MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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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 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;