MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance shiporig

This model designs a vertically corrugated transverse bulkhead of an oil tanker.
The objective is to design for minimum weight and meet stress, moment of inertia and plate thickness constraints.
This version of ship corresponds to the current version of ship from the GAMS model library.
It corresponds to the original version from the paper, plus an extra lower bound on variable x10.
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
5.54091471 p1 ( gdx sol )
(infeas: 4e-12)
Other points (infeas > 1e-08)  
Dual Bounds
0.00000000 (ANTIGONE)
0.00000000 (BARON)
0.00000000 (COUENNE)
5.54091471 (LINDO)
-99999999809999994880.00000000 (SCIP)
References Bracken, Jerome and McCormick, Garth P, Chapter 6. In Bracken, Jerome and McCormick, Garth P, Selected Applications of Nonlinear Programming, John Wiley and Sons, New York, 1968.
Source GAMS Model Library model ship
Application Structural Optimization
Added to library 15 Aug 2014
Problem type NLP
#Variables 10
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature indefinite
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 6
#Constraints 17
#Linear Constraints 10
#Quadratic Constraints 0
#Polynomial Constraints 3
#Signomial Constraints 3
#General Nonlinear Constraints 1
Operands in Gen. Nonlin. Functions mul sqrt
Constraints curvature indefinite
#Nonzeros in Jacobian 48
#Nonlinear Nonzeros in Jacobian 23
#Nonzeros in (Upper-Left) Hessian of Lagrangian 41
#Nonzeros in Diagonal of Hessian of Lagrangian 3
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 10
Maximal blocksize in Hessian of Lagrangian 10
Average blocksize in Hessian of Lagrangian 10.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 3.9000e-03
Maximal coefficient 4.9500e+02
Infeasibility of initial point 407.3
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
*         18        5       13        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11       11        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         55       26       29        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18;


e1.. -0.5*x9*x4*(0.8*x7 + 0.333333333333333*x8) + x1 =E= 0;

e2.. -0.5*x9*x5*(0.8*x7 + 0.333333333333333*x8) + x2 =E= 0;

e3.. -0.5*x9*x6*(0.8*x7 + 0.333333333333333*x8) + x3 =E= 0;

e4.. -sqrt(x8*x8 - x9*x9) - x7 + x10 =E= 0;

e5..    x1 - 8.4652734375*x10 =G= 0;

e6..    x2 - 9.65006510416667*x10 =G= 0;

e7..    x3 - 8.8716796875*x10 =G= 0;

e8.. 0.5*x1*x9 - 2.2*(8.4652734375*x10)**1.33333333333333 =G= 0;

e9.. 0.5*x2*x9 - 2.2*(9.65006510416667*x10)**1.33333333333333 =G= 0;

e10.. 0.5*x3*x9 - 2.2*(8.8716796875*x10)**1.33333333333333 =G= 0;

e11..    x4 - 0.0111771747883801*x7 =G= 0.2;

e12..    x5 - 0.0137655360411427*x7 =G= 0.2;

e13..    x6 - 0.0155663872253648*x7 =G= 0.2;

e14..    x4 - 0.0111771747883801*x8 =G= 0.2;

e15..    x5 - 0.0137655360411427*x8 =G= 0.2;

e16..    x6 - 0.0155663872253648*x8 =G= 0.2;

e17..    x8 - x9 =G= 0;

e18.. -(0.0039*x7 + 0.0039*x8)*(495*x4 + 385*x5 + 315*x6)/x10 + objvar =E= 0;

* set non-default bounds
x4.lo = 1.05;
x5.lo = 1.05;
x6.lo = 1.05;
x10.lo = 1;

* set non-default levels
x1.l = 934.032;
x2.l = 934.032;
x3.l = 1011.868;
x4.l = 1.2;
x5.l = 1.2;
x6.l = 1.3;
x7.l = 45.8;
x8.l = 43.2;
x9.l = 30.5;
x10.l = 76.3939536510076;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


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