$\mathrm{T}$	Task group	${\mathrm{X}}_{\mathrm{i},\mathrm{j}}$	Population
$\mathrm{m}$	Count of fogs	${\mathrm{X}}_{\mathrm{p}}$	Location of the target
$\mathrm{v}$	Number of virtual machines	$\overrightarrow{{\mathrm{r}}_1}$ and $\overrightarrow{{\mathrm{r}}_2}$	Randomly selected vectors between [0, 1]
n	Count of VMs	$\mathsf{\alpha }$	Best search agent
m	Count of fogs	$\mathsf{\beta }$	2nd best optimal solution
$\mathrm{x}$	Count of consumers on fog ${\mathrm{F}}_1$	$\mathsf{\delta }$	3rd best optimal solution
$\mathrm{u}$	Fixed factor	$\overrightarrow{{\mathrm{x}}_{\mathsf{\alpha }}}$, $\overrightarrow{{\mathrm{x}}_{\mathsf{\beta }}}$ and $\overrightarrow{{\mathrm{x}}_{\mathsf{\delta }}}$	Optimal solutions achieved in the ${\mathrm{t}}^{\mathrm{th}}$ iteration
$\mathsf{\beta }$	Per GB transferring price	${\mathrm{D}}_{\mathsf{\alpha }}$	Position of the $\mathsf{\alpha }$ search agent
${\mathrm{P}}_{\mathrm{ij}}$	Length of task	${\mathrm{D}}_{\mathsf{\beta }}$	Position of the $\mathsf{\beta }$ search agent
${\mathrm{A}}_{\mathrm{i}}$	Task specified for every request	${\mathrm{D}}_{\mathsf{\delta }}$	Position of the $\mathsf{\delta }$ search agent
${\mathrm{Arrival}}_{\mathrm{Time}}$	The time when the task began	$\mathrm{F}$	Scaling factor
${\mathrm{Finish}}_{\mathrm{Time}}$	The time when the task execution is finished	$\mathrm{v}$	Mutant vectors
${\mathrm{Delay}}_{\mathrm{Time}}$	Delay time from customer transmitting the request till the task began to execute	Max. iter	Maximal number of iterations
${\mathrm{Cos}\mathrm{t}}_{\mathrm{DT}}$	Cost of DT	$\mathrm{POP}$	Whole population
${\mathrm{Cos}\mathrm{t}}_{\mathrm{VM}}$	Cost of VM	$\mathrm{h}$	Whole time intervals
${\mathrm{Cos}\mathrm{t}}_{\mathrm{MG}}$	Cost of MG	$\mathrm{CR}$	Crossover factor
${\mathrm{VM}}_{\mathrm{final}\mathrm{time}}$	The final time of VM	$\mathrm{u}$	Mutant vector
${\mathrm{VM}}_{\mathrm{InitialTime}}$	Start time of VM	$\mathsf{\mu }$	Test vector
${\mathrm{Data}}_{\mathrm{Used}}$	Transmitted data which is used to execute	$\mathrm{x}$	Target vector
${\mathrm{Total}}_{\mathrm{Time}}$	The overall time of VM	D	All counts of devices
${\mathrm{P}}_{\mathrm{ij}}$	Length of task	A and C	Fitness coefficients
${\mathrm{K}}_{\mathrm{minimizw}}$	Minimizing response time and processing	X	Location of the wolf for the ${\mathrm{t}}^{\mathrm{th}}$ iteration
${\mathrm{EXC}}_{{\mathrm{vm}}_1}\left({\mathrm{F}}_1\right)$	Working time of performing the group of tasks on fog ${\mathrm{F}}_1$ on ${\mathrm{VM}}_1$	$\mathrm{a}$	Graded from two to zero in all iterations
${\mathrm{F}}_1$	Group of clusters of consumers	$\mathrm{PT}$	Processing time
${\mathrm{Start}}_{\mathrm{Time}}$	The start time of VM execution	$\mathrm{RT}$	Time duration from when a request of uses is sent to fog and when a response has been obtained
${\mathrm{Finish}}_{\mathrm{Time}}$	The finish time of VM execution	$\mathrm{VM}$	Virtual machines
${\mathrm{l}}_{\mathrm{j}}$ and ${\mathrm{u}}_{\mathrm{j}}$	Lower and upper bounds