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Eﬃcient Scheduling of Smart Home

Appliances for Energy Management

by Cost and PAR Optimization

Algorithm in Smart Grid

Sahibzada Muhammad Shuja1, Nadeem Javaid1(B

), Sajjad Khan1,

Hina Akmal2, Murtaza Hanif3, Qazi Fazalullah1, and Zain Ahmad Khan4

1COMSATS University Islamabad, Islamabad 44000, Pakistan

nadeemjavaidqau@gmail.com

2University of Lahore (Islamabad Campus), Islamabad 44000, Pakistan

3Central South University, Changsha 410083, China

4COMSATS University Islamabad, Abbottabad 22010, Pakistan

http://www.njavaid.com

Abstract. As the energy demand for consumption is comparably higher

than the generation of energy, which produce the shortage of energy.

Many new schemes are being developed to fulﬁll the energy consumer

demand. In this paper, we proposed our meta-heuristic algorithm Runner

Updation Optimization Algorithm (RUOA) to schedule the consumption

pattern of residential appliances. We compared the results of our scheme

with other meta-heuristic algorithm Strawberry Algorithm (SBA) and

Fireﬂy Algorithm (FA). Critical Peak Price (CPP) and Real Time Price

(RTP) are the two electricity pricing scheme that we used in this paper

for calculation of electricity cost. The main objective of this paper is to

minimize the electricity cost and Peak to Average Ratio (PAR). However,

consumer comfort is not satisﬁed.

Keywords: SA ·FA ·RUOA ·Meta-heuristic techniques ·

Home Energy Management System ·Smart Grid

1 Introduction

The traditional Grid (TG) has insuﬃcient capabilities to solve electricity grid chal-

lenges: security of transmission line, bi-directional communication scalability and

robustness against any fault [1]. Therefore, advanced architecture of the TG is

strongly wished to overcome these challenges in an eﬃcient way. Smart Grid (SG)

integrates various communications information to TG. SG allow consumer to con-

trol electricity consumption through bi-directional communication between con-

sumers and source via Smart Meter (SM) in Advanced Metering Infrastructure

(AMI) [2]. Demand Side Management (DSM) is the main section of SG to cre-

ate balance for both demand and supply sides [3]. DSM has two main features:

c

Springer Nature Switzerland AG 2019

L. Barolli et al. (Eds.): WAINA 2019, AISC 927, pp. 398–411, 2019.

https://doi.org/10.1007/978-3-030-15035-8_37

Eﬃcient Scheduling of Smart Home Appliances 399

Demand Response (DR) action taken by consumer on dynamic pricing scheme and

load management to schedule the electricity consumption in an eﬃcient way. Elec-

tricity consumption is optimize to reduce electricity cost by DR Program in [4] i.e.

diﬀerent electricity consumption patter dynamic electricity price.

The main concern of SG is to reduce the PAR, electricity bills and maximize

the consumer comfort. Electricity bills and PAR are reduced at demand side by

eﬃcient management of electricity consumption pattern. Utility provide diﬀer-

ent pricing scheme: Real Time Price (RTP), Critical Peak Price (CPP), Inclined

Block Rate (IBR) etc. Electricity can be managed for the home appliances for

reduction of cost and Peak to Average Ratio (PAR) by pricing schemes. Cur-

rently many DSM mechanisms deployed to overcome previously mention chal-

lenges. In past research work, many of non-heuristic technique are presented to

optimize the home appliances [5], the researcher used Integer Linear Program-

ming (ILP) for reducing load at low price time slot to increase consumer comfort

(CC). However, this technique is not consider for complex energy consumption

pattern.

Scheduling of residential appliances in architecture of SG is provided by Home

Energy Management System (HEMS). HEMS is an intelligent system that opti-

mizes the load consumption pattern in peak hours. In previous work of HEMS,

authors categories the load management as real-time and predictable based. In

[6], predictable approach of load management is deployed. However, this app-

roach is costly and complex to produce uncertainty of solution. While real-time

optimization is employed to overcome the uncertainty issues that is deployable

for large scale of area [7].

In [8], real-time approach of load management is deployed for peak hours.

The exclusively management of energy utilization pattern in residential area is

feasible for optimization of diﬀerent appliances at home. However, CC is not

satisﬁed. In this paper, we deployed the meta-heuristic algorithm for real-time

environment. In our work, Strawberry Algorithm (SA) and Fireﬂy Algorithm

(FA) are simulated for their results to compare with our proposed scheme Runner

Updation Optimization Algorithm (RUOA). We developed a new scheme to get

optimal solution for reduction of total electricity cost and PAR as compared

with SA and FA scheme, while CC is sacriﬁced in our scheme. However, there

is trade-oﬀ exist for CC to cost and PAR. Moreover, many spaces exist to ﬁll

the area of load management and more researches are going on to overcome the

energy crises.

The rest of the work is organized as follows: In Sect.2, we present the related

work for scheduling of appliances in according with diﬀerent technique. Section 3

explains the problem statement to tackle the issues. In Sect.4, we discussed

our proposed scheme in detail along with pricing scheme that has been used.

Scheduling techniques are presented in Sect. 5to work out our proposed scheme.

Simulation results are discussed in Sect. 6. At the end paper conclusions are

drawn in Sect. 7.

400 S. M. Shuja et al.

2 Related Work

In HEMS lot of research has been presented by many authors for optimization

of residential appliances’ scheduling. Researchers trying to induce the eﬃcient

scheduling of electricity consumption pattern by the appliances placed at any

home. Diﬀerent authors have main objective to consumed electricity in reliable

and eﬃcient way by reducing electricity cost and PAR or increasing CC. Further,

some related research works are discussed below and summarized in Table 1.

Authors highlighted the multi residential electricity load scheduling problem

in [9]. According to author, in previous research only single residential area is

considered, to keep this thing in mind they want to maximize the user comfort for

large residential area. They proposed electricity load scheduling algorithm named

as PL-Generalized Benders Algorithm. The aim of their proposed algorithm is

to schedule the load of appliances and maximize the user comfort. However, it

is not deﬁned how will they schedule load when appliances are near optimal to

each other.

Discussion about the trend by authors in [10], to schedule the electrical load

from on peak hours to oﬀ peak hours. The consumer needs scheduling in an

online manner that they can easily ﬁnd out the prices of electricity and schedule

the load of their appliances according to that manner. To make electricity users

aware about their load scheduling of appliances online Load Scheduling Learning

(LSL) algorithm is proposed in [10]. The aim of their algorithm is to reduce PAR.

However, cost of electricity and performance of proposed algorithm is not deﬁned

by them.

Community based cooperative energy scheme is proposed in [11]. The aim of

proposed scheme is to discuss the electricity cost consumption of the user and

smart grid. In their work, they want to minimize the cost and PAR, to fulﬁll

their aim they considered community between SG to consumer and consumer to

SG. To evaluate the results of their proposed C2C (community to community)

scheme, MATLAB is used. The cost is minimized because of reducing PAR dur-

ing on peak hours. However, User comfort and security issues are compromised.

In [12], the HEMS system is proposed to schedule the operation of electric

appliances. Authors perceive about Quality of Experience in their work because

they want to check the eﬀects of the proposed system. For this purpose they

consider the proﬁles of the users and also proposed allocation algorithm. By

applying the proposed system and algorithm electricity cost is minimized. On

the other hand, they have not consider PAR and CC in their proposed work.

The Binary Particle Swarm Optimization (BPSO), Genetic Algorithm (GA)

and cuckoo search meta-heuristic algorithm is used in [13]. In their paper, the aim

of authors is to schedule the load of homes appliances and convert them in smart

homes. They also want to reduce the peak load and electricity bill reduction.

To schedule the appliances load of the homes they also used renewable energy

resources in their work. The electricity bill is minimized. However, the electricity

bill can be reduced further.

The multiple problems such as reducing electricity bill cost and peak reduc-

tion is considered in [14]. They want to solve above mentioned problems, to

Eﬃcient Scheduling of Smart Home Appliances 401

solve these problems meta-heuristic algorithm is proposed in their work. The

MATLAB is used to perform the simulations of their proposed meta-heuristic

algorithm. The simulations show the reduction of peak during peak hours and

it also aﬀects the electricity bill. On the other hand, the CC is compromised.

The GA and Grey Wolf Optimization (GWO) algorithms are proposed in

[15]. The aim of these proposed algorithms in this work is to minimize the peak

load of SHs. They also want to reduce the electricity bills of the users without

compromising their comfort. Multiple SHs are considered at diﬀerent time slot

to check the results of their proposed algorithms, which shows that reduction in

the load and electric bill is performed. However, the performance of optimization

is decreased.

Short term decision making model is proposed in [16]. In this paper, the renew-

able energy resources are used to manage the load of SHs and minimize the elec-

tricity cost. The mixed-ILP method is also used in this paper to make system more

eﬃcient. The proposed model with this method also gives the oﬀer for electricity

to use in fewer rates at speciﬁc hours. However, the implementation cost of this

proposed model on the basis of renewable energy resources is very high.

3 Problem Statement

The reduction of electricity cost and energy management in SG is our main

objective due to irregular behavior of energy consumption. Consumer comfort

is usually neglected while considering reduction of electricity price. A scheme is

presented in [17], to optimize the operation of residential appliances in such a

way that minimize the total electricity consumption cost and maximize the CC.

There is always trade oﬀ exist between cost and CC.

A model of Energy Management System (EMS) is presented in [18]. It pro-

poses a meta-heuristic technique with RTP and IBR pricing signal for eﬃcient

optimization of home energy to manage the home appliances. Simulations depict

that the signiﬁcant minimization of electricity cost and PAR. However, the CC

is not considered. In this paper, we performed simulation on SBA and FA algo-

rithms to compared the results with our new proposed RUOA algorithm for

scheduling of home appliances.

3.1 System Description

The proposed system model is shown in Fig. 1. Our system model is working for

scheduling SH appliances. Cost of electricity and PAR is increasing periodically

so there is need of well adaptable system, which can minimize average electricity

price and PAR. A HEMS is used for optimization of home appliances to regulate

the schedule of their operational time. HEMS ease the consumer with respect

of reduction in electricity dissipation and electricity cost. For optimization the

appliances are classiﬁed into three diﬀerent categories; Shiftable appliances, Non-

Shiftable appliances and ﬁxed appliances. Shiftable are those appliances whose

operational time can be shifted from peak hour time slots to non-peak hour time

402 S. M. Shuja et al.

slots, while Non-Shiftable operational time cannot be shifted or interrupted dur-

ing their operational time and ﬁxed appliances operate on the basis of consumer

demand which cannot be ﬁxed for speciﬁc time slots. Appliances of diﬀerent

classiﬁcation with their power rating are given in Table 2.

Fig. 1. Proposed system model

In SG system consumer can bi-directionally communicate with utility

through SM, this communication can give information to the consumer for

recently consumed electricity and estimated cost of electricity. In this paper

we used CPP and RTP pricing scheme through which load is shifted from peak

hours to non-peak hours, which enable us to know the energy consumed and cost

charged against per hour. We can reduce our electricity cost by knowing the con-

sumption of energy. In our work, we used our proposed algorithm RUOA in EMC

of SM, compared the result with SA and Fireﬂy algorithm. The results shows

that proposed algorithm RUOA perform in a better way from other algorithm

for scheduling of residential appliances.

To estimate the cost of electricity CPP and RTP pricing scheme is used in

our work. The main objective of our work is to reduce the consumption of energy

to reduce PAR and electricity cost. In Eq. 1, total electricity cost is estimated

with PAR reduction.

Cost =

24

hour=1

(EHour

Rate ×PApp

Rate ×App(hour)),App(hour)=[1/0] (1)

In above equation EHour

Rate shows the electricity cost per hour, PApp

Rate shows the

power rating of each appliance and App(hour) values present the ON/OFF status

of appliances. In Eqs. 3and 4total load and PAR is estimated.

Load =

24

hour=1

(PApp

Rate ×App(hour)),App(hour)=[1/0] (2)

PAR =(Max(LoadApp)/Avg(LoadApp)) (3)

Eﬃcient Scheduling of Smart Home Appliances 403

Table 1. Appliances classiﬁcation

Appliances class Appliances Power rating

(kWh)

Operational

time (hours)

Shiftable Vacuum cleaner 1.2 6

Electric water heater 2.6 8

Water pump 1 8

Dish washer 2.5 4

Steam iron 1.2 3

Refrigerator 0.225 20

Air conditioner 1.5 14

Non-Shiftable Washing machine 3 5

Tumble d ryer 3.3 4

Fixed Oven 1.23 4

Blender 0.3 2

Ceiling fan 0.1 12

Desktop PC 0.3 10

TV 0.3 9

Laptop 0.1 8

4 Scheduling Techniques

Many of the mathematical techniques are presented for scheduling of residen-

tial appliances; MILP, DP, MINLP etc. However, due to slow computation for

large number of appliances consumer demand is not satisﬁed. Therefore, meta-

heuristic algorithms are used for eﬃcient optimization of home appliances to

reduce the electricity price and manage the load between peak and non-peak

hour. In this paper, we choose some meta- heuristic algorithm SBA and FA to

propose our algorithm RUOA for optimization of energy consumption pattern

of appliances. Algorithms are described further in below subsection.

4.1 Strawberry Algorithm

SBA is a nature based meta-heuristic algorithm of strawberry plant presented in

[19]. These plants grow through runner because of their intelligent nature; they

get their food from nutrient, light and water. If a plant found a good location

for enough food, then it will never move from this location. In another case, if

plant is placed at a location where it found not enough food for its growth then

it try to ﬁnding some optimal location by sending long runner for its survival.

The plant propagates some long runner to calculate maximum optimal solution

for survival in Eq.(4). It is hard to provide enough sources to runner especially

when plant is located at place where no good resources for survival. Natural

resources decide the location for plant that its good or not.

r2=[r1+drunner ∗(rand(m, N)−0.5)r1+droot ∗(rand(m, N )−0.5)].(4)

404 S. M. Shuja et al.

r1=ul +(uh −ul)∗(rand(m, N ).(5)

SA generates population in form of 1 and 0 for optimization of appliances

using Eq. (5). Every binary number represents a solution for respective time

slot and binary representation of number show the ON/OFF status of home

appliances. The SBA searches for local best solution of minimizing cost and

PAR through runner on the basis of ﬁtness function. SBA performs global best

solutions for search in reproduction step from local solutions.

4.2 Fireﬂy Algorithm

FA is developed on the basis of ﬂashing feature of ﬁreﬂy in [20]. As the entire ﬁre-

ﬂy attracts toward the brighter light so brightness is the main objective function

of ﬁreﬂy. The quality of best solution is depend on the intensity of light emitted

by ﬁreﬂy. Every ﬁreﬂy has values for ﬁtness of brightness as solution and attract

toward the brighter ﬁreﬂy. In simple understanding of FA, basic step of rules are

deﬁned as:

•Present brightness objective function.

•Generate ﬁreﬂy population.

•Calculate the light intensity of ﬁreﬂy.

•Calculate attractiveness of ﬁreﬂy.

•Movement toward the brighter ﬁreﬂy.

•Update the light intensity rank and select the best solution.

4.3 Runner Updation Optimization Algorithm

RUOA is our proposed scheme for optimal scheduling of residential appliances. It

is derived from two other above mentioned nature based meta-heuristic scheme

SBA and FA. We built a feature of population updation of runner from SBA in

ﬂashing scenario of FA. In SBA, the plant propagates few runners upon lower

and upper limit of resources to ﬁnd optimal solution for survival. We get a

reﬁned updated location of resources by comparing rand number of location.

When condition is satisﬁed then best solution is being updated for population

through runner [19].

While in FA ideal ﬂashing algorithm is perform for the random population

to acquire the possible optimal solution. They get reﬁned value when condition

for brighter ﬁreﬂy is true, which not better for optimal solution. The value of

updated population is unreﬁned output, because every time FA takes random

number for optimization so in comparison step population may not achieve the

best solution [20]. In RUOA, we reﬁned the updated population with best ﬁtness

feature of runner from SBA to deploy in FA.

5 Simulations Results and Reasoning

In this section, results of proposed algorithm and comparison with other algo-

rithm are evaluated. MATLAB based simulations are analyzed to verify the

Eﬃcient Scheduling of Smart Home Appliances 405

Algorithm 1. Algorithm of Runner Updation Optimization Algorithm.

Require: Input: [Initialize random population, MaxIt, Electricity Price;]

1: Determine Length of operational time for appliances and their power rating;

2: for t=1:24do

3: Evaluate the value of xl and ul limits random population;

4: Evaluate LOT;

5: Find local best solution;

6: for i=1:10do

7: Determine the Population Size and no of appliances;

8: Identify initial random population between xl and ul;

9: for iter ≤iterMaxIt do

10: Propagate Runner from SBA on search spaces;

11: Identify ﬁtness criteria of notify location;

12: Evaluate the location and update it;

13: end for

14: end for

15: Rank the population;

16: Find the best population for identiﬁed location;

17: end for

18: end for

19: Update the LOT of appliances;

20: Decrement from currently selected appliances LOT;

21: end for

22: end for

results of proposed algorithm RUOA. In our work, we compared the result with

existing meta-heuristic SBA and FA algorithm. CPP and RTP pricing scheme

are used for our main objective of cost minimization, PAR reduction and load

management in simulations. Figures2and 3shows the hourly electricity cost

along with plots of pricing signal CPP and RTP.

The hourly load consumptions are shown in Fig. 4for CPP and Fig. 5for RTP

along with scheduled and unscheduled pattern of consumption. Our proposed

Fig. 2. Hourly cost with CPP signal

406 S. M. Shuja et al.

algorithm RUOA show that its peaks for hourly load graph are better than other

meta-heuristic algorithm SBA and FA for both CPP and RTP. We realize that pat-

tern of per hour load consumption of schedule is much better than unscheduled.

Our simulation result depict that proposed algorithm RUOA optimize the hourly

load consumption by shifting load from peak hours to non-peak hours.

Fig. 3. Hourly cost with RTP signall

Fig. 4. CPP hourly load

Fig. 5. RTP hourly load

Eﬃcient Scheduling of Smart Home Appliances 407

The result of PAR value generated by SBA, FA and proposed scheme RUOA

for CPP and RTP are shown in Figs. 6and 7. Both CPP and RTP signals in

ﬁgure verify that proposed algorithm outperformed than other algorithm. PAR

is reduced by 70.76% in SBA, 45.21% in FA and 75.1% in proposed RUOA

for CPP, while 65.45% in SBA, 45.2% in FA and 75.02% in proposed RUOA

for RTP with refer to unscheduled PAR. Simulations show that our proposed

scheme RUOA performed in a better way than other algorithm.

The hourly cost of electricity shown in Figs.8and 9for CPP and RTP, which

simulated by SBA, FA and our proposed algorithm RUOA. Simulations depict

the result of our proposed scheme is good enough from other scheme, as schedule

peak of graph show the lower cost at higher price time slot as compared with

unscheduled peaks.

Total electricity cost value is estimated in Figs. 10 and 11 simulated by SBA,

FA and RUOA for CPP and RTP pricing scheme. Simulation shows that perfor-

mance of our proposed scheme is outclassing as compared with SBA and FA. In

Total Cost plots, the total electricity cost is reducing by 24.53% in SBA, 55.4%

in FA and 65.97% in proposed RUOA for CPP, while 19.78% in SBA, 15.21% in

FA and 35.19% in proposed RUOA with respect of unscheduled case. There is

trade-oﬀ between cost and waiting time, which mean that our proposed scheme

RUOA is reducing cost while sacriﬁcing consumer waiting time.

Fig. 6. CPP PAR

Fig. 7. RTP PAR

408 S. M. Shuja et al.

Fig. 8. CPP hourly cost

Fig. 9. RTP hourly cost

Fig. 10. CPP total cost

Consumer waiting time for CPP and RTP pricing signal are presented in

Figs. 12 and 13. In our case, waiting time shows the time limit to turn ON the

home appliances. The consumer comfort level is calculated in term of consumer

waiting time, we have to minimize the waiting time for consumer to maximize the

comfort level and vice versa. The waiting time calculated for CPP is 3.8876 h by

SBA, 6.7775 h by FA and 4.9879 h by proposed RUOA, while for RTP is 3.8409 h

by SBA, 6.7775 h by FA and 4.5403 h by proposed RUOA. Simulation shows that

Eﬃcient Scheduling of Smart Home Appliances 409

Fig. 11. RTP total cost

Fig. 12. CPP waiting time

Fig. 13. RTP waiting time

SBA well performed than other algorithm in consumer waiting time. However,

there is trade-oﬀ for our proposed RUOA to SBA and FA in waiting time and

total electricity price.

6 Conclusion

An electricity load management is concerned to evaluate at DSM. In this

paper, we develop the scheme for load management from existing meta-heuristic

410 S. M. Shuja et al.

technique SBA and FA with pricing scheme of CPP and RTP. We proposed an

RUOA algorithm to optimize the residential appliances based on their electric-

ity consumption pattern. We analyzed the performance of our simulation, which

shows that the performance of our proposed technique is better than other meta-

heuristic technique SBA and FA in term of total electricity price and PAR. On

the other hand SBA outperformed for consumer comfort as compared with our

proposed algorithm.

References

1. Gungor, V.C., Sahin, D., Kocak, T., Ergut, S., Buccella, C., Cecati, C., et al.:

Smart grid technologies: communication technologies and standards. IEEE Trans.

Ind. Inform. 7(4), 529–539 (2011)

2. Esther, B.P., Kumar, K.S.: A survey on residential demand side management archi-

tecture, approaches, optimization models and methods. Renew. Sustain. Energy

Rev. 59, 342–351 (2016)

3. Wu, Z., Tazvinga, H., Xia, X.: Demand side management of photovoltaic-battery

hybrid system. Appl. Energy 148, 294–304 (2015)

4. Strbac, G.: Demand side management: beneﬁts and challenges. Energy Policy 36,

4419–4426 (2008). Vancouver

5. Zhu, Z., Jie, T., Lambotharan, S., Chin, W.H., Fan, Z.: An integer linear pro-

gramming based optimization for home demand-side management in smart grid.

In: 2012 IEEE PES Innovative Smart Grid Technologies (ISGT), pp. 1–5. IEEE

(2012)

6. Agnetis, A., de Pascale, G., Detti, P., Vicino, A.: Load scheduling for household

energy consumption optimization. Smart Grid IEEE Trans. 4, 2364–2373 (2013)

7. Colmenar-Santos, A., de Lober, L.N.T., Borge-Diez, D., Castro-Gil, M.: Solutions

to reduce energy consumption in the management of large buildings. Energy Build.

56, 66–77 (2013)

8. Marzband, M., Ghazimirsaeid, S.S., Uppal, H., Fernando, T.: A real-time evalu-

ation of energy management systems for smart hybrid home Microgrids. Electr.

Power Syst. Res. 143, 624–633 (2017)

9. Moon, S., Lee, J.-W.: Multi-residential demand response scheduling with multi-

class appliances in smart grid. IEEE Trans. Smart Grid 9(4), 2518–2528 (2018)

10. Bahrami, S., Wong, V.W.S., Huang, J.: An online learning algorithm for demand

response in smart grid. IEEE Trans. Smart Grid 9(5), 4712–4725 (2018)

11. Bera, S., Misra, S., Chatterjee, D.: C2C: community-based cooperative energy

consumption in smart grid. IEEE Trans. Smart Grid 9(5), 4262–4269 (2018)

12. Behrens, D., Schoormann, T., Knackstedt, R.: Developing an algorithm to consider

mutliple demand response objectives. Eng. Technol. Appl. Sci. Res. 8(1), 2621–2626

(2018)

13. Javaid, N., Ullah, I., Akbar, M., Iqbal, Z., Khan, F.A., Alra jeh, N., Alabed, M.S.:

An intelligent load management system with renewable energy integration for

smart homes. IEEE Access 5, 13587–13600 (2017)

14. Aslam, S., Iqbal, Z., Javaid, N., Khan, Z.A., Aurangzeb, K., Haider, S.I.: Towards

eﬃcient energy management of smart buildings exploiting heuristic optimization

with real time and critical peak pricing schemes. Energies 10(12), 2065 (2017)

15. Khan, I.U., Ma, X., Taylor, C.J., Javaid, N., Gamage, K.: Heuristic algorithm

based dynamic scheduling model of home appliances in smart grid (2018)

Eﬃcient Scheduling of Smart Home Appliances 411

16. do Prado, J.C., Qiao, W.: A stochastic decision-making model for an electricity

retailer with intermittent renewable energy and short-term demand response. IEEE

Trans. Smart Grid (2018)

17. Ma, K., Yao, T., Yang, J., Guan, X.: Residential power scheduling for demand

response in smart grid. Int. J. Electr. Power Energy Syst. 78, 320–325 (2016). 129,

452–470

18. Marzband, M., Yousefnejad, E., Sumper, A., Domnguez-Garca, J.L.: Real time

experimental implementation of optimum energy management system in stan-

dalone microgrid by using multi-layer ant colony optimization. Int. J. Electr. Power

Energy Syst. 75, 265–274 (2016)

19. Merrikh-Bayat, F.: A Numerical Optimization Algorithm Inspired by the Straw-

berry Plant. arXiv 2014, arXiv:1407.7399 (2014)

20. Yang, X.-S.: Fireﬂy Algorithms for multimodal optimization. In: International

Symposium on Stochastic Algorithms. Springer, Berlin (2009)