makeViennetFunction {smoof}R Documentation

Viennet function generator

Description

The Viennet test problem VNT is designed for three objectives only. It has a discrete set of Pareto fronts. It is defined by the following formulae.

f(x)=(f1(x),f2(x,f3(x)f(\mathbf{x}) = \left(f_1(\mathbf{x}), f_2(\mathbf{x}, f_3(\mathbf{x}\right)

with

f1(x)=0.5(x12+x22)+sin(x12+x22)f_1(\mathbf{x}) = 0.5(\mathbf{x}_1^2 + \mathbf{x}_2^2) + \sin(\mathbf{x}_1^2 + \mathbf{x}_2^2)

f2(x)=(3x1+2x2+4)28+(x1x2+1)227+15f_2(\mathbf{x}) = \frac{(3\mathbf{x}_1 + 2\mathbf{x}_2 + 4)^2}{8} + \frac{(\mathbf{x}_1 - \mathbf{x}_2 + 1)^2}{27} + 15

f3(x)=1x12+x22+11.1exp((x11+x22))f_3(\mathbf{x}) = \frac{1}{\mathbf{x}_1^2 + \mathbf{x}_2^2 + 1} - 1.1\exp(-(\mathbf{x}_1^1 + \mathbf{x}_2^2))

with box constraints 3x1,x23-3 \leq \mathbf{x}_1, \mathbf{x}_2 \leq 3.

Usage

makeViennetFunction()

Value

[smoof_multi_objective_function]

References

Viennet, R. (1996). Multicriteria optimization using a genetic algorithm for determining the Pareto set. International Journal of Systems Science 27 (2), 255-260.


[Package smoof version 1.6.0.3 Index]