Table 1.

Mathematical modeling of the five main position-changing strategies of dragonfly [8].

Position Updating Strategies	Equations	Description
Separation	$S_i=-{\displaystyle \sum _{j=1}^N}X- X_j$	$X$: position of the current individual $X_j$: position of the j-th neighboring individual $N$: number of the neighboring individuals $V_j$: velocity of the j-th neighboring individual $X^{+}$: position of the food source $X^{-}$: position of the enemy ($s$, $a$, $c$, $f$, $e)$: separation, alignment, cohesion, food, and enemy factors $w$: inertia weight $t$: current iteration
Alignment	$A_i=\frac{{{\displaystyle \sum }}_{j=1}^N{V}_j}{N}$
Cohesion	$C_i=\frac{{{\displaystyle \sum }}_{j=1}^N{X}_j}{N}-X$
Attraction to food	$F_i=X^{+}-X$
Distraction from enemy	$E_i=X^{-}+X$
Position updating	$∆X_{t+1}=\left(s{S}_i+a{A}_i+c{C}_i+f{F}_i+e{E}_i\right)+w∆X_t$ $X_{t+1}= X_t+ ∆X_{t+1}$
Position updating with Lévy flight	$X_{t+1}= X_t+ Levy\left(d\right)\times X_t$ Lévy $\left(x\right)=0.10\times \frac{r_1\times \sigma }{{\left|r_2\right|}^{\frac{1}{\beta }}}$ $\sigma ={\left(\frac{\mathsf{\Gamma }\left(1+\beta \right)\times sin\left(\frac{\pi \beta }{2}\right)}{\mathsf{\Gamma }\left(\frac{1+\beta }{2}\right)\times \beta \times 2^{\left(\frac{\beta -1}{2}\right)}}\right)}^{\frac{1}{\beta }}$ $\mathsf{\Gamma }\left(x\right)= \left(x-1\right)!$	$d$: dimension of the position vectors $r_1$, $r_2$: random numbers in [0, 1] $\beta$: constant