MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance procsel

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1.92309874 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.92309874 (ANTIGONE) -1.92309874 (BARON) -1.92309874 (COUENNE) -1.92309874 (LINDO) -1.92309874 (SCIP) -1.92309874 (SHOT)
Referencesⓘ	Kocis, Gary R and Grossmann, I E, Relaxation Strategy for the Structural Optimization of Process Flow Sheets, Industrial and Engineering Chemistry Research, 26:9, 1987, 1869-1880.
Sourceⓘ	GAMS Model Library model procsel
Applicationⓘ	Process Flowsheets
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	10
#Binary Variablesⓘ	3
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	9
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	7
#Linear Constraintsⓘ	5
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	2
Operands in Gen. Nonlin. Functionsⓘ	exp
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	16
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
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ⓘ	8.3333e-01
Maximal coefficientⓘ	1.1000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        5        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11        8        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         26       24        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,b8,b9,b10,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7;

Binary Variables  b8,b9,b10;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1..  - 0.9*x6 + x7 =E= 0;

e2.. exp(x3) - x1 =E= 1;

e3.. exp(0.833333333333333*x4) - x2 =E= 1;

e4..  - x3 - x4 - x5 + x6 =E= 0;

e5..    x7 - 2*b8 =L= 0;

e6..    x3 - 4*b9 =L= 0;

e7..    x4 - 5*b10 =L= 0;

e8..    1.8*x1 + 1.8*x2 + x3 + 1.2*x4 + 7*x5 - 11*x7 + 3.5*b8 + b9 + 1.5*b10
      - objvar =E= 0;

* set non-default bounds
x7.up = 1;

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% minimizing objvar;