b49 =L= 1;

e83..    b50 + b51 =L= 1;

e84..    b50 + b51 =L= 1;

e85..    b32 - b42 =L= 0;

e86..  - b32 + b33 - b43 =L= 0;

e87..    b34 - b44 =L= 0;

e88..  - b34 + b35 - b45 =L= 0;

e89..    b36 - b46 =L= 0;

e90..  - b36 + b37 - b47 =L= 0;

e91..    b38 - b48 =L= 0;

e92..  - b38 + b39 - b49 =L= 0;

e93..    b40 - b50 =L= 0;

e94..  - b40 + b41 - b51 =L= 0;

e95..    b32 + b34 =E= 1;

e96..    b33 + b35 =E= 1;

e97..    b32 + b34 - b36 =G= 0;

e98..    b33 + b35 - b37 =G= 0;

e99..    b32 + b34 - b38 =G= 0;

e100..    b33 + b35 - b39 =G= 0;

e101..    b32 + b34 - b40 =G= 0;

e102..    b33 + b35 - b41 =G= 0;

* set non-default bounds
x2.up = 40;
x3.up = 40;
x24.up = 30;
x25.up = 30;

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% maximizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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