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Meta Heuristic and Nature Inspired Hybrid

Approach for Home Energy Management using

Flower Pollination Algorithm and Bacterial foraging

Optimization Technique

Muhammad Awais1, Nadeem Javaid1,∗, Abdul Mateen1,

Nasir Khan1, Ali Mohiuddin1, Malik Hassan Abdul Rehman1

1COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

∗Corresponding author: www.njavaid.com, nadeemjavaidqau@gmail.com

Abstract—Nowadays, different schemes and ways are proposed

to meet the user’s load requirement of energy towards the

Demand Side (DS) in order to encapsulate the energy resources.

However, this Load Demand (LD) increases day by day. This

increase in LD is causing serious energy crises to the utility

and DS. As the usage of energy increases with the increase in

user’s demand respectively, the peak is increased in these hours

which affect the customer’s in term of high-cost prices. This

issue is tackled using some schemes and their proper integration.

Two-way communication is done by the utility through Smart

Grid (SG) between utility and customers. Customers that show

some good behavior and helps the utility to control this LD, can

perform a key role here. In this paper, our main focus is to

control the Customer Side Management (CSM) by reducing the

peak generation from on-peak hours. In our scenario, we focus

on saving the cost expenditure of users by giving them comfort

and shifting the load of appliances from high LD hours to low

LD hours. In this study, we adopt the optimization algorithms,

like Bacterial Foraging Optimization Algorithm (BFOA), Flower

Pollination Algorithm (FPA) and proposed our Hybrid Bacterial

Flower Pollination Algorithm (HBFPA) to optimize the solution

of our problem using the famous electricity scheme named as

Critical Peak Pricing(CPP) with three different Operational Time

intervals (OTIs). Simulations and results show that our scheme

reduces the cost and peak to the average ratio by proper shifting

the appliances from highly load demanding hours to the low

demanding hours with the negligibly small difference between

the maximum and minimum 90% of conﬁdence interval.

Index Terms—Demand side management, Bacterial foraging

optimization algorithm, Flower pollination algorithm, Hybrid

bacterial ﬂower pollination algorithm, Smart grid, Home energy

management

I. INTRODUCTION

Science and its miracles have made the people life easy in

all aspects. As blessings are for manhood, electricity is also

one of these blessings which is for human-being and can be

used for multipurpose. As the world is progressing, population

of this world is also growing. World is going towards the

automation, due to which demand of electricity has been in-

creased. To handle this critical situation, utility starts teaching

the user to avoid their maximum electricity consumption in

few selected hours. This consumption of load varies from city

to city and country to country. The energy which is needed

by the residential buildings are 30 to 45 percent of the total

electricity [1]. In International Energy Outlook (IEO), it is

clearly mentioned that the Energy Demand (ED) is increasing

continuously, which will keep on increasing till 2040 up to

56% of the present. By using some intelligent systems, we can

also control this high demand of load. This paper presents CPP

price tariff in Home Energy Management (HEM) to reduce the

Electricity Price (EP) by reducing the Peak to Average Ratio

(PAR). 18% of the electricity is consumed by domestic sectors,

viewed in a survey in 2011 [2], which has been increasing

continuously.

In this paper, we extended the FPA with BFOA to its hybrid,

to optimize our problem. We designed a model using 14

appliances, each of these appliance has been categories on the

basis of their behavior. Length of Operational Time (LOT)

is different for all appliances taken from our base paper [4].

Parameters taken in consideration are PAR, cost reduction,

energy consumption and waiting Time (WT). As our main

focus is to shift the load from on-peak to off-peak hours by

applying different schemes and strategies i.e. load clipping we

have to minimized energy consumption using DSM by proper

planning of utility electricity usage and their deployment

techniques, which directly impact the customers LD. We will

optimize the problem by using the hybrid approach of BFOA

and FPA both for single and multiple homes i.e. 10, 30 and

50 homes with different power ratings and power consumption

patterns using three different OTIs of 20, 30 and 60 minutes.

Rest of the paper is organized as: related work is discussed

in section II, section III covers the problem statement, and

the proposed solution is discussed in section IV with de-

tailed description of previously proposed techniques. Proposed

methodology is explained in section V. Results and discussions

are veriﬁed via simulations which are illustrated in section VI

and conclusion is summarized in section VII respectively.

882

2018 IEEE 32nd International Conference on Advanced Information Networking and Applications

1550-445X/18/$31.00 ©2018 IEEE

DOI 10.1109/AINA.2018.00130

II. RELATED WORK

In few years back, many researchers proposed many opti-

mization techniques to achieve common objective functions

like reduction in cost. Many efforts have been made for the

purpose of economical usage of electricity. In this section,

existing work done on these optimization techniques are

presented.

The Harmony Search Algorithm (HSA), FPA are the meta-

heuristic techniques that are used by the author to evaluate the

performance in HEM [3]. Author considered a single home

with multiple smart appliances working automatic and man-

ually. The CPP is used as price signal and purposed scheme

shifts the load from on-peak to off-peak hours very well by

keeping in view of cost minimization and User Comforts (UC).

However, author did not consider the appliances power rating

as it varies from home to home.

In [6], authors present an efﬁcient DSM model for res-

idential area people. DSM uses Genetic Algorithm (GA),

Binary Particle Swarm Optimization Algorithm (BPSO) and

Ant Colony Algorithm (ACO) which are totally heuristic

algorithms, which minimizes the user’s cost by reduction in

PAR by maximizing the user comfort. The main objective of

this paper was deduced from three techniques: GA, BPSO and

ACO. TOU and Inclined Block Rate (IBR) pricing schemes

were used by him.

Designing a HEM controller using heuristic algorithms,

controllers, BFOA, GA, BPSO, Wind Driven Optimization

Algorithm (WDO) and Genetic Binary Particle Swarm Op-

timization (GBPSO) in [7] to deals with RTP. Author’s focus

is on reducing the price while retaining PAR. GA performs

well in PAR reduction while BPSO and HEM controls the cost

reduction as well. Basically author tried to show that there is

a trade-off between cost and delay. Results shows that given

techniques performed well according to the given conditions.

HEM system is proposed in paper [8], which helps in

Renewable Energy Resources (RES), energy supplements side

and works with DSM simultaneously. The proposed HEM

helps the user in minimizing the cost of the electricity bill

and schedule household appliances to a certain threshold. If

the limit crosses the certain threshold, appliances will get-off

by utility itself. Basically author used the DAP signals and

then applied the heuristic algorithms to get optimal solution.

The Power Scheduling Technique (PST) was proposed for

an optimization problem in which user can adjust the starting

and ending time of the appliances and reduce the power

consumption of the appliances. Electricity cost used by the

author was announced by electricity providers before time [9].

Simulations demonstrate that scheduling technique can get the

required results in terms of less cost efﬁciently.

With consideration of service providers, there is a need to

balance the load to avoid much electricity consumption. In

this regard, utility has to generate extra electricity to fulﬁll

the load requirement. To minimize this problem, there is an

essential need to increase power usage convention with less

pricing rate [10]. Simulations and results show that, there is a

certain threshold after which we have to schedule the running

appliances and to stop some appliances temporarily. This is

done to maintain the LD for less cost and to stop the appliances

for being used later when cost will be low. Author uses the

TOU scheme for on-peak and off-peak hours to balance the

load properly.

When the load shifts, we can deﬁne new limits for maximum

LD. It can be crucial for the checker since the investor’s

capacity of adding energy resources, which can be limited

[11]. Only with new selected load shifting impacts, DSM can

be achieved. Basically, peaks can be reduced and valleys can

be fulﬁlled. Due to which LD will increase and Operating

System (OS) will keep on going at higher demand.

In [12], with consideration of the SM facility this model

involves DS generation to optimize the market cost. The

market cost was estimated by sensitive marketing teams to

regulate the standardization variables for quality solution. This

paper stops a new space-based pricing model for optimal

operations of the SG, which identify variables of Master

Control Program (MCP) and uses PSO to reach an optimal

solution, Demand Response (DR) stability and loss limits.

The BFOA is used in paper [13], which is a hybrid with

GA. In this paper, author used RTP scheme to optimize the

user’s load and the cost by keeping in mind about user’s

comfort, cost minimization and reduction in PAR. However,

the author did not consider the variable Power Rating (PR) for

variable homes and multiple homes with different number of

appliances.

The author reviews that DR patterns, procedures and clas-

sifying schemes in [14], affording to their device mechanism

and to reduce power for DR variables. In this paper, author

reduces the overall power consumption by successfully imple-

menting DR procedure, relies on the participation of user and

contributor to reduce power intake in peak hours by consuming

Dynamic Pricing Patterns (DPP). According to the author, it

is required to generate the DPP for forecasting techniques that

consider the probabilistic behavior of the appliances.

In [15], with consideration of pricing parameters to bal-

ance asymptotic stability and social welfare optimality of

equilibrium point using DR program, the system shows that

the Input to the State Stable (ISS). In this paper author

balances the supply and demand with the proper stability of

the system without disturbance. The power system is dividing

into different OTIs.

DSM strategy is used to achieve the objective of the

load ﬂowing through the detraction problem for residential,

the commercial and industrial zone too [16] using PSO. It

decreases the request of the load in peak eras by reducing

the bill. Results and simulation shows a clear decrease in cost

while applying PSO.

In [18], this paper an efﬁcient HSA algorithm was imple-

mented for scheduling the users DSM. The pricing scheme

used by the author was TOU. Finally, the author did many

simulations and their results shows that HSA is good in

performance than GA.

Fuzzy inference structure and FPA with hybrid approach is

883

used to adopt probability which uses different mechanism by

which they accept change in both global and local pollination

[19] and FPA performs in a much better way as it is hybrid

with Fuzzy structures. The author compare its results with

the mathematical models but this technique performs better.

However, the author ignores the time computation.

The modiﬁed FPA is presented in [20], in which Scaling

Factor (SF) is used to control local pollination and some

phases were added to get better solution. The effectiveness is

calculated from different simulations, mathematical formulas

and four different power systems. However, author did not

considered the continuous objective function and convex prob-

lems.

Below is the Table (I) of brief summarized related work.

III. PROBLEM STATEMENT

By using scheduler we can schedule the home appliances

with which energy consumption is reduced in DSM. Many of

the researchers try to minimize the price of electricity which is

our main problem by shifting the load towards off-peak hours

[28] using GA and [13] BFOA. PAR reduction, minimization

of EC, UC maximization and minimize the power consumption

are the most common objectives of electricity management in

SG. A large amount of electricity is used by residential area

and its consumption is growing rapidly. To overcome these

issues, we proposed an proﬁcient home energy management

using a meta heuristic hybrid approach named as HBFPA.

As in next section our proposed solution will be discussed.

However, many of scientists and researchers ignore the change

in power generation in these resources, which may came due to

change in atmosphere and weather. In these scenarios model

helps us to provide justiﬁcation in cost reduction and peak

load. The main purpose of our work is to scheduling of home

appliances, for minimum cost and PAR reduction, we have to

balance the load, maximize the users comfort with minimum

delay. Then we will discuss trade-off between the cost and

user comfort.

IV. PROPOSED SOLUTION

In order to tackle the above problem, our focus is to

minimize the total cost as explain in Eq. (1) on CPP tariff for

cents and power consumption of different appliances in Kilo

Watt hour (kWh). Here,‘ Pap

rate’ is the PR of an appliance ‘ap’

and per slot electric rate is denoted as ‘EPt

rate’ of ‘t’ slots.

we have done load shifting using ﬁtness calculation Eq.

(2). ‘Load’ donates load of the appliance as general while

‘Lsch

oad’ shows scheduled load, ‘Lunsch

oad ’ shows unscheduled

load, ‘Erate’ is the domain of electric rate where as ‘EF’

represents our ﬁtness function. We applied sum functions in

this equation one is of taking ‘mean’ other was of taking

minimum represented as ‘min’ and the last one was taking

‘standard deviation’ denoted as ‘std’.

In the next level, We used Eq. (3) to calculate total load

consumption of a complete day. ‘Lt

oad’ represents load per

slot and Eq. (4) evaluates the load per slot where alpha is the

TABLE I: Summarized related work

Techniques Objectives Limitations

GA, BPSO, ACO [6] Cost and PAR reduc-

tion

Users cost not consid-

ered

BFA, BFOA, GA,

BPSO, WDO,

GBPSO [7]

IT reduces the elec-

tricity cost and limits

PAR

Not considered the

trade-off between cost

and PAR

GA, PSO, WDO,

BFO, HGPSO [8]

Minimize the electric-

ity bill by scheduling

home hold appliances

The overall is not

considered reduction

in cost and PAR

BFOA [9] To reduce the cost

and increase the

user’s comfort

The trade-off among

expenses and the user

awkwardness is not

considered

BPSO [10] To develop an efﬁ-

cient system, reduce

the cost but you also

have to uplift the ap-

pliances; utility

Cost, minimization

and appliances;

utility uplifting, and

not considering the

privacy of user

MOEA [11] Cost minimization

and reducing the WT

Consumer exceeds

the threshold limit is

not focused

DR programs [13] Reduce the overall

power consumption

Implement the DR

program Successfully

in peak demand hours

BPSO [16] Reducing the excess

demand from peak

hours along with re-

duce in the bill

Reduction in peak de-

mand and saving util-

ity bills are not con-

sidered,

FPA [17] side lobe level

minimization and

null placement

ignore interferences

in undesired direction

HSA [18] Have to reduce oper-

ational cost

User comfort is not

considered

DSM model was pre-

sented using GA [19]

Have to reduce oper-

ational cost, PAR

The time complexity

is completely ignored

In-place algorithm

(PL) generalized

algorithm [20]

deals with cost and

user comfort and dis-

cuss their trade-off

The writer ignores the

system complexity

GA, Advanced in-

ﬂight measurement

techniques,

current procedural

terminology [21]

Cost and Par reduc-

tion

System complexity

increases which is

ignored

GA [22] Cost and PAR is min-

imized by the pro-

posed scheme

RER installation cost

is completely ignored

GA [23] Cost is reduced by us-

ing GA

User comfort is ig-

nored by the author

and PAR is also ne-

glected

GA [24] User’s electricity cost

is minimized with re-

duction in PAR

User comfort is ne-

glected

Hybrid scheme using

FPA and TS [25]

hybrid version to op-

timize unconstrained

problems

Ignored the

optimization problem

with multiple

constrains

884

‘ON/Off’ status of an appliance as shown in Eq. (5) where as

app shows appliance.

T otal cost =

24

t=1

(EPt

rate ×Pap

rate)(1)

Ef=min

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎩

li∈NPop

oad ≥mean(lUnsch

oad ),

(EPt

rate ≤mean(Erate)

li∈NPop

oad >(std(lUnsch

oad )∧

li∈NPop

oad < mean(lUnsch

oad )),

(EPt

rate > mean(Erate)

(2)

Lsch

oad =

24

t=1

(Lt

oad)(3)

Lt

oad =(Pap

rate ×app)(4)

alpha =1, if the appliance is ON

0, if the appliance is OF F (5)

Our main focus is on our objective functions. We not only

have to reduce electric cost as shown in Eq. (1) but also to

minimize PAR gained as in Eq. (7). One of our main objective

is load shifting as evaluated in Eq. (8). For the purpose of this

idea we divided our day of 24 hours into two different parts;

one is on-peak hours where electricity cost is high and the

second is off-peak hours where electricity cost is quite low

while considering the ‘mean’ of given price tariff. As we have

to meet our objective function we will shift load from on to

off-peak hours where price is comparatively low. This idea will

deﬁnitely reduces the PAR and cost. PAR can be calculated

from the formula in equation Eq. (9) where we take ratio of

maximum of ‘Lsch

oad’ and average of ‘Lsch

oad’.

Object1=min(cost)(6)

Object2=min(PAR)(7)

Object3=(Load)(8)

PAR =max(Lsch

oad)

Average(Lsch

oad)(9)

V. P ROPOSED METHODOLOGY

A. System Model

In this section, the architecture of our proposed system is

discussed in detail and the model is shown in Fig. (1). We

have proposed a HEM scheme to schedule smart appliances

in order to reduce the electricity cost and PAR in order to

gain maximum user comfort. As a smart home is full of smart

appliances, Electric Management Controller (EMC) and SMs.

The SM acts as a server between home and utility. Appliances

have to send their usage pattern to EMC which schedules them

according to price signals sent by utility. SM picks up the price

signals from utility and then forward it to EMC. Then it picks

up the consumption pattern from EMC and drop it at utility

side. They communicate through Z-waves. They exchange info

through home area network.

TABLE II: PR and length of operational time for 20

minutes OTIs

Group Appliances PR(kWh) OTIs

Non-schedulable appliances

Oven 1.30 10.0

Kettle 2.00 1.00

Coffee Maker 0.80 4.00

Rice Cooker 0.85 2.00

Blender 0.30 2.00

Frying Pan 1.10 3.00

Toaster 0.90 1.00

Fan 0.20 15.0

Uninterruptible appliances Washing-Machine 0.50 6.00

Cloth Dryer 1.20 6.00

Schedulable appliances

Dish Washer 0.70 8.00

Vacuum Cleaner 0.40 8.00

Hair Dryer 1.50 2.00

Iron 1.00 6.00

B. Load Categories

•Interruptible appliances

•Uninterruptible appliances

1) Interruptible Appliances: Deferrable appliances are

called ‘interruptible appliances’. These can be shifted and

scheduled. The appliances in a particular time slot can be

shown as ON or OFF using [0, 1] notation.

•0 if the appliance is OFF

•1 if the appliance is ON

2) Uninterruptible Appliances: Un-interruptible appliances

are schedulable, but they cannot be interruptible. The

appliances in a particular time slot can be shown as ON or

OFF using [0, 1] notation.

•0 if the appliance is OFF

•1 if the appliance is ON

All appliances with their power rating and length of opera-

tional time using CPP are listed in Table (II).

C. Price Model

Price is calculated according to utility deﬁnitions. For this,

different pricing schemes are used to reduce the cost and the

PAR which encourages the user to shift load from on-peak to

off-peak hours. Dynamic pricing scheme includes TOU, IBR,

CPP, DAP and RTP etc. Among all mentioned before we use

CPP.

D. Optimization Techniques

1) BFOA: Nature has a beautiful rule, it eliminates animals

with reduced foraging schemes. It favors those who have best

searching tricks and schemes. After couple of generations, the

weak one is replaced with the healthy one as per rule of life.

First BFOA algorithm is given by ‘Passsino’ and ‘Kevin’ [26]

in 2002. The strategy includes in BFOA is that ﬁrstly it permits

the cells to swarm randomly and jointly by going towards

optimum condition.

The terms used in algorithm are; ‘Ne’ shows number of

elimination step, ‘Np’ shows maximum population size, ‘Nr’

shows number of reproduction steps, ‘Nc’ shows number of

885

Fig. 1: Proposed System Model

chemotaxis steps, ‘Ns’ shows Swarming Length, ‘Ef’ shows

ﬁtness function for BFOA and ‘Pe’ denotes elimination dis-

persion probability while ‘Xnew’ shows the newly generated

population and ‘X’ shows old population. Three consecutive

steps are performed to achieve this which are; ‘Chemotaxis’,

‘Reproduction’ and ‘Elimination and Dispersal’. Algorithm for

BFOA is explained in Algorithm (1).

2) FPA: It is expected that there are more than one million

kinds of plants in nature, maximum of them are from ﬂowering

classiﬁcation. It is the still a secret that how these plants came

to land and dominate the land. The basic purpose of ﬂower is

ﬁnally to reproduce their offspring’s via pollination process,

which is basically linked with the movement of pollen grains

from one ﬂower to another using different pollinators such

as birds. There is a co-evolved in some ﬂowers and insects,

such as a speciﬁc type of species of birds or insects should be

used for pollination to be successful. Types of FPA pollination

includes; ‘Biotic pollination’ and ‘Abiotic pollination’ while

pollination can be achieved by two different processes; ﬁrst

one is ‘self-pollination’ and second is ‘cross-pollination’.

a) FPA steps: The FPA was developed by ‘Xin-She’

Yang in 2012 ‘FPA for Global Optimization’ [27]. For eas-

iness, the following four steps are used.

•Biotic cross-pollination can be measured as a process

of global-pollination, and pollen vectors are carrying

pollinators which move in a path that follow Levy ﬂights

(Rule I).

•For ‘local-pollination’, ‘abiotic-pollination’ and ‘self-

pollination’ is used (Rule II).

•Pollinators such as birds can maintain ﬂower consistency,

Algorithm 1 Algorithm 1 BFOA

Require: Deﬁne the optimization problem and optimization

parameters

for Elim and disp ←1toNedo

for Reproduction ←1toNrdo

for Chemotaxis ←1toNcdo

for Population ←1toNpdo

Bacteria tumble ﬁrst randomly

Go to new position

Compute the Ef

for i←1toNsdo

if EfXnew < EfXthen

Update solution

Using swimming

Compute the Ef

else

Bacteria Tumble

Move in that path

Compute the Ef

end if

end for

end for

end for

Calculate Ef

Select the best bacteria using Eq. (2)

end for

end for

886

which is equivalent to a reproduction probability, which

is directly proportional to the resemblance of two ﬂowers

involved in pollination (Rule III).

•The switching of local-pollination and global-pollination

can be measured by a switch probability ‘p’ belongs to

[0, 1], which is slightly partial towards local pollination

(Rule IV).

Here ‘ηa’ shows WT after scheduling and ‘γa’ shows WT be-

fore scheduling. Algorithm for FPA is discussed in Algorithm

(2).

Terms used in FPA are represented as; ‘t’ shows OTI, ‘T’

denotes total time in hours, ‘α’ denotes ‘upper bound’ while

‘lower bound’ is denoted by ‘β’, ‘D’ shows appliances, Np

shows maximum population size, ‘F’ shows ﬁtness function

for FPA, ‘x’ shows old population, ‘Xnew’ shows new

population and probability is taken (0.5) in our scenario.

Fitness ‘F’ in FPA can be calculated using Eq. (10) and in

Eq. (11).

3) Hybridization: Our proposed ‘HBFPA’ steps are ex-

plained in Algorithm (3). Terms used in HBFPA are repre-

sented as; ‘t’ shows OTI, ‘T’ denotes total time in hours,

‘α’ denotes ‘upper bound’ while ‘lower bound’ is denoted by

‘β’, ‘D’ shows appliances, ‘Np’ shows maximum population

size, ‘Ef’ shows ﬁtness function for HBFPA, ‘x’ shows old

population, ‘Xnew’ shows new population and probability

is taken (0.5) in our scenario. Fitness in ‘HBFPA’ can be

calculated using Eq. (2).

F=(1−u(1))2+D(10)

Where ‘D’ is

D= 100 ∗(u(2) −u(1)2)2+ 100 ∗(u(3) −u(2)2)2(11)

Here uis the appliance’s cost.

VI. SIMULATION RESULTS AND DISCUSSION

A. For Single Home

In this portion, we discuss about the simulations and re-

sults with proper justiﬁcation. So, as to judge the hybrid

scheme performance, the superiority interval, effectiveness and

productivity of our proposed technique, we have done some

simulations in order to describe the optimality for a single

home. However, this scheduling is performed over multiple

homes too. BFA and FPA are well executed by us and we make

a hybrid version of these two algorithms to do scheduling of

single home appliances. We have done different simulations

and get different results using three different scenarios of 20,

30 and for 60 minutes OTIs respectively for 24 hours, starting

from 1 am to 1 am. The load, total cost, PAR and waiting

time plots are given below:

1) Electricity Load Consumption: The load consumption

peak of BFOA and FPA is smaller but our proposed hybrid

technique have better results as compared to unscheduled

load. This technique is intended to avoid peak formation in

any explicit slot of daily working hours including both on-

peak hours and off-peak. Shifting the load effect consumer’s

Algorithm 2 Algorithm 2 FPA

Initialize the optimization problem and optimization pa-

rameters

Set the bounds (α,β)

For all appliances dD

ForallOTIstinT

for Population ←1toNpdo

for j←1toD-1do

Random ﬂowers generation

end for

end for

Take a Levy ﬂight

N=Max-Iteration

for j←1toNdo

for Population ←1toNpdo

if rand>probability then

Switch

Levy ﬂight

Update population

Using local pollination

Calculate F

else

Check

Random Population

Check

Simple bounds

Update population

Using global pollination

Calculate F

end if

if Fitness of Xnew <Fitness of x then

Update solution

Using new ‘F’

end if

Update global population

end for

end for

Return best solution

comfort. However, they will get reward in terms of price

reduction. The additional a client shifts the load and tolerates

changes in energy consumption pattern, the additional proﬁt

will be given to him in terms of price reduction. There are

creating different peaks in our ﬁgures, but it will not affects

user much because of peaks in off-peak hours where cost is

low. Our planned techniques performed well and load plots

are given in Fig. (2) below respectively, for all three different

OTIs.

2) Overall Electricity cost: We computed the electricity

price using the Eq. (1). The performance of home appliances

in terms of cost is evaluated with the assistance of the

corresponding hybrid heuristic optimization techniques using

BFOA and FPA. We can clearly judge from the ﬁgures that

BFOA and FPA also responded better in terms of total cost

but over proposed hybrid algorithm performed better. Here,

887

Algorithm 3 Proposed Algorithm 3 HBFPA

Initialize the optimization problem and optimization pa-

rameters

Set the bounds (α,β)

For all appliances d D

ForallOTIstinT

Np= Maximum population size

for Population←1toNpdo

for j←1toD-1do

Random ﬂowers generation

end for

end for

Take a Levy ﬂight

N=Max-Iteration

for j←1toNdo

for Population←1toNpdo

for i←1toNsdo

Bacteria Tumble using Levy ﬂight

Compute the Ef

Go to new position

Compute the Efagain

if Ef(Xnew)<E

f(X)then

Update solution

Using swimming

Compute the Ef

else

Bacteria Tumble

Using levy ﬂight

Move in that path

Compute the Ef

end if

end for

Update global population

end for

end for

Return best solution

a trend is making which elaborates clearly that more a user

sacriﬁce his comfort and bear the load consumption patterns,

more reward will be given to him by utility in terms of low

cost price. Overall Electricity cost plots are given in Fig. (3)

respectively for all three different OTIs.

3) User comfort: By applying our proposed algorithm and

CPP price tariff, users have to wait for off-peak hours where

cost is low and as a reward users have to pay less cost from

utility. OTI size effects WT very much i.e. if the size of OTI

will be larger then there will be some appliances which may

get their work complete before their proper given running time,

then their remaining time will be wasted. WT against different

OTIs are plotted below. You can easily see that our proposed

hybrid algorithm has maximum user’s comfort with minimum

delay. Fig. (4) shows waiting time respectively for all three

different OTIs.

4) PAR: When same technique is implemented to calculate

PAR using CPP, our proposed technique performed better than

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72

Time (Minutes)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(a) Load for OTI 20 minutes

4 8 12 16 20 24 28 32 36 40 44 48

Time (Minutes)

0

0.5

1

1.5

2

2.5

3

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(b) Load for OTI 30 minutes

24681012141618202224

Time (Minutes)

0

0.5

1

1.5

2

2.5

3

3.5

4

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(c) Load for OTI 60 minutes

Fig. 2: Load for OTI 20, 30 and 60 using CPP

unscheduled PAR. However, rest of the techniques performed

well as compared to unscheduled case. DSM is not solely

used for customer’s, however, additionally for utility too. The

Reduction in PAR helps utility to retain its stability and

ultimately it ends up in the reduction in the price. PAR concept

can easily be understood from the PAR plots given as in Fig.

(5) respectively, for three different OTIs.

B. For Multiple Homes

The load consumption peak of BFOA and FPA is also

smaller than unscheduled load but our proposed hybrid tech-

nique performed well than both FPA and BFOA using OTI of

60 with CPP price tariff for 10, 30 and 60 homes. Our tech-

888

OTI 20 OTI 30 OTI 60

0

200

400

600

800

1000

1200

Total Cost (Cents)

Unschedule

BFA

FPA

HBFPA

Fig. 3: Cost for OTI 20, 30 and 60

OTI 20 OTI 30 OTI 60

0

50

100

150

200

250

Waiting Time (Minutes)

BFA

FPA

HBFPA

Fig. 4: User’s comfort for OTI 20, 30 and 60

OTI 20 OTI 30 OTI 60

0

1

2

3

4

5

6

7

PAR

Unschedule

BFA

FPA

HBFPA

Fig. 5: PAR for OTI 20, 30 and 60

24681012141618202224

Time (Minutes)

0

5

10

15

20

25

30

35

40

45

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(a) Load for 10 homes

24681012141618202224

Time (Minutes)

0

20

40

60

80

100

120

140

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(b) Load for 30 homes

24681012141618202224

Time (Minutes)

0

50

100

150

200

250

Load (kWh)

Unschedule

BFA

FPA

HBFPA

(c) Load for 50 homes

Fig. 6: Load for 10, 30 and 50 homes using OTI 60

nique is intended to avoid peak formation in any explicit slot

of daily working hours including both on-peak hours and off-

peak. Shifting the load effect consumer’s comfort. However,

they will get reward in terms of price reduction. Load plots

for multiple homes are given in Fig. (6) below respectively for

all three different scenarios with different power ratings and

power consumption patterns. Figures show that BFOA and

FPA also responded better in terms of total cost for multiple

homes but over proposed algorithm performed better. HBFPA

reduces the overall cost and PAR from unscheduled cost.

Daily cost is minimized i.e. in Fig. (7) clearly shown that

proposed hybrid technique optimize the solution and schedule

the appliances for multiple homes in worth of less cost by

889

sacriﬁcing user comfort i.e. in Fig. (8) and PAR i.e. in Fig. (9)

Here, also a trend is made which elaborates clearly that more

a user sacriﬁce his comfort and bear the load consumption

patterns more reward will be given to him by the utility in

terms of low cost price.

10 Homes 30 Homes 50 Homes

0

1

2

3

4

5

6

7

Total Cost (Cents)

×104

Unschedule

BFA

FPA

HBFPA

Fig. 7: Cost for 10, 20 and 50 homes using OTI 60

10 Homes 30 Homes 50 Homes

0

2000

4000

6000

8000

Waiting Time (Minutes)

BFA

FPA

HBFPA

Fig. 8: User’s comfort for 10, 20 and 50 homes using OTI 60

10 Homes 30 Homes 50 Homes

0

50

100

150

200

250

PAR

Unschedule

BFA

FPA

HBFPA

Fig. 9: PAR for 10, 20 and 50 homes using OTI 60

C. Feasible Region

In mathematical optimization, a feasible region is a search

space which contains the set of all possible points or values of

the choice variables for an optimization problem that fulﬁll the

problem’s constraints, inequalities and integer constraints. This

is the original set of candidate solutions to the problematic

approach, before the set of candidates has been tightened

down. Fig. (10) shows the feasible region of our purposed

hybrid scheme, respectively for all three different OTIs which

may change according to scenario varies. Four parameters

should be kept in mind while calculating feasible regions as

in Fig. (10)

•Minimum cost, Minimum load consumption

•Minimum cost, Maximum load consumption

•Maximum cost, Minimum load consumption

•Maximum cost, Maximum load consumption

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Power consumption (kWh)

0

50

100

150

200

250

Cost (Cents)

P5

P4

P1

P2P3

(a) Feasible region for OTI 20

0 0.2 0.4 0.6 0.8 1 1.2

Power consumption (kWh)

0

50

100

150

Cost (Cents)

P5

P2

P1

P3

P4

(b) Feasible region for OTI 30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Power consumption (kWh)

0

50

100

150

200

250

Cost (Cents)

P3

P1

P2

P5

P4

(c) Feasible region for OTI 60

Fig. 10: Feasible region per slot with OTI 20, 30 and 60 for

single home

D. Performance Trade-off

There may exit some trade-off between different parameters

in order to attain the objective function. Simulations and

results show that there exits a trade-off between cost and WT

in our proposed hybrid algorithm. The electricity cost reduces

as the user scarify his comfort by delaying his activity work as

per our proposed model. So to get one beneﬁt he has to scarify

his second wish. Plots clearly shows difference between FPA,

BFOA and our newly proposed hybrid version by reducing

cost, PAR with maximum user’s comfort with minimum delay.

890

VII. CONCLUSION

A traditional grid is modiﬁed into a SG to maintain its

stability. DSM provides help in minimizing of cost and helps to

maintain stability of grid station. In this paper, we visualize the

performance of HEM using CPP price tariff. On the basis of

BFOA and FPA techniques and show that our hybrid technique

performed better than both, for single and multiple homes

equally. In this paper, we visualize the performance of HEM

using CPP on the basis of BFOA and FPA and show that our

hybrid technique performed better both for single and multiple

homes. We took simulations for single home and multiple

homes with different power ratings and different power con-

sumption patterns. All simulations showed that our purposed

technique performed well in reducing overall cost and PAR

by giving maximum user’s comfort with minimum delay. Our

simulations also showed the exiting trade-off between cost and

user’s comfort.

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