makeZDT4Function

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 multimodal problems.

Provides generators for a high number of both single- and multi-
objective test functions which are frequently used for the benchmarking of
(numerical) optimization algorithms. Moreover, it offers a set of convenient
functions to generate, plot and work with objective functions.

Jakob Bossek

smoof

Single and Multi-Objective Optimization Test Functions

Pascal Kerschke

makeZDT4Function function

<dl><dt>dimensions</dt>
<dd>[<code>integer(1)</code>] 
Number of decision variables.</dd></dl>

Arguments

ZDT4 Function — makeZDT4Function

<dl>

<dt>dimensions</dt>
<dd>[<code>integer(1)</code>] 
Number of decision variables.</dd>

</dl>

makeZDT4Function: ZDT4 Function

Description

Usage

Value

Arguments

References