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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance syn15m

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)
853.28472920 p1 ( gdx sol )
(infeas: 4e-14)
Other points (infeas > 1e-08)  
Dual Bounds
853.28473000 (ALPHAECP)
853.28500000 (ANTIGONE)
853.28473000 (BARON)
853.28473000 (BONMIN)
853.28474660 (COUENNE)
853.28473000 (LINDO)
853.28478490 (SCIP)
853.28500760 (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 Syn15M.gms from CMU-IBM MINLP solver project page
Application Synthesis of processing system
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 55
#Binary Variables 15
#Integer Variables 0
#Nonlinear Variables 11
#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 89
#Linear Constraints 78
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 11
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 223
#Nonlinear Nonzeros in Jacobian 11
#Nonzeros in (Upper-Left) Hessian of Lagrangian 11
#Nonzeros in Diagonal of Hessian of Lagrangian 11
#Blocks in Hessian of Lagrangian 11
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 5.0000e+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
*         90       12       27       51        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         56       41       15        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        246      235       11        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,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52
          ,b53,b54,b55,b56;

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,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40,x41;

Binary Variables  b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55,b56;

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;


e1..    objvar - 5*x8 - 500*x26 - 350*x27 - 200*x38 - 250*x39 - 200*x40
      - 200*x41 + 5*b42 + 8*b43 + 6*b44 + 10*b45 + 6*b46 + 7*b47 + 4*b48
      + 5*b49 + 2*b50 + 4*b51 + 3*b52 + 7*b53 + 3*b54 + 2*b55 + 4*b56 =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..    x14 - x17 - x18 =E= 0;

e7..    x16 - x19 - x20 - x21 =E= 0;

e8..    x24 - x28 - x29 =E= 0;

e9..  - x25 - x31 + x32 =E= 0;

e10..    x26 - x33 - x34 =E= 0;

e11..    x27 - x35 - x36 - x37 =E= 0;

e12.. -log(1 + x3) + x5 + b42 =L= 1;

e13..    x3 - 10*b42 =L= 0;

e14..    x5 - 2.39789527279837*b42 =L= 0;

e15.. -1.2*log(1 + x4) + x6 + b43 =L= 1;

e16..    x4 - 10*b43 =L= 0;

e17..    x6 - 2.87747432735804*b43 =L= 0;

e18..  - 0.75*x10 + x14 + b44 =L= 1;

e19..  - 0.75*x10 + x14 - b44 =G= -1;

e20..    x10 - 2.87747432735804*b44 =L= 0;

e21..    x14 - 2.15810574551853*b44 =L= 0;

e22.. -1.5*log(1 + x11) + x15 + b45 =L= 1;

e23..    x11 - 2.87747432735804*b45 =L= 0;

e24..    x15 - 2.03277599268042*b45 =L= 0;

e25..  - x12 + x16 + b46 =L= 1;

e26..  - x12 + x16 - b46 =G= -1;

e27..  - 0.5*x13 + x16 + b46 =L= 1;

e28..  - 0.5*x13 + x16 - b46 =G= -1;

e29..    x12 - 2.87747432735804*b46 =L= 0;

e30..    x13 - 7*b46 =L= 0;

e31..    x16 - 3.5*b46 =L= 0;

e32.. -1.25*log(1 + x17) + x22 + b47 =L= 1;

e33..    x17 - 2.15810574551853*b47 =L= 0;

e34..    x22 - 1.43746550029693*b47 =L= 0;

e35.. -0.9*log(1 + x18) + x23 + b48 =L= 1;

e36..    x18 - 2.15810574551853*b48 =L= 0;

e37..    x23 - 1.03497516021379*b48 =L= 0;

e38.. -log(1 + x15) + x24 + b49 =L= 1;

e39..    x15 - 2.03277599268042*b49 =L= 0;

e40..    x24 - 1.10947836929589*b49 =L= 0;

e41..  - 0.9*x19 + x25 + b50 =L= 1;

e42..  - 0.9*x19 + x25 - b50 =G= -1;

e43..    x19 - 3.5*b50 =L= 0;

e44..    x25 - 3.15*b50 =L= 0;

e45..  - 0.6*x20 + x26 + b51 =L= 1;

e46..  - 0.6*x20 + x26 - b51 =G= -1;

e47..    x20 - 3.5*b51 =L= 0;

e48..    x26 - 2.1*b51 =L= 0;

e49.. -1.1*log(1 + x21) + x27 + b52 =L= 1;

e50..    x21 - 3.5*b52 =L= 0;

e51..    x27 - 1.6544851364539*b52 =L= 0;

e52..  - 0.9*x22 + x38 + b53 =L= 1;

e53..  - 0.9*x22 + x38 - b53 =G= -1;

e54..  - x30 + x38 + b53 =L= 1;

e55..  - x30 + x38 - b53 =G= -1;

e56..    x22 - 1.43746550029693*b53 =L= 0;

e57..    x30 - 5*b53 =L= 0;

e58..    x38 - 5*b53 =L= 0;

e59.. -log(1 + x23) + x39 + b54 =L= 1;

e60..    x23 - 1.03497516021379*b54 =L= 0;

e61..    x39 - 0.710483612536911*b54 =L= 0;

e62.. -0.7*log(1 + x28) + x40 + b55 =L= 1;

e63..    x28 - 1.10947836929589*b55 =L= 0;

e64..    x40 - 0.522508489006913*b55 =L= 0;

e65.. -0.65*log(1 + x29) + x41 + b56 =L= 1;

e66.. -0.65*log(1 + x32) + x41 + b56 =L= 1;

e67..    x29 - 1.10947836929589*b56 =L= 0;

e68..    x32 - 8.15*b56 =L= 0;

e69..    x41 - 1.43894002153683*b56 =L= 0;

e70..    b42 + b43 =E= 1;

e71..  - b44 + b47 + b48 =G= 0;

e72..  - b47 + b53 =G= 0;

e73..  - b48 + b54 =G= 0;

e74..  - b45 + b49 =G= 0;

e75..  - b49 + b55 + b56 =G= 0;

e76..  - b46 + b50 + b51 + b52 =G= 0;

e77..  - b50 + b56 =G= 0;

e78..    b42 + b43 - b44 =G= 0;

e79..    b42 + b43 - b45 =G= 0;

e80..    b42 + b43 - b46 =G= 0;

e81..    b44 - b47 =G= 0;

e82..    b44 - b48 =G= 0;

e83..    b45 - b49 =G= 0;

e84..    b46 - b50 =G= 0;

e85..    b46 - b51 =G= 0;

e86..    b46 - b52 =G= 0;

e87..    b47 - b53 =G= 0;

e88..    b48 - b54 =G= 0;

e89..    b49 - b55 =G= 0;

e90..    b49 - b56 =G= 0;

* set non-default bounds
x2.up = 10;
x13.up = 7;
x30.up = 5;
x31.up = 5;

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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