MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance syn10hfsg

Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
Equivalent perspective reformulation of syn10.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
1267.35355000 p1 ( gdx sol )
(infeas: 4e-16)
Other points (infeas > 1e-08)  
Dual Bounds
1267.35355000 (ALPHAECP)
1267.35355100 (ANTIGONE)
1267.35355200 (BARON)
1267.35355000 (BONMIN)
1267.35355000 (COUENNE)
1267.35355000 (LINDO)
1267.35355100 (SCIP)
1267.35387200 (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.
Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019.
Application Synthesis of processing system
Added to library 25 Sep 2019
Problem type MBNLP
#Variables 77
#Binary Variables 10
#Integer Variables 0
#Nonlinear Variables 18
#Nonlinear Binary Variables 6
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 18
#Nonlinear Nonzeros in Objective 0
#Constraints 112
#Linear Constraints 106
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 6
Operands in Gen. Nonlin. Functions div log mul
Constraints curvature convex
#Nonzeros in Jacobian 242
#Nonlinear Nonzeros in Jacobian 18
#Nonzeros in (Upper-Left) Hessian of Lagrangian 36
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 6
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-03
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
*        113       55       10       48        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         78       68       10        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        261      243       18        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,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,b69
          ,b70,b71,b72,b73,b74,b75,b76,b77,b78;

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,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
          ,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68;

Binary Variables  b69,b70,b71,b72,b73,b74,b75,b76,b77,b78;

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,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113;


e1..    objvar - 5*x8 + 2*x13 - 200*x21 - 250*x22 - 200*x23 - 200*x24 - 500*x25
      - 350*x26 + 5*b69 + 8*b70 + 6*b71 + 10*b72 + 6*b73 + 7*b74 + 4*b75
      + 5*b76 + 2*b77 + 4*b78 =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.. (x31/(0.001 + 0.999*b69) - log(1 + x27/(0.001 + 0.999*b69)))*(0.001 + 
     0.999*b69) =L= 0;

e9..    x28 =E= 0;

e10..    x32 =E= 0;

e11..    x3 - x27 - x28 =E= 0;

e12..    x5 - x31 - x32 =E= 0;

e13..    x27 - 10*b69 =L= 0;

e14..    x28 + 10*b69 =L= 10;

e15..    x31 - 2.39789527279837*b69 =L= 0;

e16..    x32 + 2.39789527279837*b69 =L= 2.39789527279837;

e17.. (x33/(0.001 + 0.999*b70) - 1.2*log(1 + x29/(0.001 + 0.999*b70)))*(0.001
       + 0.999*b70) =L= 0;

e18..    x30 =E= 0;

e19..    x34 =E= 0;

e20..    x4 - x29 - x30 =E= 0;

e21..    x6 - x33 - x34 =E= 0;

e22..    x29 - 10*b70 =L= 0;

e23..    x30 + 10*b70 =L= 10;

e24..    x33 - 2.87747432735804*b70 =L= 0;

e25..    x34 + 2.87747432735804*b70 =L= 2.87747432735804;

e26..  - 0.75*x35 + x43 =E= 0;

e27..    x36 =E= 0;

e28..    x44 =E= 0;

e29..    x10 - x35 - x36 =E= 0;

e30..    x14 - x43 - x44 =E= 0;

e31..    x35 - 2.87747432735804*b71 =L= 0;

e32..    x36 + 2.87747432735804*b71 =L= 2.87747432735804;

e33..    x43 - 2.15810574551853*b71 =L= 0;

e34..    x44 + 2.15810574551853*b71 =L= 2.15810574551853;

e35.. (x45/(0.001 + 0.999*b72) - 1.5*log(1 + x37/(0.001 + 0.999*b72)))*(0.001
       + 0.999*b72) =L= 0;

e36..    x38 =E= 0;

e37..    x47 =E= 0;

e38..    x11 - x37 - x38 =E= 0;

e39..    x15 - x45 - x47 =E= 0;

e40..    x37 - 2.87747432735804*b72 =L= 0;

e41..    x38 + 2.87747432735804*b72 =L= 2.87747432735804;

e42..    x45 - 2.03277599268042*b72 =L= 0;

e43..    x47 + 2.03277599268042*b72 =L= 2.03277599268042;

e44..  - x39 + x49 =E= 0;

e45..  - 0.5*x41 + x49 =E= 0;

e46..    x40 =E= 0;

e47..    x42 =E= 0;

e48..    x50 =E= 0;

e49..    x12 - x39 - x40 =E= 0;

e50..    x13 - x41 - x42 =E= 0;

e51..    x16 - x49 - x50 =E= 0;

e52..    x39 - 2.87747432735804*b73 =L= 0;

e53..    x40 + 2.87747432735804*b73 =L= 2.87747432735804;

e54..    x41 - 7*b73 =L= 0;

e55..    x42 + 7*b73 =L= 7;

e56..    x49 - 3.5*b73 =L= 0;

e57..    x50 + 3.5*b73 =L= 3.5;

e58.. (x59/(0.001 + 0.999*b74) - 1.25*log(1 + x51/(0.001 + 0.999*b74)))*(0.001
       + 0.999*b74) =L= 0;

e59..    x52 =E= 0;

e60..    x60 =E= 0;

e61..    x17 - x51 - x52 =E= 0;

e62..    x22 - x59 - x60 =E= 0;

e63..    x51 - 2.15810574551853*b74 =L= 0;

e64..    x52 + 2.15810574551853*b74 =L= 2.15810574551853;

e65..    x59 - 1.43746550029693*b74 =L= 0;

e66..    x60 + 1.43746550029693*b74 =L= 1.43746550029693;

e67.. (x61/(0.001 + 0.999*b75) - 0.9*log(1 + x53/(0.001 + 0.999*b75)))*(0.001
       + 0.999*b75) =L= 0;

e68..    x54 =E= 0;

e69..    x62 =E= 0;

e70..    x18 - x53 - x54 =E= 0;

e71..    x23 - x61 - x62 =E= 0;

e72..    x53 - 2.15810574551853*b75 =L= 0;

e73..    x54 + 2.15810574551853*b75 =L= 2.15810574551853;

e74..    x61 - 1.03497516021379*b75 =L= 0;

e75..    x62 + 1.03497516021379*b75 =L= 1.03497516021379;

e76.. (x63/(0.001 + 0.999*b76) - log(1 + x46/(0.001 + 0.999*b76)))*(0.001 + 
      0.999*b76) =L= 0;

e77..    x48 =E= 0;

e78..    x64 =E= 0;

e79..    x15 - x46 - x48 =E= 0;

e80..    x24 - x63 - x64 =E= 0;

e81..    x46 - 2.03277599268042*b76 =L= 0;

e82..    x48 + 2.03277599268042*b76 =L= 2.03277599268042;

e83..    x63 - 1.10947836929589*b76 =L= 0;

e84..    x64 + 1.10947836929589*b76 =L= 1.10947836929589;

e85..  - 0.9*x55 + x65 =E= 0;

e86..    x56 =E= 0;

e87..    x66 =E= 0;

e88..    x19 - x55 - x56 =E= 0;

e89..    x25 - x65 - x66 =E= 0;

e90..    x55 - 3.5*b77 =L= 0;

e91..    x56 + 3.5*b77 =L= 3.5;

e92..    x65 - 3.15*b77 =L= 0;

e93..    x66 + 3.15*b77 =L= 3.15;

e94..  - 0.6*x57 + x67 =E= 0;

e95..    x58 =E= 0;

e96..    x68 =E= 0;

e97..    x20 - x57 - x58 =E= 0;

e98..    x26 - x67 - x68 =E= 0;

e99..    x57 - 3.5*b78 =L= 0;

e100..    x58 + 3.5*b78 =L= 3.5;

e101..    x67 - 2.1*b78 =L= 0;

e102..    x68 + 2.1*b78 =L= 2.1;

e103..    b69 + b70 =E= 1;

e104..  - b71 + b74 + b75 =G= 0;

e105..  - b72 + b76 =G= 0;

e106..    b69 + b70 - b71 =G= 0;

e107..    b69 + b70 - b72 =G= 0;

e108..    b69 + b70 - b73 =G= 0;

e109..    b71 - b74 =G= 0;

e110..    b71 - b75 =G= 0;

e111..    b72 - b76 =G= 0;

e112..    b73 - b77 =G= 0;

e113..    b73 - b78 =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: 2022-04-26 Git hash: de668763
Imprint / Privacy Policy / License: CC-BY 4.0