Smart Home Battery for the MultiObjective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer
Abstract
:1. Introduction
2. Power Scheduling Problem in Smart Home Formulation
2.1. Power Consumption
2.2. Electricity Bill (EB)
2.3. PeaktoAverage Ratio (PAR)
2.4. User Comfort (UC) Level
3. MultiObjective Approach for PSPSH
3.1. MultiObjective Approach: Overview
3.2. MultiObjective Approach for PSPSH (MOPSPSH)
 Step 1:
 Choosing a convenient method to address MOPSPSH.The first step of formulating MOPSPSH is to choose a method to solve the problem. As mentioned previously, the weighted sum method is the simplest method because it is easy to implement and has no complexity. Besides, this method is mostly used by PSPSH stateoftheart methods. Therefore, this method is chosen to address the proposed MOPSPSH. The procedure of the weighted sum method is to assign a convenient weight $w>0$ to each objective function as follows:$$F\left(x\right)=\sum _{c=1}^{r}{w}_{c}\times {F}_{c}\left(x\right),$$
 Step 2:
 Normalize the objective functionThe second step of formulating MOPSPSH is normalize the fitness values of EB, PAR, WTR, and CPR to equate their value ranges. In PSPSH, the value ranges of WTR and CPR are between 0 and 1, whereas the value ranges of EB and PAR are unknown. EB and PAR have unknown values of ${F}^{0}$ and ${F}^{max}$. Therefore, their fitness values can be normalized using Equation (25), as follows:$$E{B}^{trans}=\frac{EB}{EB+A}\phantom{\rule{1.em}{0ex}}A\in {Z}^{+},$$$$PA{R}^{trans}=\frac{PAR}{PAR+B}\phantom{\rule{1.em}{0ex}}B\in {Z}^{+},$$
 Step 3:
 Modeling the MOPSPSHAfter choosing a convenient method for MOPSPSH and normalizing their fitness values, modeling MOPSPSH is conducted in this step. Based on the objective functions in Equations (11), (14), (16) and (21), PSPSH is modeled in Equation (29) as a MOP.$$\begin{array}{c}\hfill minF\left(x\right)={w}_{1}\times E{B}^{trans}+{w}_{2}\times PA{R}^{trans}\\ \hfill \phantom{\rule{1.em}{0ex}}+{w}_{3}\times WT{R}_{avg}+{w}_{4}\times CP{R}_{avg}\end{array},$$
4. Smart Home Battery (SHB)
4.1. Smart Home Battery (SHB): Overview
4.2. Smart Home Battery for MOPSPSH (BMOPSPSH)
 Step 1:
 Initialize the SHB parametersAs discussed previously, the charging operations of SHB will be scheduled as SAs in the smart home. Several SHB parameters should be initialized, including the maximum amount of power that can be stored in SHB, known as the capacity of SHB ($Ca{p}_{B}$), the charging and discharging efficiency, known as the round trip of SHB efficiency (${\mu}_{B}$), the number of charging operations (CO) represented as $CO=(c{o}_{1},c{o}_{2},\dots ,c{o}_{u})$, the beginning and ending OTP of each charging operation $OTPsc$ and $OTPec$ represented as $OTPsc=(OTPs{c}_{1},OTPs{c}_{2},\dots ,OTPs{c}_{u})$ and $OTPec=(OTPe{c}_{1},OTPe{c}_{2},\dots ,OTPe{c}_{u})$ respectively, and LOC for each charging operation ($LOCc$), such that $LOCc=(l{c}_{1},l{c}_{2},\dots ,l{c}_{u})$. The $Ca{p}_{B}$ and ${\mu}_{B}$ are initialized by users, whereas CO, $OTPsc$, $OTPec$, and $LOCc$ are initialized by the proposed BSA.A constraint of the total number of COs (u) should be considered in this step as follows:$$Ach=n/2$$$$Ach\ge u,$$$OTPsc$ and $OTPec$ for each CO are initialized to be the beginning and ending, respectively, of the available period for SHB to be charged. $OTPsc$ is set to the beginning of T, and $OTPec$ is set to $n1$ to ensure that SHB not charging at the last time slot. For $LOCc$, each $lc$ is set to be onetime slot (the smallest period to be scheduled).Algorithm 1 shows the pseudocode for initializing the SHB parameters.
Algorithm 1 Pseudocode of SHB parameters initialization  Parameters initialized by users ($Ca{p}_{B},{\mu}_{B}$)
 Parameters initialized by BSA ($CO,OTPsc,OTPec,LOCc$) with respecting the $Ach$
 Return SHB parameters;
 Step 2:
 Initialize the SHB charging populationEach solution of charging operations is represented as a vector containing the starting time for each charging operation ($stc$). The population of charging operations contains an N number of solutions initialized randomly, as shown in Equation (32).$$\begin{array}{cc}\hfill \mathit{SHB}\text{}\mathit{charging}\text{}\mathit{population}=& \left[\begin{array}{cccc}st{c}_{1}^{1}& st{c}_{2}^{1}& \cdots & st{c}_{u}^{1}\\ st{c}_{1}^{2}& st{c}_{2}^{2}& \cdots & st{c}_{u}^{2}\\ \vdots & \vdots & \cdots & \vdots \\ st{c}_{1}^{N}& st{c}_{2}^{N}& \cdots & st{c}_{u}^{N}\end{array}\right],\end{array}$$Algorithm 2 shows the pseudocode for generating the SHB charging population.
Algorithm 2 Pseudocode for generating the SHB charging population  Create a charging operations population matrix of size ($u\times N$)
 for each solution (y) do
 for each charging operation (c) do
 Initialize the values ($stc$) randomly with respecting $OTPsc$, $OTPec$, and $LOCc$ of c
 end for
 end for
 Return SHB charging population;
 Step 3:
 Calculate the power consumed by the SHB charging operationsIn this step, the power charged in SHB by charging operation c at time slot j ($PBc{o}_{c}^{j}$) is calculated. $PBco$ can be calculated as follows:$$PBc{o}_{c}^{j}={\mu}_{ch}\times Pc{h}_{c}^{j},$$$$0\le Pc{h}_{c}^{j}\le C{H}^{j},$$$$C{H}^{j}=CH\times h,$$$$\sum _{c=1}^{u}PBc{o}_{c}\le Ca{p}_{B},$$u and $Pch$ are generated randomly by the BSA to increase their flexibility and allow the adapted algorithm to deal with the four objectives of PSPSH. After the PBco for all COs are calculated, the BSA will send COs to the adapted algorithm to be scheduled.Algorithm 3 shows the pseudocode for calculating the power consumed by the SHB charging operation.
Algorithm 3 Pseudocode for calculating power consumed by the charging operation  for each solution (y) do
 for each charging operation (c) do
 end for
 end for
 Return charged SHB
 Return $PBco$ for all $COs$
 Send $COs$ to the adapted algorithm to be scheduled
 Step 4:
 Discharge the SHBAs mentioned previously, the discharging mode of SHB is considered as an additional source. In other words, discharging operations will not be scheduled by the adapted algorithm. However, the discharging mode is managed by the BSA to discharge power using the roulette wheel method, where the charged power will be discharged on the basis of the sizes of the parts on the wheel assigned for each time slot with considering the amount of power consumed at that time slots. In the roulette wheel method, big parts are assigned to highpricing time slots and small parts to lowpricing time slots. The reason for assigning the part sizes this way in the distribution is to reduce the amount of power consumed at highpricing time slots due to its effect on the stability of the power system and EBs. The roulette wheel method is used in this study due to its popularity and its performance in distributing individuals on the basis of their importance. Therefore, it gives a high chance for BSA to reduce the amount of power consumed at highpricing time slots.The possible time slots for SHB to be discharged is calculated using Equation (36).$$Adi{s}^{j}=\left\{\begin{array}{c}1\phantom{\rule{1.em}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}\phantom{\rule{1.em}{0ex}}P{S}^{j}>0\phantom{\rule{1.em}{0ex}}\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}PBc{o}^{j}=0\phantom{\rule{1.em}{0ex}}\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}\sum _{b=1}^{j}PBc{o}^{b}>0\hfill \\ 0\phantom{\rule{1.em}{0ex}}\mathrm{Otherwise}\hfill \end{array}\right.,$$After choosing a time slot to discharge SHB using the roulette wheel method, BSA will define the amount of power to discharge $PBdo$ on the basis of the power consumed at that time slot as follows:$$PBd{o}^{j}={\mu}_{dis}\times Pdi{s}^{j},$$$Pdi{s}^{j}$ will be released from SHB on the basis of Equation (38). BSA will keep choosing the discharging time slots and update the value of $Adis$ until all of the power stored in SHB is discharged.$$\sum _{c=1}^{u}\sum _{b=1}^{j}PBc{o}_{c}^{b}=\sum _{c=1}^{u}\sum _{b=1}^{j1}PBc{o}_{c}^{b}Pdi{s}^{j},$$$$\sum _{c=1}^{u}\sum _{b=1}^{j1}PBc{o}_{c}^{b}\ge Pdi{s}^{j},$$However, if the value of ${\sum}_{j=1}^{n}Adi{s}^{j}$ is equal to 0 and some power is still considered as stored in SHB, then BSA will update the power of the last CO (i.e., $PBc{o}_{u}$) to be equal to 0 and release it from SHB. The BSA will repeat this process until all of the remaining power in SHB is released$Pdi{s}^{j}$ should not exceed the maximum allowable discharge $DI{S}^{j}$ at time slot j as follows:$$0\le PBd{o}^{j}\le DI{S}^{j},$$$$DI{S}^{j}=DIS\times h,$$DIS is the maximum allowable discharge. Note that the capacity of any SHB is defined according to the amount of power that can be discharged and not the amount that can be stored. For instance, the capacity of an SHB is 5 kWh, but the usable power is 4.5 kWh. Therefore, ${\mu}_{ch}$ of the proposed SHB is set equal to ${\mu}_{B}$, while the ${\mu}_{dis}$ is set equal to 1 [74].
Algorithm 4 Pseudocode of discharge the SHB 

Algorithm 5 Pseudocode of the four steps of the proposed BSA 

5. Grey Wolf Optimizer for PSPSH
5.1. Grey Wolf Optimizer (GWO)
 Social Hierarchy
 The pack of grey wolves has an austere social hierarchy, which is classified into alpha ($\alpha $), beta ($\beta $), delta ($\delta $), and omega ($\omega $). Wolves belong to the class alpha are considered as the leader of the grey wolves’ hierarchy due to their domination and power to manage the pack. The beta wolves are playing the primary role in support the alpha in leading the pack. Delta wolves are in the third level of the hierarchy, and they in charge of leading the lowest level in the hierarchy. Omega wolves are considered as the lowest level in the hierarchy.In GWO, the solutions are represented as grey wolves in the social hierarchy, where the best solution is represented as $\alpha $ wolf, $\beta $ and $\delta $ wolves are the second and third best solutions, respectively, and $\omega $ wolves are considered as the rest of the solutions.
 Encircling Prey
 In addition to this deep social hierarchy, the intelligent behavior of group hunting is also procedurally modeled. This behavior involves three main phases: chasing, encircling, and attacking.The grey wolves can change/update their locations closer to the prey by encircling the prey mechanism. The encircling behavior of grey wolves is formulated as follows:$$\overrightarrow{D}=\overrightarrow{C}\times {\overrightarrow{X}}_{p}\left(itr\right)\overrightarrow{X}\left(itr\right),$$$$\overrightarrow{X}(itr+1)={\overrightarrow{X}}_{p}\left(itr\right)\overrightarrow{A}\times \overrightarrow{D},$$The coefficient vectors $\overrightarrow{C}$ and $\overrightarrow{A}$ are calculated as$$\overrightarrow{A}=2\times \overrightarrow{a}\times {\overrightarrow{r}}_{1}\overrightarrow{a},$$$$\overrightarrow{C}=2\times {\overrightarrow{r}}_{2},$$
 Search for Prey (Exploration)
 The grey wolves searching mechanism for prey can be done on the basis of the wolves’ positions, where the wolves diverge and converge to find the best position to attack prey. The coefficient vectors $\overrightarrow{A}$ and $\overrightarrow{C}$ manage the divergence (exploration) and convergence (exploitation) of the wolves in GWO. GWO exploit a search space if $\overrightarrow{A}<1$ and explore a search space if $\overrightarrow{A}>1$.The changing values in $\overrightarrow{C}$ is not similar to $\overrightarrow{A}$, where $\overrightarrow{C}$ is changing randomly to emphasize exploration/exploitation and local optima stagnation avoidance throughout iterations.
 Hunting
 As mentioned previously, in GWO, the best three solutions are $\alpha $, $\beta $, and $\delta $ wolves, respectively, and $\omega $ wolves are the rest of the solutions.Owing to the domination and leadership of $\alpha $ wolf on the pack, $\alpha $ usually guides the hunting. $\beta $ and $\delta $ wolves occasionally can engage in hunting to help $\alpha $ wolf. $\omega $ wolves are usually changing their location according to the three best solutions ($\alpha ,\beta $, and $\delta $).The hunting mechanism on the basis of these wolves (solutions) is formulated as follows:$${\overrightarrow{D}}_{\alpha}={\overrightarrow{C}}_{1}\times {\overrightarrow{X}}_{\alpha}\overrightarrow{X},$$$${\overrightarrow{D}}_{\beta}={\overrightarrow{C}}_{2}\times {\overrightarrow{X}}_{\beta}\overrightarrow{X},$$$${\overrightarrow{D}}_{\delta}={\overrightarrow{C}}_{3}\times {\overrightarrow{X}}_{\delta}\overrightarrow{X},$$$${\overrightarrow{X}}_{1}={\overrightarrow{X}}_{\alpha}{\overrightarrow{A}}_{1}\times {\overrightarrow{D}}_{\alpha},$$$${\overrightarrow{X}}_{2}={\overrightarrow{X}}_{\beta}{\overrightarrow{A}}_{2}\times {\overrightarrow{D}}_{\beta},$$$${\overrightarrow{X}}_{3}={\overrightarrow{X}}_{\delta}{\overrightarrow{A}}_{3}\times {\overrightarrow{D}}_{\delta},$$$$\overrightarrow{X}(itr+1)=\frac{{\overrightarrow{X}}_{1}+{\overrightarrow{X}}_{2}+{\overrightarrow{X}}_{3}}{3},$$To change the location of the $\omega $ wolves for hunting in accordance with the $\alpha ,\beta $ and $\delta $ wolves, the location of the prey should be estimated by these three wolves.
Grey Wolf Optimizer for PSPSH
 GWO adaptation for MOPSPSH (MOPSPSHGWO)The adaptation of the GWO for MOPSPSH is discussed in this section. This adaptation contains five main steps, which are illustrated below.The flowchart of the proposed MOPSPSHGWO is provided in Figure 4.
 Step 1:
 Initialize MOPSPSHGWO parametersThe adaptation the MOPSPSHGWO is started by initializing the parameters of PSPSH and GWO. The PSPSH parameters are $\mathbf{S}$, $\mathbf{NS}$, $\mathbf{T}$, $\mathbf{PS}$, $\mathbf{PNS}$, $\mathbf{LOC}$, $\mathbf{OTPs}$, $\mathbf{OTPe}$, and $\mathbf{pc}$. The GWO parameters are $\overrightarrow{A}$, $\overrightarrow{C}$, $\overrightarrow{a}$, $\overrightarrow{{r}_{1}}$, $\overrightarrow{{r}_{2}}$, the minimum ($lb$) and maximum ($ub$) ranges for the search agent, the maximum number of iterations ($\mathbf{I}$), and the number of search agents in the pack ($\mathbf{N}$).
 Step 2:
 Initialize MOPSPSHGWO populationEach wolf in the pack is presented as a solution of MOPSPSHGWO, and each solution is containing the starting time $st$ for each appliance i, as shown in Figure 5.The MOPSPSHGWO population is containing of y number of solutions initialized randomly as shown in Equation (51).$$\begin{array}{cc}\hfill \mathit{MO}\text{}\mathit{PSPSH}\text{}\mathit{GWO}\text{}\mathit{population}=& \left[\begin{array}{cccc}s{t}_{1}^{1}& s{t}_{2}^{1}& \cdots & s{t}_{m}^{1}\\ s{t}_{1}^{2}& s{t}_{2}^{2}& \cdots & s{t}_{m}^{2}\\ \vdots & \vdots & \cdots & \vdots \\ s{t}_{1}^{y}& s{t}_{2}^{y}& \cdots & s{t}_{m}^{y}\end{array}\right],\end{array}$$
 Step 3:
 Fitness function calculationThe fitness value of each solution is calculated on the basis of Equation (29). In the MOPSPSHGWO method, the best solution and its fitness value are assigned to ${X}_{\alpha}$ and $f\left({X}_{\alpha}\right)$,respectively, and the second and third best solutions and their fitness values are assigned to ${X}_{\beta}$, ${X}_{\delta}$, and $f\left({X}_{\beta}\right)$, $f\left({X}_{\delta}\right)$, respectively.
 Step 4:
 Update the MOPSPSHGWO populationThe MOPSPSHGWO population is updated in the step, where the Equations (42)–(50) are in charge of this update.The updating mechanism of MOPSPSHGWO is utilized to estimate the distance between ${X}_{\omega}$ solutions and the ${X}_{\alpha}$ solution and then generate a new solution ${\overrightarrow{X}}_{1}$ Equations (42)–(44) and (47). The same steps for ${X}_{\alpha}$ are repeated for ${X}_{\beta}$ and ${X}_{\delta}$ to generate ${\overrightarrow{X}}_{2}$ using Equations (42), (43), (45) and (48) and to generate ${\overrightarrow{X}}_{3}$ using Equations (42), (43), (46) and (49). In Equation (50), a new solution ${X}^{\prime}(itr+1)$ is generated based on ${\overrightarrow{X}}_{1}$, ${\overrightarrow{X}}_{2}$, and ${\overrightarrow{X}}_{3}$.
 Step 5:
 Check the stop criterionSteps 3 and 4 of MOPSPSHGWO are repeated until the stop criterion is met.Algorithm 6 presents the pseudocode of the five steps of the proposed MOPSPSHGWO.
Algorithm 6 Pseudocode of the five steps of the proposed MOPSPSHGWO  1:
 Step 1: Initialize MOPSPSHGWO parameters;/
 2:
 Initialize all PSPSH parameters ($S,NS,T,PS,PNS,OT{P}_{s},OT{P}_{e},LOC,pc$)
 3:
 Initialize all GWO parameters ($a,{r}_{1},{r}_{2}\overrightarrow{A},\overrightarrow{C},lb,ub,I,N$)
 4:
 Step 2: Initialize MOPSPSHGWO population
 5:
 Initialize MOPSPSHGWO population matrix of size ($m\times N$)
 6:
 Step 3: Social Hierarchy
 7:
 while (itr $<=$ I) do
 8:
 for each solution (y) do
 9:
 Calculate the fitness of each solution
 10:
 $f\left({X}_{\alpha}\right)$ = the best fitness value
 11:
 $f\left({X}_{\beta}\right)$ = the second fitness value
 12:
 $f\left({X}_{\delta}\right)$ = the third fitness value
 13:
 ${X}_{\alpha}$ = the best solution
 14:
 ${X}_{\beta}$ = the second best solution
 15:
 ${X}_{\delta}$ = the third best solution
 16:
 end for
 17:
 Step 4: Update MOPSPSHGWO population
 18:
 for each solution (y) do
 19:
 for each appliance (i) do
 20:
 Update ${r}_{1},{r}_{2}$ (Random number in [0, 1])
 21:
 Update the value of ${A}_{1}$ (Equation (42))
 22:
 Update the value of ${C}_{1}$ (Equation (43))
 23:
 24:
 Update ${r}_{1},{r}_{2}$ (Random number in [0, 1])
 25:
 Update the value of ${A}_{2}$ (Equation (42))
 26:
 Update the value of ${C}_{2}$ (Equation (43))
 27:
 28:
 Update ${r}_{1},{r}_{2}$ (Random number in [0, 1])
 29:
 Update the value of ${A}_{3}$ (Equation (42))
 30:
 Update the value of ${C}_{3}$ (Equation (43))
 31:
 32:
 Generate a new solution $X(itr+1)$ (Equation (50))
 33:
 end for
 34:
 end for
 35:
 Step 5: Check the stop criterion
 36:
 if The maximum number of the iteration is not reached then
 37:
 $t=t+1$
 38:
 end if
 39:
 end while
 40:
 Return $f\left({X}_{\alpha}\right)$ and ${X}_{\alpha}$
 GWO adaptation for BMOPSPSH (BMOPSPSHGWO)BMOPSPSHGWO has six main steps, which will be thoroughly discussed below.The flowchart of BMOPSPSHGWO is provided in Figure 6.
 Step 1:
 Initialize BMOPSPSHGWO parametersThe adaptation of BMOPSPSHGWO is started by initializing the parameters of SHB, PSPSH, and GWO. The SHB parameters are $Ca{p}_{B},{\mu}_{B},CO,OTPsc,OTPec,$ and $LOCc$. The PSPSH and GWO are the same as initialized in the first step of MOPSPSHGWO, including $\mathbf{S},\mathbf{NS},\mathbf{T},\mathbf{PS},\mathbf{PNS},\mathbf{LOC},\mathbf{OTPs},\mathbf{OTPe},$ and $\mathbf{pc}$ for PSPSH and $\mathbf{I},\mathbf{N},\overrightarrow{A},\overrightarrow{C},\overrightarrow{a},\overrightarrow{{r}_{1}},\overrightarrow{{r}_{2}},lb,$ and $ub$ for GWO.
 Step 2:
 Initialize BMOPSPSHGWO populationIn this step, BMOPSPSHGWO solutions are initialized randomly, where each solution is presented as two vectors. The first vector contains the starting time $st$ for SAs and second vector contains the starting time $stc$ for charging operations, as shown in Figure 7The BMOPSPSHGWO population is presented as a matrix of size $(m+u)\times N$, in which m is the number of SAs, u is the number of charging operations, and N is the number of solutions. Equation (52) shows the presentation of the BMOPSPSHGWO population.$$\begin{array}{cc}\hfill \mathit{BMO}\text{}\mathit{PSPSH}\text{}\mathit{GWO}\text{}\mathit{population}=& \left[\begin{array}{cccc}s{t}_{1}^{1}& s{t}_{2}^{1}& \cdots & s{t}_{m+u}^{1}\\ s{t}_{1}^{2}& s{t}_{2}^{2}& \cdots & s{t}_{m+u}^{2}\\ \vdots & \vdots & \cdots & \vdots \\ s{t}_{1}^{N}& s{t}_{2}^{N}& \cdots & s{t}_{m+u}^{N}\end{array}\right]\end{array}$$
 Step 3:
 Calculate the power consumed by the charging operationsIn this step, the power charged in SHB by each charging operation will be calculated as discussed in the third step of designing BSA in Section 4.2.
 Step 4:
 Calculate the fitness valuesThis step is divided into two parts, namely, discharging the SHB and calculating the fitness values of the solution in the population. As discussed in Section 4.2, the time slots for discharging the SHB are determined using the roulette wheel method and the amount of power chosen randomly on the basis of several equations and constraints. In this step, the processes of discharging the SHB are the same as discussed in Section 4.2. For calculating the fitness values, the three best fitness values and their solutions are assigned as $f\left({X}_{\alpha}\right)$, $f\left({X}_{\beta}\right)$, and $f\left({X}_{\delta}\right)$, and ${X}_{\alpha}$, ${X}_{\beta}$, and ${X}_{\delta}$, respectively.
 Step 5:
 Update BMOPSPSHGWO populationThe BMOPSPSHGWO population is updated in the step, where the Equations (42)–(50) are in charge of this update.The updating mechanism of BMOPSPSHGWO is utilized to estimate the distance between ${X}_{\omega}$ solutions and the ${X}_{\alpha}$ solution and then generate a new solution ${\overrightarrow{X}}_{1}$ Equations (42)–(44) and 47. The same steps for ${X}_{\alpha}$ are repeated for ${X}_{\beta}$ and ${X}_{\delta}$ to generate ${\overrightarrow{X}}_{2}$ using Equations (42), (43), (45) and (48) and to generate ${\overrightarrow{X}}_{3}$ using Equations (42), (43), (46) and (49). In Equation (50), a new solution ${X}^{\prime}(itr+1)$ is generated on the basis of ${\overrightarrow{X}}_{1}$, ${\overrightarrow{X}}_{2}$, and ${\overrightarrow{X}}_{3}$.
 Step 6:
 Check the stop criterionSteps 4 and 5 of BMOPSPSHGWO are repeated until the stop criterion (maximum number of iterations) is met. The resulting BMOPSPSHGWO solution is ${X}_{\alpha}$.Algorithm 7 presents the pseudocode of the six steps of the proposed BMOPSPSHGWO.
Algorithm 7 Pseudocode of the six steps of the proposed BMOPSPSHGWO  1:
 Step 1: Initialize BMOPSPSHGWO parameters
 2:
 Initialize PSPSH parameters($S,NS,T,RS,RNS,OT{P}_{s},OT{P}_{e},LOC,pc$)
 3:
 Initialized SHB parameters ($Ca{p}_{B},{\mu}_{B},CO,OTPsc,OTPec,LOCc$)
 4:
 Initialize GWO parameters($a,{r}_{1},{r}_{2}\overrightarrow{A},\overrightarrow{C},lb,ub,I,N$)
 5:
 Step 2: Initialize BMOPSPSHGWO population
 6:
 Initialize a BMOPSPSHGWO population matrix of size ($(m+u)\times N$)
 7:
 Step 3:Calculate the power consumed by charging operations
 8:
 for each solution (y) do
 9:
 for each charging operation (c) do
 10:
 11:
 end for
 12:
 end for
 13:
 Step 4: Calculate the fitness values
 14:
 while (itr $<=$ I) do
 15:
 for each solution (y) do
 16:
 Discharge the SHB of the solution
 17:
 Calculate the fitness of the solution
 18:
 $f\left({X}_{\alpha}\right)$ = the best fitness value
 19:
 $f\left({X}_{\beta}\right)$ = the second best fitness value
 20:
 $f\left({X}_{\delta}\right)$ = the third best fitness value
 21:
 ${X}_{\alpha}$ = the best solution
 22:
 ${X}_{\beta}$ = the second best solution
 23:
 ${X}_{\delta}$ = the third best solution
 24:
 end for
 25:
 Step 5: Update BMOPSPSHGWO population
 26:
 for each solution (y) do
 27:
 for each appliance (i) do
 28:
 Update ${r}_{1},{r}_{2}$ (random number in [0, 1])
 29:
 Update the value of ${A}_{1}$ (Equation (42))
 30:
 Update the value of ${C}_{1}$ (Equation (43))
 31:
 32:
 Update ${r}_{1},{r}_{2}$ (random number in [0, 1])
 33:
 Update the value of ${A}_{2}$ (Equation (42))
 34:
 Update the value of ${C}_{2}$ (Equation (43))
 35:
 36:
 Update ${r}_{1},{r}_{2}$ (random number in [0, 1])
 37:
 Update the value of ${A}_{3}$ (Equation (42))
 38:
 Update the value of ${C}_{3}$ (Equation (43))
 39:
 40:
 Generate a new solution $X(itr+1)$ (Equation (50))
 41:
 end for
 42:
 end for
 43:
 Step 6: Check the stop criterion
 44:
 if The maximum number of the iteration is not reached then
 45:
 $itr=itr+1$
 46:
 end if
 47:
 end while
 48:
 Return $f\left({X}_{\alpha}\right)$ and ${X}_{\alpha}$
6. Experiments and Results
6.1. Dataset Description
6.2. Experimental Evaluation
6.2.1. Effect of The Proposed Approaches on EB
6.2.2. Effect of The Proposed Approaches on PAR
6.2.3. Effect of The Proposed Approaches on UC Level
6.2.4. Discussion
6.3. Comparative Evaluation
6.3.1. Comparison with StateoftheArt Methods Using Their Datasets
6.3.2. Comparison with StateoftheArt Methods Using the Proposed Datasets
7. Conclusions and Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
BFOA  Bacterial Foraging Optimization Algorithm 
BMOPSPSH  Smart Home Battery for MOPSPSH 
BSA  SHB Scheduling Algorithm 
CPP  Critical Period Price 
CPR  Capacity Power Limit Rate 
CO  Charging Operations 
EB  Electricity Bill 
GA  Genetic Algorithm 
GWO  Grey Wolf Optimizer 
HEMS  Home Energy Management System 
HSA  Harmony Search Algorithm 
IBR  Inclining Block Rate 
LOC  Length of Operation Cycle 
MOPSPSH  MultiObjective Approach for PSPSH 
MOP  Multiobjective Optimization Problem 
NSA  NonShiftable Appliance 
OTP  Operation Time Period 
PAR  PeaktoAverage Ratio 
PSC  Power Supplier Company 
PSO  Particle Swarm Optimization 
PSPSH  Power Scheduling Problem in Smart Home 
PSPSHGWO  Grey Wolf Optimizer for PSPSH 
RES  Renewable Energy Source 
RTP  Real Time Price 
SA  Shiftable Appliance 
SG  Smart Grid 
SHB  Smart Home Battery 
TOU  TimeOfUse 
UC  User Comfort 
WTR  Waiting Time Rate 
References
 Fadlullah, Z.M.; Quan, D.M.; Kato, N.; Stojmenovic, I. GTES: An optimized gametheoretic demandside management scheme for smart grid. IEEE Syst. J. 2014, 8, 588–597. [Google Scholar] [CrossRef]
 Yan, Y.; Qian, Y.; Sharif, H.; Tipper, D. A survey on smart grid communication infrastructures: Motivations, requirements and challenges. IEEE Commun. Surv. Tutor. 2013, 15, 5–20. [Google Scholar] [CrossRef] [Green Version]
 Ayodele, E.; Misra, S.; Damasevicius, R.; Maskeliunas, R. Hybrid microgrid for microfinance institutions in rural areas—A field demonstration in West Africa. Sustain. Energy Technol. Assess. 2019, 35, 89–97. [Google Scholar] [CrossRef]
 Woźniak, M.; Połap, D. Intelligent Home Systems for Ubiquitous User Support by Using Neural Networks and RuleBased Approach. IEEE Trans. Ind. Inform. 2020, 16, 2651–2658. [Google Scholar] [CrossRef]
 Wozniak, M.; Zielonka, A.; Sikora, A.; Piran, M.J.; Alamri, A. 6Genabled IoT Home Environment control using Fuzzy Rules. IEEE Internet Things J. 2020. [Google Scholar] [CrossRef]
 Khan, A.R.; Mahmood, A.; Safdar, A.; Khan, Z.A.; Khan, N.A. Load forecasting, dynamic pricing and DSM in smart grid: A review. Renew. Sustain. Energy Rev. 2016, 54, 1311–1322. [Google Scholar] [CrossRef]
 Mostafa, S.A.; Gunasekaran, S.S.; Mustapha, A.; Mohammed, M.A.; Abduallah, W.M. Modelling an adjustable autonomous multiagent internet of things system for elderly smart home. In Proceedings of the International Conference on Applied Human Factors and Ergonomics; Springer: Berlin/Heidelberg, Germany, 2019; pp. 301–311. [Google Scholar] [CrossRef]
 Venckauskas, A.; Stuikys, V.; Damasevicius, R.; Jusas, N. Modelling of Internet of Things units for estimating securityenergyperformance relationships for quality of service and environment awareness. Secur. Commun. Netw. 2016, 9, 3324–3339. [Google Scholar] [CrossRef]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Abasi, A.K.; Alyasseri, Z.A.A. A novel hybrid grey wolf optimizer with minconflict algorithm for power scheduling problem in a smart home. Swarm Evol. Comput. 2021, 60, 100793. [Google Scholar] [CrossRef]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Alyasseri, Z.A.A.; Abasi, A.K. A minconflict algorithm for power scheduling problem in a smart home using battery. In Proceedings of the 11th National Technical Seminar on Unmanned System Technology 2019; Springer: Berlin/Heidelberg, Germany, 2020; pp. 489–501. [Google Scholar] [CrossRef]
 Colak, I.; Kabalci, E.; Fulli, G.; Lazarou, S. A survey on the contributions of power electronics to smart grid systems. Renew. Sustain. Energy Rev. 2015, 47, 562–579. [Google Scholar] [CrossRef]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S. Multiobjective power scheduling problem in smart homes using grey wolf optimiser. J. Ambient Intell. Humaniz. Comput. 2019, 10, 3643–3667. [Google Scholar] [CrossRef]
 Ghani, M.K.A.; Mohammed, M.A.; Ibrahim, M.S.; Mostafa, S.A.; Ibrahim, D.A. Implementing an efficient expert system for services center management by fuzzy logic controller. J. Theor. Appl. Inf. Technol. 2017, 95, 13. [Google Scholar]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Abasi, A.K.; Alyasseri, Z.A.A. Optimization methods for power scheduling problems in smart home: Survey. Renew. Sustain. Energy Rev. 2019, 115, 109362. [Google Scholar] [CrossRef]
 Zhao, Z.; Lee, W.C.; Shin, Y.; Song, K.B. An optimal power scheduling method for demand response in home energy management system. IEEE Trans. Smart Grid 2013, 4, 1391–1400. [Google Scholar] [CrossRef]
 Rahim, S.; Javaid, N.; Ahmad, A.; Khan, S.A.; Khan, Z.A.; Alrajeh, N.; Qasim, U. Exploiting heuristic algorithms to efficiently utilize energy management controllers with renewable energy sources. Energy Build. 2016, 129, 452–470. [Google Scholar] [CrossRef]
 Iftikhar, H.; Asif, S.; Maroof, R.; Ambreen, K.; Khan, H.N.; Javaid, N. Biogeography Based Optimization for Home Energy Management in Smart Grid. In Proceedings of the International Conference on NetworkBased Information Systems; Springer: Berlin/Heidelberg, Germany, 2017; pp. 177–190. [Google Scholar] [CrossRef]
 Faiz, Z.; Bilal, T.; Awais, M.; Gull, S.; Javaid, N. Demand Side Management Using Chicken Swarm Optimization. In Proceedings of the International Conference on Intelligent Networking and Collaborative Systems; Springer: Berlin/Heidelberg, Germany, 2017; pp. 155–165. [Google Scholar] [CrossRef]
 Asif, S.; Ambreen, K.; Iftikhar, H.; Khan, H.N.; Maroof, R.; Javaid, N. Energy Management in Residential Area using Genetic and Strawberry Algorithm. In Proceedings of the International Conference on NetworkBased Information Systems; Springer: Berlin/Heidelberg, Germany, 2017; pp. 165–176. [Google Scholar] [CrossRef]
 Rehman, A.U.; Aslam, S.; Abideen, Z.U.; Zahra, A.; Ali, W.; Junaid, M.; Javaid, N. Efficient Energy Management System Using Firefly and Harmony Search Algorithm. In Proceedings of the International Conference on Broadband and Wireless Computing, Communication and Applications; Springer: Berlin/Heidelberg, Germany, 2017; pp. 37–49. [Google Scholar] [CrossRef]
 Batool, S.; Khalid, A.; Amjad, Z.; Arshad, H.; Aimal, S.; Farooqi, M.; Javaid, N. Pigeon Inspired Optimization and Bacterial Foraging Optimization for Home Energy Management. In Proceedings of the International Conference on Broadband and Wireless Computing, Communication and Applications; Springer: Berlin/Heidelberg, Germany, 2017; pp. 14–24. [Google Scholar] [CrossRef]
 Okewu, E.; Misra, S.; Maskeliunas, R.; Damasevicius, R.; FernandezSanz, L. Optimizing green computing awareness for environmental sustainability and economic security as a stochastic optimization problem. Sustainability 2017, 9, 1857. [Google Scholar] [CrossRef] [Green Version]
 Alyasseri, Z.A.A.; Khader, A.T.; AlBetar, M.A.; Papa, J.P.; Alomari, O.A.; Makhadme, S.N. An efficient optimization technique of eeg decomposition for user authentication system. In Proceedings of the 2018 2nd International Conference on BioSignal Analysis, Processing and Systems (ICBAPS), Kuching, Malaysia, 24–26 July 2018; pp. 1–6. [Google Scholar] [CrossRef]
 Alyasseri, Z.A.A.; Khadeer, A.T.; AlBetar, M.A.; Abasi, A.; Makhadmeh, S.; Ali, N.S. The effects of EEG feature extraction using multiwavelet decomposition for mental tasks classification. In Proceedings of the International Conference on Information and Communication Technology, Kuala Lumpur, Malaysia, 24–26 July 2019; pp. 139–146. [Google Scholar] [CrossRef]
 Połap, D.; Kęsik, K.; Woźniak, M.; Damaševičius, R. Parallel technique for the metaheuristic algorithms using devoted local search and manipulating the solutions space. Appl. Sci. 2018, 8, 293. [Google Scholar] [CrossRef] [Green Version]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Makhadmeh, S.N.; Alyasseri, Z.A.A. Linkbased multiverse optimizer for text documents clustering. Appl. Soft Comput. 2020, 87, 106002. [Google Scholar] [CrossRef]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Makhadmeh, S.N.; Alyasseri, Z.A.A. An improved text feature selection for clustering using binary grey wolf optimizer. In Proceedings of the 11th National Technical Seminar on Unmanned System Technology 2019; Springer: Berlin/Heidelberg, Germany, 2019; pp. 503–516. [Google Scholar] [CrossRef]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Alyasseri, Z.A.A.; Makhadmeh, S.N. An ensemble topic extraction approach based on optimization clusters using hybrid multiverse optimizer for scientific publications. J. Ambient Intell. Humaniz. Comput. 2020, 1–37. [Google Scholar] [CrossRef]
 Abdulkareem, K.H.; Mohammed, M.A.; Gunasekaran, S.S.; AlMhiqani, M.N.; Mutlag, A.A.; Mostafa, S.A.; Ali, N.S.; Ibrahim, D.A. A review of Fog computing and machine learning: Concepts, applications, challenges, and open issues. IEEE Access 2019, 7, 153123–153140. [Google Scholar] [CrossRef]
 Alyasseri, Z.A.A.; Khader, A.T.; AlBetar, M.A.; Abasi, A.K.; Makhadmeh, S.N. EEG signals denoising using optimal wavelet transform hybridized with efficient metaheuristic methods. IEEE Access 2019, 8, 10584–10605. [Google Scholar] [CrossRef]
 Alyasseri, Z.A.A.; Khader, A.T.; AlBetar, M.A.; Abasi, A.K.; Makhadmeh, S.N. EEG signal denoising using hybridizing method between wavelet transform with genetic algorithm. In Proceedings of the 11th National Technical Seminar on Unmanned System Technology 2019; Springer: Berlin/Heidelberg, Germany, 2019; pp. 449–469. [Google Scholar] [CrossRef]
 Alyasseri, Z.A.A.; Khader, A.T.; AlBetar, M.A.; Papa, J.P.; Alomari, O.A.; Makhadmeh, S.N. Classification of eeg mental tasks using multiobjective flower pollination algorithm for person identification. Int. J. Integr. Eng. 2018, 10. [Google Scholar] [CrossRef]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Makhadmeh, S.N.; Alyasseri, Z.A.A. A text feature selection technique based on binary multiverse optimizer for text clustering. In Proceedings of the 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT), Amman, Jordan, 9–11 April 2019; pp. 1–6. [Google Scholar] [CrossRef]
 Alyasseri, Z.A.A.; Khader, A.T.; AlBetar, M.A.; Alomari, O.A. Person identification using EEG channel selection with hybrid flower pollination algorithm. Pattern Recognit. 2020, 105, 107393. [Google Scholar] [CrossRef]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Alyasseri, Z.A.A.; Makhadmeh, S.N. A novel hybrid multiverse optimizer with Kmeans for text documents clustering. Neural Comput. Appl. 2020, 32, 17703–17729. [Google Scholar] [CrossRef]
 Alrosan, A.; Alomoush, W.; Norwawi, N.; Alswaitti, M.; Makhadmeh, S.N. An improved artificial bee colony algorithm based on mean bestguided approach for continuous optimization problems and real brain MRI images segmentation. Neural Comput. Appl. 2020, 1–27. [Google Scholar] [CrossRef]
 Abasi, A.K.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Makhadmeh, S.N.; Alyasseri, Z.A.A. A novel ensemble statistical topic extraction method for scientific publications based on optimization clustering. Multimed. Tools Appl. 2020, 1–46. [Google Scholar] [CrossRef]
 Mostafa, S.A.; Mustapha, A.; Hazeem, A.A.; Khaleefah, S.H.; Mohammed, M.A. An agentbased inference engine for efficient and reliable automated car failure diagnosis assistance. IEEE Access 2018, 6, 8322–8331. [Google Scholar] [CrossRef]
 Jouhari, H.; Lei, D.; Alqaness, M.A.A.; Abd Elaziz, M.; Damaševičius, R.; Korytkowski, M.; Ewees, A.A. Modified Harris Hawks optimizer for solving machine scheduling problems. Symmetry 2020, 12, 1460. [Google Scholar] [CrossRef]
 Desale, S.; Rasool, A.; Andhale, S.; Rane, P. Heuristic and metaheuristic algorithms and their relevance to the real world: A survey. Int. J. Comp. Eng. Res. Trends 2015, 2, 296–304. [Google Scholar]
 Javaid, N.; Javaid, S.; Abdul, W.; Ahmed, I.; Almogren, A.; Alamri, A.; Niaz, I.A. A hybrid genetic wind driven heuristic optimization algorithm for demand side management in smart grid. Energies 2017, 10, 319. [Google Scholar] [CrossRef] [Green Version]
 Rahim, M.H.; Khalid, A.; Javaid, N.; Alhussein, M.; Aurangzeb, K.; Khan, Z.A. Energy efficient smart buildings using coordination among appliances generating large data. IEEE Access 2018, 6, 34670–34690. [Google Scholar] [CrossRef]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S.; Alyasseri, Z.A.A.; Abasi, A.K. Particle Swarm optimization Algorithm for Power Scheduling Problem Using Smart Battery. In Proceedings of the 2019 IEEE Jordan International Joint Conference on Electrical Engineering and Information Technology (JEEIT), Amman, Jordan, 9–11 April 2019; pp. 672–677. [Google Scholar] [CrossRef]
 Makhadmeh, S.N.; Khader, A.T.; AlBetar, M.A.; Naim, S. An optimal power scheduling for smart home appliances with smart battery using grey wolf optimizer. In Proceedings of the 2018 8th IEEE International Conference on Control System, Computing and Engineering (ICCSCE), Penang, Malaysia, 23–25 November 2018; pp. 76–81. [Google Scholar] [CrossRef]
 Barbato, A.; Capone, A. Optimization models and methods for demandside management of residential users: A survey. Energies 2014, 7, 5787–5824. [Google Scholar] [CrossRef]
 Ahmad, A.; Khan, A.; Javaid, N.; Hussain, H.M.; Abdul, W.; Almogren, A.; Alamri, A.; Azim Niaz, I. An optimized home energy management system with integrated renewable energy and storage resources. Energies 2017, 10, 549. [Google Scholar] [CrossRef] [Green Version]
 Guo, Y.; Pan, M.; Fang, Y. Optimal power management of residential customers in the smart grid. IEEE Trans. Parallel Distrib. Syst. 2012, 23, 1593–1606. [Google Scholar] [CrossRef]
 Hemmati, R. Technical and economic analysis of home energy management system incorporating smallscale wind turbine and battery energy storage system. J. Clean. Prod. 2017, 159, 106–118. [Google Scholar] [CrossRef]
 Rasheed, M.B.; Javaid, N.; Ahmad, A.; Awais, M.; Khan, Z.A.; Qasim, U.; Alrajeh, N. Priority and delay constrained demand side management in realtime price environment with renewable energy source. Int. J. Energy Res. 2016, 40, 2002–2021. [Google Scholar] [CrossRef]
 Arun, S.; Selvan, M. Smart residential energy management system for demand response in buildings with energy storage devices. Front. Energy 2019, 13, 715–730. [Google Scholar] [CrossRef]
 Aslam, S.; Iqbal, Z.; Javaid, N.; Khan, Z.; Aurangzeb, K.; Haider, S. Towards efficient energy management of smart buildings exploiting heuristic optimization with real time and critical peak pricing schemes. Energies 2017, 10, 2065. [Google Scholar] [CrossRef] [Green Version]
 Aslam, S.; Javaid, N.; Khan, F.; Alamri, A.; Almogren, A.; Abdul, W. Towards efficient energy management and power trading in a residential area via integrating a gridconnected microgrid. Sustainability 2018, 10, 1245. [Google Scholar] [CrossRef] [Green Version]
 Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 2014, 69, 46–61. [Google Scholar] [CrossRef] [Green Version]
 Cui, Y.; Geng, Z.; Zhu, Q.; Han, Y. Multiobjective optimization methods and application in energy saving. Energy 2017, 125, 681–704. [Google Scholar] [CrossRef]
 Marler, R.T.; Arora, J.S. Survey of multiobjective optimization methods for engineering. Struct. Multidiscip. Optim. 2004, 26, 369–395. [Google Scholar] [CrossRef]
 Deb, K. Multiobjective optimization. In Search Methodologies; Springer: Berlin/Heidelberg, Germany, 2014; pp. 403–449. [Google Scholar] [CrossRef]
 Simon, D. Evolutionary Optimization Algorithms: BiologicallyInspired and PopulationBased Approaches to Computer Intelligence; Wiley: Hoboken, NJ, USA, 2013. [Google Scholar]
 Gunantara, N. A review of multiobjective optimization: Methods and its applications. Cogent Eng. 2018, 5, 1502242. [Google Scholar] [CrossRef]
 Plonis, D.; Katkevicius, A.; Gurskas, A.; Urbanavicius, V.; Maskeliunas, R.; Damasevicius, R. Prediction of Meander Delay System Parameters for InternetofThings Devices Using ParetoOptimal Artificial Neural Network and Multiple Linear Regression. IEEE Access 2020, 8, 39525–39535. [Google Scholar] [CrossRef]
 Mirjalili, S.; Dong, J.S. MultiObjective Optimization Using Artificial Intelligence Techniques; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar]
 Ehrgott, M. A discussion of scalarization techniques for multiple objective integer programming. Ann. Oper. Res. 2006, 147, 343–360. [Google Scholar] [CrossRef]
 Fei, Z.; Li, B.; Yang, S.; Xing, C.; Chen, H.; Hanzo, L. A survey of multiobjective optimization in wireless sensor networks: Metrics, algorithms, and open problems. IEEE Commun. Surv. Tutor. 2017, 19, 550–586. [Google Scholar] [CrossRef] [Green Version]
 Marler, R.T.; Arora, J.S. Functiontransformation methods for multiobjective optimization. Eng. Optim. 2005, 37, 551–570. [Google Scholar] [CrossRef]
 Cho, J.H.; Wang, Y.; Chen, R.; Chan, K.S.; Swami, A. A Survey on Modeling and Optimizing MultiObjective Systems. IEEE Commun. Surv. Tutor. 2017, 19, 1867–1901. [Google Scholar] [CrossRef]
 Farina, M.; Amato, P. A fuzzy definition of “optimality” for manycriteria optimization problems. IEEE Trans. Syst. Man, Cybern. Part A Syst. Hum. 2004, 34, 315–326. [Google Scholar] [CrossRef]
 López Jaimes, A.; Coello Coello, C.A. Some techniques to deal with manyobjective problems. In Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference, Montreal, QC, Canada, 8–12 July 2009; pp. 2693–2696. [Google Scholar] [CrossRef]
 Farina, M.; Amato, P. Fuzzy optimality and evolutionary multiobjective optimization. In Proceedings of the International Conference on Evolutionary MultiCriterion Optimization; Springer: Berlin/Heidelberg, Germany, 2003; pp. 58–72. [Google Scholar] [CrossRef]
 HidalgoLeón, R.; Siguenza, D.; Sanchez, C.; León, J.; JácomeRuiz, P.; Wu, J.; Ortiz, D. A survey of battery energy storage system (BESS), applications and environmental impacts in power systems. In Proceedings of the 2017 IEEE Second Ecuador Technical Chapters Meeting (ETCM), Salinas, Ecuador, 16–20 October 2017; pp. 1–6. [Google Scholar] [CrossRef]
 Torkzadeh, R.; Eliassi, M.; Mazidi, P.; Rodriguez, P.; Brnobić, D.; Krommydas, K.F.; Stratigakos, A.C.; Dikeakos, C.; Michael, M.; Tapakis, R.; et al. Synchrophasor based monitoring system for grid interactive energy storage system control. In Proceedings of the International Symposium on High Voltage Engineering; Springer: Berlin/Heidelberg, Germany, 2019; pp. 95–106. [Google Scholar] [CrossRef] [Green Version]
 Agamah, S.U.; Ekonomou, L. Energy storage system scheduling for peak demand reduction using evolutionary combinatorial optimisation. Sustain. Energy Technol. Assess. 2017, 23, 73–82. [Google Scholar] [CrossRef]
 Agamah, S.U.; Ekonomou, L. A heuristic combinatorial optimization algorithm for loadleveling and peak demand reduction using energy storage systems. Electr. Power Compon. Syst. 2017, 45, 2093–2103. [Google Scholar] [CrossRef]
 Mladenov, V.; Chobanov, V.; Zafeiropoulos, E.; Vita, V. Flexibility Assessment Studies WorldwideBridging with the Adequacy Needs. In Proceedings of the 2019 11th Electrical Engineering Faculty Conference (BulEF), Varna, Bulgaria, 11–14 September 2019; pp. 1–5. [Google Scholar] [CrossRef]
 Javaid, N.; Ullah, I.; Akbar, M.; Iqbal, Z.; Khan, F.A.; Alrajeh, N.; Alabed, M.S. An intelligent load management system with renewable energy integration for smart homes. IEEE Access 2017, 5, 13587–13600. [Google Scholar] [CrossRef]
 Belfkira, R.; Zhang, L.; Barakat, G. Optimal sizing study of hybrid wind/PV/diesel power generation unit. Sol. Energy 2011, 85, 100–110. [Google Scholar] [CrossRef]
 Commonwealth Edison Company. 2017. Available online: https://hourlypricing.comed.com/liveprices/ (accessed on 1 February 2021).
 Central Main Diesel. Generator Sales. 2017. Available online: http://www.centralmainediesel.com/wattagecalculator.asp (accessed on 1 February 2021).
 Ogwumike, C.; Short, M.; Abugchem, F. Heuristic optimization of consumer electricity costs using a generic cost model. Energies 2015, 9, 6. [Google Scholar] [CrossRef] [Green Version]
 Forsati, R.; Mahdavi, M.; Shamsfard, M.; Meybodi, M.R. Efficient stochastic algorithms for document clustering. Inf. Sci. 2013, 220, 269–291. [Google Scholar] [CrossRef]
 Tesla Powerwall. 2018. Available online: https://www.tesla.com/powerwall (accessed on 1 February 2021).
 Hafeez, G.; Javaid, N.; Iqbal, S.; Khan, F.A. Optimal residential load scheduling under utility and rooftop photovoltaic units. Energies 2018, 11, 611. [Google Scholar] [CrossRef] [Green Version]
 Iqbal, M.M.; Sajjad, M.I.A.; Amin, S.; Haroon, S.S.; Liaqat, R.; Khan, M.F.N.; Waseem, M.; Shah, M.A. Optimal Scheduling of Residential Home Appliances by Considering Energy Storage and Stochastically Modelled Photovoltaics in a Grid Exchange Environment Using Hybrid Grey Wolf Genetic Algorithm Optimizer. Appl. Sci. 2019, 9, 5226. [Google Scholar] [CrossRef] [Green Version]
 Ullah, I.; Hussain, I.; Singh, M. Exploiting Grasshopper and Cuckoo Search BioInspired Optimization Algorithms for Industrial Energy Management System: Smart Industries. Electronics 2020, 9, 105. [Google Scholar] [CrossRef] [Green Version]
 Hussain, I.; Ullah, M.; Ullah, I.; Bibi, A.; Naeem, M.; Singh, M.; Singh, D. Optimizing energy consumption in the home energy management system via a bioinspired dragonfly algorithm and the genetic algorithm. Electronics 2020, 9, 406. [Google Scholar] [CrossRef]
NO.  Appliance  l  OTPs–OTPe  Power (kW)  NO.  Appliance  l  OTPs–OTPe  Power (kW) 

1  Dishwasher  105  540–780  0.6  19  Dehumidifier  30  1–120  0.05 
2  Dishwasher  105  840–1080  0.6  20  Dehumidifier  30  120–240  0.05 
3  Dishwasher  105  1200–1440  0.6  21  Dehumidifier  30  240–360  0.05 
4  Air Conditioner  30  1–120  1  22  Dehumidifier  30  360–480  0.05 
5  Air Conditioner  30  120–240  1  23  Dehumidifier  30  480–600  0.05 
6  Air Conditioner  30  240–360  1  24  Dehumidifier  30  600–720  0.05 
7  Air Conditioner  30  360–480  1  25  Dehumidifier  30  720–840  0.05 
8  Air Conditioner  30  480–600  1  26  Dehumidifier  30  840–960  0.05 
9  Air Conditioner  30  600–720  1  27  Dehumidifier  30  960–1080  0.05 
10  Air Conditioner  30  720–840  1  28  Dehumidifier  30  1080–1200  0.05 
11  Air Conditioner  30  840–960  1  29  Dehumidifier  30  1200–1320  0.05 
12  Air Conditioner  30  960–1080  1  30  Dehumidifier  30  1320–1440  0.05 
13  Air Conditioner  30  1080–1200  1  31  Electric Water Heater  35  300–420  1.5 
14  Air Conditioner  30  1200–1320  1  32  Electric Water Heater  35  1100–1440  1.5 
15  Air Conditioner  30  1320–1440  1  33  Coffee Maker  10  300–450  0.8 
16  Washing Machine  55  60–300  0.38  34  Coffee Maker  10  1020–1140  0.8 
17  Clothes Dryer  60  300–480  0.8  35  Robotic Pool Filter  180  1–540  0.54 
18  Refrigerator  1440  1–1440  0.5  36  Robotic Pool Filter  180  900–1440  0.54 
Scenarios  Appliances 

1  1, 3, 4, 5, 6, 7, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35 
2  1, 2, 4, 5, 6, 7, 10, 11, 12, 18, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36 
3  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35 
4  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 
5  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35 
6  1, 2, 3, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35 
7  1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36 
No.  Appliances  Power (kW) 

1  Light [16]  0.6 
2  Attic Fan [76]  0.3 
3  Table Fan [76]  0.8 
4  Iron [16]  1.5 
5  Toaster [76]  1 
6  Computer Charger [76]  1.5 
7  Cleaner [15]  1.5 
8  TV [76]  0.3 
9  Hair Dryer [76]  1.2 
10  Hand Drill [76]  0.6 
11  Water Pump [76]  2.5 
12  Blender [76]  0.3 
13  Microwave [16]  1.18 
14  Electric Vehicle [77]  1 
Parameter  Value 

N  40 
I  1000 
lb  $OT{P}_{s}$ 
ub  $OT{P}_{e}LOC$ 
Parameter  Value 

$Ca{p}_{B}$  13.5 kWh 
$C{H}_{max}$  5 kW 
$DI{S}_{max}$  5kW 
${\mu}_{B}$  90% 
Scenarios  MOPSPSHGWO  BMOPSPSHGWO 

S 1  43.5041  41.9042 
S 2  64.5597  59.6252 
S 3  66.1138  62.7707 
S 4  62.5916  55.9692 
S 5  46.2879  43.6999 
S 6  52.2998  49.1431 
S 7  62.6367  56.4908 
Average  56.8562  52.8004 
Total  397.993  369.603 
Scenarios  MOPSPSHGWO  BMOPSPSHGWO 

S 1  2.6002  2.9418 
S 2  2.4451  2.4796 
S 3  2.2267  2.5710 
S 4  2.2277  2.3167 
S 5  2.2310  2.5207 
S 6  2.5233  2.5375 
S 7  2.0423  2.4931 
Average  2.3280  2.5515 
Scenarios  MOPSPSHGWO  BMOPSPSHGWO 

S 1  0.0658  0.0645 
S 2  0.1030  0.0534 
S 3  0.0889  0.0629 
S 4  0.1358  0.0787 
S 5  0.0872  0.0695 
S 6  0.1004  0.0598 
S 7  0.1310  0.0771 
Average  0.1017  0.0666 
Scenarios  MOPSPSHGWO  BMOPSPSHGWO 

S 1  0.3206  0.3216 
S 2  0.3528  0.3529 
S 3  0.3913  0.3871 
S 4  0.5236  0.5062 
S 5  0.3924  0.3880 
S 6  0.3647  0.3546 
S 7  0.4857  0.4590 
Average  0.4044  0.3956 
Scenarios  MOPSPSHGWO  BMOPSPSHGWO 

S 1  80.67  80.68 
S 2  77.20  79.67 
S 3  75.98  77.49 
S 4  67.02  70.75 
S 5  76.01  77.12 
S 6  76.74  79.27 
S 7  69.16  73.18 
Average  74.68  76.88 
Study  Method  Appliances  Pricing Scheme  Time Slot 

[42]  HSA, BFOA  13  TOU  1 h 
[80]  GA, BPSO, WDO  9  RTP  1 h 
[81]  GA, GWO  12  RTP, CPP  1 h 
[82]  GOA, CSA, ACO, FA, MFO  6  RTP  1 h 
[83]  GA, DA  12  RTP  1 h 
Study  Algorithm  EB  PAR 

HSA  1523.9  2.24  
[42]  BFOA  1558.8  2.15 
(Summer Scenario)  HBH  1557.2  2.12 
BPSPSHGWO  1082.4  2.47  
HSA  1155.8  3.26  
[42]  BFOA  1082.9  3.18 
(Winter Scenario)  HBH  1143.6  3.5 
BPSPSHGWO  954.8  3.7  
GA  64  2.2  
BPSO  42  2  
[80]  WDO  41.6  1.9 
GWDO  37  1.7  
BPSPSHGWO  30.2  2.28  
[81]  GA  462.67  3.639 
(RTP Scenario)  GWO  474.06  3.774 
HGWGA  449.35  3.108  
BPSPSHGWO  426.18  3.95  
GA  523.96  3.639  
[81]  GWO  541.45  3.774 
(CPP Scenario)  HGWGA  508.35  3.108 
BPSPSHGWO  474.21  3.95  
[82]  GOA  1768.27  7.41 
CSA  2147.28  9.47  
ACO  2001.16  4.13  
FA  2104.23  8.02  
MFO  1794.61  8.31  
BPSPSHGWO  1673.79  8.50  
GA  1.683  3.56  
[83]  DA  1.561  3.76 
BPSPSHGWO  1.23  3.94 
Scenarios  GWO  GA  PSO  HSA  BFOA 

S 1  41.90  44.54  42.05  43.72  42.39 
S 2  59.62  62.00  59.76  61.46  60.18 
S 3  62.77  65.10  63.01  63.92  63.24 
S 4  55.96  56.56  56.14  56.44  56.32 
S 5  43.69  47.90  43.77  44.96  43.93 
S 6  49.14  52.55  49.21  50.86  49.95 
S 7  56.49  59.22  56.60  58.11  57.10 
Average  52.80  55.41  52.93  54.21  53.30 
Scenarios  GWO  GA  PSO  HSA  BFOA 

S 1  2.94  2.96  2.89  2.95  2.94 
S 2  2.47  2.57  2.49  2.53  2.50 
S 3  2.57  2.92  2.58  2.86  2.61 
S 4  2.31  2.33  2.30  2.35  2.33 
S 5  2.52  2.73  2.54  2.71  2.59 
S 6  2.53  2.70  2.55  2.72  2.65 
S 7  2.49  2.65  2.51  2.62  2.54 
Average  2.54  2.694  2.55  2.691  2.58 
Scenarios  GWO  GA  PSO  HSA  BFOA 

S 1  0.064  0.102  0.072  0.100  0.084 
S 2  0.053  0.135  0.061  0.112  0.076 
S 3  0.062  0.100  0.065  0.083  0.069 
S 4  0.078  0.142  0.083  0.122  0.089 
S 5  0.069  0.098  0.070  0.081  0.080 
S 6  0.059  0.088  0.062  0.085  0.077 
S 7  0.077  0.110  0.078  0.095  0.091 
Average  0.066  0.110  0.070  0.096  0.080 
Scenarios  GWO  GA  PSO  HSA  BFOA 

S 1  0.321  0.340  0.322  0.339  0.328 
S 2  0.352  0.361  0.357  0.363  0.357 
S 3  0.387  0.401  0.386  0.400  0.390 
S 4  0.506  0.519  0.505  0.519  0.510 
S 5  0.388  0.411  0.393  0.409  0.399 
S 6  0.354  0.370  0.355  0.373  0.361 
S 7  0.459  0.469  0.460  0.463  0.463 
Average  0.395  0.410  0.396  0.409  0.401 
Scenarios  GWO  GA  PSO  HSA  BFOA 

S 1  80.68  77.90  80.30  78.05  79.4 
S 2  79.67  75.20  79.10  76.25  78.35 
S 3  77.49  74.95  77.45  75.85  77.05 
S 4  70.75  66.95  70.60  67.95  70.05 
S 5  77.12  74.55  76.85  75.50  76.05 
S 6  79.27  77.10  79.15  77.10  78.10 
S 7  73.18  71.05  73.10  72.10  72.30 
Average  76.88  73.95  76.65  74.68  75.90 
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Makhadmeh, S.N.; AlBetar, M.A.; Alyasseri, Z.A.A.; Abasi, A.K.; Khader, A.T.; Damaševičius, R.; Mohammed, M.A.; Abdulkareem, K.H. Smart Home Battery for the MultiObjective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer. Electronics 2021, 10, 447. https://doi.org/10.3390/electronics10040447
Makhadmeh SN, AlBetar MA, Alyasseri ZAA, Abasi AK, Khader AT, Damaševičius R, Mohammed MA, Abdulkareem KH. Smart Home Battery for the MultiObjective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer. Electronics. 2021; 10(4):447. https://doi.org/10.3390/electronics10040447
Chicago/Turabian StyleMakhadmeh, Sharif Naser, Mohammed Azmi AlBetar, Zaid Abdi Alkareem Alyasseri, Ammar Kamal Abasi, Ahamad Tajudin Khader, Robertas Damaševičius, Mazin Abed Mohammed, and Karrar Hameed Abdulkareem. 2021. "Smart Home Battery for the MultiObjective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer" Electronics 10, no. 4: 447. https://doi.org/10.3390/electronics10040447