MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex1264a

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	8.60000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	8.60000000 (ANTIGONE) 8.60000000 (BARON) 8.60000000 (COUENNE) 8.60000000 (GUROBI) 8.60000000 (LINDO) 8.60000000 (SCIP) 8.60000000 (SHOT)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Harjunkoski, Iiro, Westerlund, Tapio, Pörn, Ray, and Skrifvars, Hans, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP, European Journal of Operational Research, 105:3, 1998, 594-603.
Sourceⓘ	modified Test Problem ex12.6.4 of Chapter 12 of Floudas e.a. handbook
Applicationⓘ	Trim loss minimization problem
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MIQCP
#Variablesⓘ	24
#Binary Variablesⓘ	4
#Integer Variablesⓘ	20
#Nonlinear Variablesⓘ	20
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	20
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	8
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	35
#Linear Constraintsⓘ	31
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	144
#Nonlinear Nonzeros in Jacobianⓘ	32
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	32
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	4
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e-01
Maximal coefficientⓘ	1.9000e+03
Infeasibility of initial pointⓘ	12
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         36        1        5       30        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         25        1        4       20        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        153      121       32        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,b17,b18,b19
          ,b20,i21,i22,i23,i24,objvar;

Binary Variables  b17,b18,b19,b20;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i21
          ,i22,i23,i24;

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;


e1..  - 0.1*b17 - 0.2*b18 - 0.3*b19 - 0.4*b20 - i21 - i22 - i23 - i24 + objvar
      =E= 0;

e2.. i21*i1 + i22*i2 + i23*i3 + i24*i4 =G= 9;

e3.. i21*i5 + i22*i6 + i23*i7 + i24*i8 =G= 7;

e4.. i21*i9 + i22*i10 + i23*i11 + i24*i12 =G= 12;

e5.. i21*i13 + i22*i14 + i23*i15 + i24*i16 =G= 11;

e6..  - 330*i1 - 360*i5 - 385*i9 - 415*i13 + 1700*b17 =L= 0;

e7..  - 330*i2 - 360*i6 - 385*i10 - 415*i14 + 1700*b18 =L= 0;

e8..  - 330*i3 - 360*i7 - 385*i11 - 415*i15 + 1700*b19 =L= 0;

e9..  - 330*i4 - 360*i8 - 385*i12 - 415*i16 + 1700*b20 =L= 0;

e10..    330*i1 + 360*i5 + 385*i9 + 415*i13 - 1900*b17 =L= 0;

e11..    330*i2 + 360*i6 + 385*i10 + 415*i14 - 1900*b18 =L= 0;

e12..    330*i3 + 360*i7 + 385*i11 + 415*i15 - 1900*b19 =L= 0;

e13..    330*i4 + 360*i8 + 385*i12 + 415*i16 - 1900*b20 =L= 0;

e14..  - i1 - i5 - i9 - i13 + b17 =L= 0;

e15..  - i2 - i6 - i10 - i14 + b18 =L= 0;

e16..  - i3 - i7 - i11 - i15 + b19 =L= 0;

e17..  - i4 - i8 - i12 - i16 + b20 =L= 0;

e18..    i1 + i5 + i9 + i13 - 5*b17 =L= 0;

e19..    i2 + i6 + i10 + i14 - 5*b18 =L= 0;

e20..    i3 + i7 + i11 + i15 - 5*b19 =L= 0;

e21..    i4 + i8 + i12 + i16 - 5*b20 =L= 0;

e22..    b17 - i21 =L= 0;

e23..    b18 - i22 =L= 0;

e24..    b19 - i23 =L= 0;

e25..    b20 - i24 =L= 0;

e26..  - 15*b17 + i21 =L= 0;

e27..  - 12*b18 + i22 =L= 0;

e28..  - 9*b19 + i23 =L= 0;

e29..  - 6*b20 + i24 =L= 0;

e30..    i21 + i22 + i23 + i24 =G= 8;

e31..  - b17 + b18 =L= 0;

e32..  - b18 + b19 =L= 0;

e33..  - b19 + b20 =L= 0;

e34..  - i21 + i22 =L= 0;

e35..  - i22 + i23 =L= 0;

e36..  - i23 + i24 =L= 0;

* set non-default bounds
i1.up = 5;
i2.up = 5;
i3.up = 5;
i4.up = 5;
i5.up = 5;
i6.up = 5;
i7.up = 5;
i8.up = 5;
i9.up = 5;
i10.up = 5;
i11.up = 5;
i12.up = 5;
i13.up = 5;
i14.up = 5;
i15.up = 5;
i16.up = 5;
i21.up = 15;
i22.up = 12;
i23.up = 9;
i24.up = 6;

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;