makeShekelFunction

Single-objective test function based on the formula
$$f(\mathbf{x}) = -\sum_{i=1}^{m} \left(\sum_{j=1}^{4} (x_j - C_{ji})^2 + \beta_{i}\right)^{-1}$$.
Here, $m \in \{5, 7, 10\}$ defines the number of local optima, $C$ is a $4 x 10$ matrix
and $\beta = \frac{1}{10}(1, 1, 2, 2, 4, 4, 6, 3, 7, 5, 5)$ is a vector. See <a href="https://www.sfu.ca/~ssurjano/shekel.html">https://www.sfu.ca/~ssurjano/shekel.html</a>
for a defintion of $C$.

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

makeShekelFunction function

<dl><dt>m</dt>
<dd>[<code>numeric(1)</code>] 
Integer parameter (defines the number of local optima).
Possible values are 5, 7 or 10.</dd></dl>

Arguments

Single-objective test function based on the formula
$$f(\mathbf{x}) = -\sum_{i=1}^{m} \left(\sum_{j=1}^{4} (x_j - C_{ji})^2 + \beta_{i}\right)^{-1}$$.
Here, $m \in \{5, 7, 10\}$ defines the number of local optima, $C$ is a $4 x 10$ matrix
and $\beta = \frac{1}{10}(1, 1, 2, 2, 4, 4, 6, 3, 7, 5, 5)$ is a vector. See <a href='https://www.sfu.ca/~ssurjano/shekel.html'>https://www.sfu.ca/~ssurjano/shekel.html</a>
for a defintion of $C$.

Shekel functions — makeShekelFunction

<dl>

<dt>m</dt>
<dd>[<code>numeric(1)</code>] 
Integer parameter (defines the number of local optima).
Possible values are 5, 7 or 10.</dd>

</dl>

makeShekelFunction: Shekel functions

Description

Usage

Value

Arguments