makeZDT6Function: ZDT6 Function

In jakobbossek/smoof: Single and Multi-Objective Optimization Test Functions

ZDT6 Function

Description

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

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

with

f_1(\mathbf{x}) = 1 - \exp(-4\mathbf{x}_1)\sin^6(6\pi\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 \left(\frac{\sum_{i = 2}^{m}\mathbf{x}_i}{m - 1}\right)^{0.25}, h(f_1, g) = 1 - \left(\frac{f_1(\mathbf{x})}{g(\mathbf{x})}\right)^2

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

Usage

makeZDT6Function(dimensions)

Arguments

dimensions

[integer(1)] Number of decision variables.

Value

[smoof_multi_objective_function] Returns an instance of the ZDT6 function as a smoof_multi_objective_function object.

References

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

jakobbossek/smoof documentation built on Feb. 17, 2024, 2:23 a.m.