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Instance syn05m

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)
837.73240090 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
837.73240090 (ALPHAECP)
837.73240090 (ANTIGONE)
837.73240090 (BARON)
837.73240090 (BONMIN)
837.73240090 (COUENNE)
837.73240090 (LINDO)
837.73240090 (SCIP)
837.73240090 (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 Syn05M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 20
#Binary Variables 5
#Integer Variables 0
#Nonlinear Variables 3
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 10
#Nonlinear Nonzeros in Objective 0
#Constraints 28
#Linear Constraints 25
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 3
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 73
#Nonlinear Nonzeros in Jacobian 3
#Nonzeros in (Upper-Left) Hessian of Lagrangian 3
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 3
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 3.0000e+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
*         29        6        6       17        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       16        5        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         84       81        3        0
*
*  Solve m using MINLP maximizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,b17,b18
          ,b19,b20,b21;

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;

Binary Variables  b17,b18,b19,b20,b21;

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;


e1..    objvar - 5*x8 + 2*x13 - 200*x14 - 250*x15 - 300*x16 + 5*b17 + 8*b18
      + 6*b19 + 10*b20 + 6*b21 =E= 0;

e2..    x2 - x3 - x4 =E= 0;

e3..  - x5 - x6 + x7 =E= 0;

e4..    x7 - x8 - x9 =E= 0;

e5..    x9 - x10 - x11 - x12 =E= 0;

e6.. -log(1 + x3) + x5 + b17 =L= 1;

e7..    x3 - 10*b17 =L= 0;

e8..    x5 - 2.39789527279837*b17 =L= 0;

e9.. -1.2*log(1 + x4) + x6 + b18 =L= 1;

e10..    x4 - 10*b18 =L= 0;

e11..    x6 - 2.87747432735804*b18 =L= 0;

e12..  - 0.75*x10 + x14 + b19 =L= 1;

e13..  - 0.75*x10 + x14 - b19 =G= -1;

e14..    x10 - 2.87747432735804*b19 =L= 0;

e15..    x14 - 2.15810574551853*b19 =L= 0;

e16.. -1.5*log(1 + x11) + x15 + b20 =L= 1;

e17..    x11 - 2.87747432735804*b20 =L= 0;

e18..    x15 - 2.03277599268042*b20 =L= 0;

e19..  - x12 + x16 + b21 =L= 1;

e20..  - x12 + x16 - b21 =G= -1;

e21..  - 0.5*x13 + x16 + b21 =L= 1;

e22..  - 0.5*x13 + x16 - b21 =G= -1;

e23..    x12 - 2.87747432735804*b21 =L= 0;

e24..    x13 - 7*b21 =L= 0;

e25..    x16 - 3.5*b21 =L= 0;

e26..    b17 + b18 =E= 1;

e27..    b17 + b18 - b19 =G= 0;

e28..    b17 + b18 - b20 =G= 0;

e29..    b17 + b18 - b21 =G= 0;

* set non-default bounds
x2.up = 10;
x13.up = 7;

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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