Author Correction: The fusion–fission optimization (FuFiO) algorithm

Correction to: Scientific Reports https://doi.org/10.1038/s41598-022-16498-4, published online 20 July 2022

The original version of this Article contained an error in the spelling of the author Nima Darabi which was incorrectly given as Nima Darabai.

The Article also contained an error in the Equation in the Analyses based on competitions on evolutionary computation (CEC) section, under the subheading ‘Computational time and complexity analyses’ where “$O\left(F,u,F,i,O\right)$” was incorrectly given as “$O\left(F,F,O\right)$”.

$$\begin{array}{cc}\hfill O\left(F,F,O\right)& =O\left(t,\times ,\left[O,\left(s,o,r,t\right),+,O,\left(n,u,c,l,e,a,r,,r,e,a,c,t,i,o,n,,l,e,v,e,l\right)\right]\right)\hfill \\ \hfill & =O\left(t,\times ,\left[n^2,+,n,\times ,d\right]\right)\hfill \\ \hfill & =O(t{n}^2+nd)\hfill \end{array}$$

now reads:

$$\begin{array}{cc}\hfill O\left(\mathit{FuFiO}\right)& =O\left(t\times \left[O\left(\mathit{sort}\right)+O\left(nuclearreactionlevel\right)\right]\right)\hfill \\ \hfill & =O\left(t\times \left[n^2+n\times d\right]\right)\hfill \\ \hfill \end{array}$$

In addition, Eq. 11 was incorrect,

$$X_i=\left\{\begin{array}{c}{X}_{i}f\left(X_i\right)isbetterthanf\left(X_i^{\mathit{new}}\right)\\ X_i^{\mathit{new}}f\left(X_{inew}\right)isbetterthanf\left(X_i\right)\end{array}\right)$$

now reads:

$$X_i=\left\{\begin{array}{cc}& X_{i}f\left(X_i\right)\text{is}\text{better}\text{than}f\left(X_i^{\mathit{new}}\right)\hfill \\ \hfill & X_i^{\mathit{new}}f\left(X_{inew}\right)\text{is}\text{better}\text{than}f\left(X_i\right)\hfill \\ \hfill \end{array}\right)$$

Furthermore, the article contained errors in Fig. 13 where label (a) was omitted and “FuFiO” was incorrectly given as “FFO” on the left Figure of panel (d).The original Article has been corrected.

Figure 13.

ANOVA test results for fixed-dimension functions.