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Instance ann_fermentation_tanh

Fermentation process of glucose to gluconic acid learned and optimized by an embedded artificial neural network.
Formats gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-99.93663292 p1 ( gdx sol )
(infeas: 3e-14)
Other points (infeas > 1e-08)  
Dual Bounds
-99.93663847 (LINDO)
References Schweidtmann, Artur M. and Mitsos, Alexander, Deterministic Global Optimization with Artificial Neural Networks Embedded, Journal of Optimization Theory and Applications, 180:3, 2019, 925-948.
Application Neural Networks
Added to library 29 Nov 2021
Problem type NLP
#Variables 12
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature indefinite
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 9
#Linear Constraints 7
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 2
Operands in Gen. Nonlin. Functions tanh
Constraints curvature indefinite
#Nonzeros in Jacobian 23
#Nonlinear Nonzeros in Jacobian 2
#Nonzeros in (Upper-Left) Hessian of Lagrangian 5
#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 2
Average blocksize in Hessian of Lagrangian 1.333333
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.5000e-02
Maximal coefficient 1.4792e+02
Infeasibility of initial point 101.2
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
*        10       10        0        0        0        0        0        0
*
* Variable counts
*                  x        b        i      s1s      s2s       sc       si
*     Total     cont   binary  integer     sos1     sos2    scont     sint
*        13       13        0        0        0        0        0        0
* FX      0
*
* Nonzero counts
*     Total    const       NL
*        26       22        4

* Solve m using NLP minimizing objvar;

Variables
    objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13;

Equations
    e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;

e1..  91.91176470588235 * x10 / x2 + objvar =E= 0;
e2..  -tanh(x12) + x8 =E= 0;
e3..  -tanh(x13) + x9 =E= 0;
e4..  -0.0949474332688833 * x8 + 0.968637250639063 * x9 + x11 =E=
      0.002499597315649;
e5..  x10 - 86.324 * x11 =E= 92.74;
e6..  -0.025 * x2 + x5 =E= -3.5;
e7..  -x3 + x6 =E= -2;
e8..  -0.04 * x4 + x7 =E= -1.4;
e9..  -24.4380718077469 * x5 - 22.0304402344789 * x6 + 147.921509281049 * x7 +
      x12 =E= 101.235018055261;
e10..  1.48567642304727 * x5 - 0.0532843142008436 * x6 + 0.910590580134437 * x7
       + x13 =E= 0.18771256886977;

* set non-default bounds
x2.lo = 100; x2.up = 180;
x3.lo = 1; x3.up = 3;
x4.lo = 10; x4.up = 60;

Model m / all /;

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

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

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


Last updated: 2022-06-23 Git hash: c4ba8ecd
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