MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance syn10m

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)ⓘ	1267.35355000 p1 ( gdx sol ) (infeas: 4e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1267.35360000 (ALPHAECP) 1267.35355100 (ANTIGONE) 1267.35355100 (BARON) 1267.35360000 (BONMIN) 1267.35355000 (COUENNE) 1267.35355000 (LINDO) 1267.35355000 (SCIP) 1267.35355000 (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ⓘ	Syn10M.gms from CMU-IBM MINLP solver project page
Applicationⓘ	Synthesis of processing system
Added to libraryⓘ	28 Sep 2013
Problem typeⓘ	MBNLP
#Variablesⓘ	35
#Binary Variablesⓘ	10
#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ⓘ	18
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	54
#Linear Constraintsⓘ	48
#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ⓘ	136
#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ⓘ	5.0000e+02
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         55        8       15       32        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         36       26       10        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        155      149        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,b27,b28,b29,b30,b31,b32,b33,b34,b35
          ,b36;

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;

Binary Variables  b27,b28,b29,b30,b31,b32,b33,b34,b35,b36;

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;


e1..    objvar - 5*x8 + 2*x13 - 200*x21 - 250*x22 - 200*x23 - 200*x24 - 500*x25
      - 350*x26 + 5*b27 + 8*b28 + 6*b29 + 10*b30 + 6*b31 + 7*b32 + 4*b33
      + 5*b34 + 2*b35 + 4*b36 =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.. -log(1 + x3) + x5 + b27 =L= 1;

e9..    x3 - 10*b27 =L= 0;

e10..    x5 - 2.39789527279837*b27 =L= 0;

e11.. -1.2*log(1 + x4) + x6 + b28 =L= 1;

e12..    x4 - 10*b28 =L= 0;

e13..    x6 - 2.87747432735804*b28 =L= 0;

e14..  - 0.75*x10 + x14 + b29 =L= 1;

e15..  - 0.75*x10 + x14 - b29 =G= -1;

e16..    x10 - 2.87747432735804*b29 =L= 0;

e17..    x14 - 2.15810574551853*b29 =L= 0;

e18.. -1.5*log(1 + x11) + x15 + b30 =L= 1;

e19..    x11 - 2.87747432735804*b30 =L= 0;

e20..    x15 - 2.03277599268042*b30 =L= 0;

e21..  - x12 + x16 + b31 =L= 1;

e22..  - x12 + x16 - b31 =G= -1;

e23..  - 0.5*x13 + x16 + b31 =L= 1;

e24..  - 0.5*x13 + x16 - b31 =G= -1;

e25..    x12 - 2.87747432735804*b31 =L= 0;

e26..    x13 - 7*b31 =L= 0;

e27..    x16 - 3.5*b31 =L= 0;

e28.. -1.25*log(1 + x17) + x22 + b32 =L= 1;

e29..    x17 - 2.15810574551853*b32 =L= 0;

e30..    x22 - 1.43746550029693*b32 =L= 0;

e31.. -0.9*log(1 + x18) + x23 + b33 =L= 1;

e32..    x18 - 2.15810574551853*b33 =L= 0;

e33..    x23 - 1.03497516021379*b33 =L= 0;

e34.. -log(1 + x15) + x24 + b34 =L= 1;

e35..    x15 - 2.03277599268042*b34 =L= 0;

e36..    x24 - 1.10947836929589*b34 =L= 0;

e37..  - 0.9*x19 + x25 + b35 =L= 1;

e38..  - 0.9*x19 + x25 - b35 =G= -1;

e39..    x19 - 3.5*b35 =L= 0;

e40..    x25 - 3.15*b35 =L= 0;

e41..  - 0.6*x20 + x26 + b36 =L= 1;

e42..  - 0.6*x20 + x26 - b36 =G= -1;

e43..    x20 - 3.5*b36 =L= 0;

e44..    x26 - 2.1*b36 =L= 0;

e45..    b27 + b28 =E= 1;

e46..  - b29 + b32 + b33 =G= 0;

e47..  - b30 + b34 =G= 0;

e48..    b27 + b28 - b29 =G= 0;

e49..    b27 + b28 - b30 =G= 0;

e50..    b27 + b28 - b31 =G= 0;

e51..    b29 - b32 =G= 0;

e52..    b29 - b33 =G= 0;

e53..    b30 - b34 =G= 0;

e54..    b31 - b35 =G= 0;

e55..    b31 - b36 =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;