makeZDT4Function: ZDT4 Function

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

ZDT4 Function

Description

Builds and returns the two-objective ZDT4 test problem. For m objective it is defined as follows

f(\mathbf{x}) = \left(f_1(\mathbf{x}_1), f_2(\mathbf{x})\right)

with

f_1(\mathbf{x}_1) = \mathbf{x}_1, f_2(\mathbf{x}) = g(\mathbf{x}) h(f_1(\mathbf{x}_1), g(\mathbf{x}))

where

g(\mathbf{x}) = 1 + 10 (m - 1) + \sum_{i = 2}^{m} (\mathbf{x}_i^2 - 10\cos(4\pi\mathbf{x}_i)), h(f_1, g) = 1 - \sqrt{\frac{f_1(\mathbf{x})}{g(\mathbf{x})}}

and \mathbf{x}_i \in [0,1], i = 1, \ldots, m. This function has many Pareto-optimal fronts and is thus suited to test the algorithms ability to tackle multi-modal problems.

Usage

makeZDT4Function(dimensions)

Arguments

dimensions

[integer(1)] Number of decision variables.

Value

[smoof_multi_objective_function] Returns an instance of the ZDT4 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.