Description

Builds and returns the two-objective ZDT6 test problem. For m objective it is defined as follows

f(\mathbf{x}) = ≤ft(f_1(\mathbf{x}), f_2(\mathbf{x})\right)

with

f_1(\mathbf{x}) = 1 - \exp(-4\mathbf{x}_1)\sin^6(6π\mathbf{x}_1), f_2(\mathbf{x}) = g(\mathbf{x}) h(f_1(\mathbf{x}_1), g(\mathbf{x}))

where

g(\mathbf{x}) = 1 + 9 ≤ft(\frac{∑_{i = 2}^{m}\mathbf{x}_i}{m - 1}\right)^{0.25}, h(f_1, g) = 1 - ≤ft(\frac{f_1(\mathbf{x})}{g(\mathbf{x})}\right)^2

and \mathbf{x}_i \in [0,1], i = 1, …, m. This function introduced two difficulities (see reference): 1. the density of solutions decreases with the closeness to the Pareto-optimal front and 2. the Pareto-optimal solutions are nonuniformly distributed along the front.

Usage

Arguments

Value

[smoof_multi_objective_function]

References

E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000