Description

Builds and returns the multi-objective ED2 test problem.

The ED2 test problem is defined as follows:

Minimize f[j](X) = (1 / (F[natmin](X) + 1)) * p(Θ(X)), for j = 1, ..., m,

with X = (x[1], ..., x[n]), where 0 ≤ x[i] ≤ 1, and Θ = (θ[1], ..., θ[m-1]), where 0 ≤ θ[j] ≤ π/2, for i = 1, ..., n and j = 1, ..., m - 1.

Moreover F[natmin](X) = b + (r(X) - a) + 0.5 + 0.5 * (2 π * (r(X) - a) + π)

with a = 0.051373, b = 0.0253235, and r(X) = sqrt(x[m]^2 + ... + x[n]^2), as well as

p[1](Θ) = cos(θ[1])^(2/γ),

p[j](Θ) = (sin(θ[1]) * ... * sin(θ[j - 1]) * cos(θ[j]))^(2/γ), for 2 ≤ j ≤ m - 1,

and p[m](Θ) = (sin(θ[1]) * ... * sin(θ[m - 1]))^(2/γ).

Usage

Arguments

Value

[smoof_multi_objective_function]

References

M. T. M. Emmerich and A. H. Deutz. Test Problems based on Lame Superspheres. Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), pp. 922-936, Springer, 2007.