Ant Colony Optimization Based Energy Management Controller for Smart Grid

Abstract

In this paper, we introduce a generic architecture for demand side management (DSM) and use combined model of time of use tariff and inclined block rates. The problem formulation is carried via multiple knapsack and its solution is obtained via ant colony optimization (ACO). Simulation results show that the designed model for energy management achieves our objectives; it is proven as a cost-effective solution to increase sustainability of smart grid. The ACO based energy management controller performs more efficiently than energy management controller without ACO based scheduling in terms of electricity bill reduction, peak to average ratio minimization and user comfort level maximization.

Full text

Ant Colony Optimization based Energy
Management Controller for Smart Grid
Sahar Rahim1, Zafar Iqbal2, Nusrat Shaheen1, Zahoor Ali Khan3,4,
Umar Qasim5, Shahid Ahmed Khan1, Nadeem Javaid1,*
1COMSATS Institute of Information Technology, Islamabad, 44000, Pakistan
2UIIT, Pir Mehr Ali Shah Arid Agriculture University, Rawalpind 46000, Pakistan
3Faculty of Engg., Dalhousie University, Halifax, NS B3J 4R2, Canada
4CIS Higher Colleges of Technology, Fujairah 4114, United Arab Emirates
5Cameron Library, University of Alberta, Edmonton, AB, T6G 2J8 Canada
∗Corresponding author: www.njavaid.com, nadeemjavaidqau@gmail.com
Abstract—In this paper, we introduce a generic architecture
for demand side management (DSM) and use combined model
of time of use tariff and inclined block rates. The problem
formulation is carried via multiple knapsack and its solution is
obtained via ant colony optimization (ACO). Simulation results
show that the designed model for energy management achieves
our objectives; it is proven as a cost-effective solution to increase
sustainability of smart grid. The ACO based energy management
controller performs more efficiently than energy management
controller without ACO based scheduling in terms of electricity
bill reduction, peak to average ratio minimization and user
comfort level maximization.
Keywords: Smart Grid; Demand Side Management; Multiple
Knapsack Problems; Time Of Use Tariff; Inclined Block Rate;
Renewable Energy Sources.
I. INTRODUCTION
TRADITIONAL electrical power system is inadequate to
meet modern power grid challenges such as reliability,
stability, robustness, etc. [1]. Thus, a new infrastructure is
needed to smartly meet these challenges and reduce pressure
on global environment. In this regard, smart grid (SG) in-
tegrates communication technologies, computational abilities,
control systems and sensors with existing grid and enables two
way flow of information between utility and end users. Main
aims of SG are to enhance efficiency, sustainability, capacity
and customer engagement [2].
One of the important aspects of SG is demand side man-
agement (DSM) which is the best way to maintain balance
between demand and supply. Two main functions of DSM are
load management and demand response (DR). Load manage-
ment focuses on the improvement of energy efficiency [3],
while DR is a responsive action taken by a customer against
dynamic price models [4]. The common objectives of SG are
electricity bill reduction, minimization of aggregated power
consumption and minimization of both electricity bill and
aggregated power. To achieve these objectives, many DSM
techniques and algorithms are proposed in the previous years;
integer linear programming [5], mixed integer linear program-
ming [6], mixed integer non-linear programming [7], convex
programming [8], etc. However, these techniques can not
tackle large number of different household appliances having
unpredictable, non-linear and complex energy consumption
patterns due to randomness in human behavior. Moreover, to
attain electricity cost minimization objective, they ignore user
comfort level and their electricity pricing model is also not
compatible with real scenarios.
In this paper, ant colony optimization (ACO) technique is
used for DR (in DSM) due to its exceptional characteristics;
flexibility for specified constraints, ease of implementation,
low computational complexity and low computational time
[9]. We first design an energy management controller (EMC)
model smart homes using multiple knapsack problem (MKP)
and then apply ACO to get feasible solution for designed
objective function. To calculate electricity bills, we use time
of use (TOU) tariff model with inclined block rate (IBR), so
that peak formation is avoided. Effectiveness of the designed
EMC model is shown via simulations where unscheduled and
ACO based schedules cases are compared in terms of energy
consumption pattern, electricity bill, peak to average ratio
(PAR), user comfort level, and execution time.
The rest of the paper is organized as follows. Section II
briefly describes related work. Section III explains motivation
for proposed work. Section IV describes system model and
section V deals with problem formulation. Simulation results
are discussed in section VI. Finally, paper is concluded in
section VII by pointing out the future work.
II. RE LATE D WO RK
In [15], authors investigate the problem of household appli-
ance scheduling to enhance energy efficiency of electrical grid
and provide benefits to end users. They proposed a solution
that optimally schedules a set of appliances. To minimize
customer electricity bills and maintain energy consumption
within a limit, they use day-ahead variable peak pricing model
and map their problem by using MKP. By limiting the energy
demand within certain capacity, problem of load shedding
can be removed. Results show that this model effectively

Fig. 1: SG architecture
reduces utility electricity bills while keeping power consump-
tion within pre-defined limits. Another model of home energy
management controller for residential users is proposed in
[16]. Objective function is formulated by knapsack problem
and dynamic programming approach is used to solve problem
and to set consumer preferences for each appliance. These
priorities were the value of appliances that are used to schedule
the appliance to satisfy their operational time constraints to
avoid peak formation and to reduce electricity cost.
In [10], authors present an efficient model of DSM that
reduces PAR and electricity bills for residential, industrial
and commercial users. Scheduling problem is formulated as
a minimization problem and then problem is evaluated by
using heuristic evolutionary approach. Heuristic algorithms
show better results because of their flexible nature that allow
the implementation of individual load pattern in order to
minimize inconvenience. Proposed model is beneficial for
both utilities and customers in a way that PAR reduction
causes minimization in the number of peak power plants
while incentive based model helps consumer to reduce their
electricity bills. Simulation results show that the proposed
DSM strategy achieves significant savings, while reducing the
peak load demand of the smart grid.
In [11], authors discuss an efficient architecture for energy
management system by using home area network (HAN) for
residential users. They combine real-time pricing (RTP) tariff
model with the IBR because when only the RTP is adopted,
there is a risk that most of the appliances operate during the
hours of lowest electricity price that cause peak formation. To
strengthen the stability of electricity system, peak formation
must be avoided. To solve these issues in an optimized way,
objective function is formulated. As this kind of optimization
problem is non-linear, therefore they use GA to optimize their
problem. Simulation results shows that proposed model is very
effective to reduce PAR and electricity cost.
Another DSM model is proposed in [12] for residential users
to reduce PAR and electricity bill minimization. GA is used
to get optimal start time of each appliance in each time slot
while satisfying its operational constraints. There is a tradeoff
between electricity cost and waiting time. When waiting time
of an appliance is zero, its electricity cost is increased and vice
versa. Combined model of RTP with IBR is used to avoid peak
formation. Simulations are carried out for single and multiple
users. Results show the effectiveness of proposed DSM model
for both single and multiple user scenarios.
An efficient heuristic approach is presented in [17] for
scheduling of smart appliances in residential area. The pro-
posed algorithm is evaluated by comparing the electricity cost
and computational time with an exact algorithm. Variable
energy price model is used for scheduling of appliances.
Hourly prices for electricity, the operation start times of set of
appliances are optimized to reduce cost of energy consumption
while satisfying the operational and peak power constraints.
Results show that electricity cost obtained by heuristic algo-
rithm is within 5% of the optimal cost of exact algorithm
whereas computational time is reduced by exponential factor.
III. PROP OS ED S YS TE M MO DE L
In SG, DSM enables more efficient and reliable grid op-
erations. Its two main functions are energy management and
demand side control activities for end users. In residential area,
every smart home is equipped with EMCs and smart meters
to make stable and reliable bi-directional communication be-
tween utilities and customers. All elements, such as electri-
cal appliances, sensors, local generation and energy storage
systems (ESSs) give their information to EMC through HAN

and EMC controls scheduling of appliances. After collecting
all information, EMC sends it to SG domain through WAN.
There are various wireless solutions for communication links
between the smart meters and the EMCs such as ZigBee, Z-
Wave, Wi-Fi, or a wired (HomePlug) protocol [1]. Simple
architecture of DSM is shown in fig. 2. In residential area
Sensors
Distributed RESs
Smart devices
Residential area
domain
ESSs
EMCs
HAN
SG domain
Distribution
Operation
Market
Service provider
Customers
WAN
Two way communication
One way communication
Fig. 2: Components of DSM
based DSM, we consider Nsmart homes and Msmart
appliances. In this model, all smart homes have smart metering
system and EMC. End users change their energy usage accord-
ing to incentive based schemes offered by utilities. In each
home, consumer inputs different parameters of appliances to
appliances scheduler and then appliance manager gives signal
to various appliances about their on/off status. For electricity
pricing model, TOU tariff is used to calculate electricity bill
against the energy consumption cost per day. In order to
design the optimization model for home energy management,
we have categorized the load according to the characteristic
of appliances and life style of end users as discussed in the
following section.
A. Load categorization
We classify appliances into three categories; fixed, shiftable
and elastic appliances according to their power consumption
pattern and time of use [18]. Detail of all these categories is
given as follow:
1) Fixed appliances: These are also called regular appli-
ances because their usage or length of operation can not be
modified. For example, lights, fans, clothes iron, microwave
oven, toaster, tv, etc. We represent fixed appliances by Fed and
its power consumption as ν.
2) Shiftable appliances: These are also called burst load
because these are manageable and can be shifted in time
without altering their load profile. For example, washing
machine, dish washer, clothes dyer, etc. We denote shiftable
appliances by Sed and their power consumption by ∆. Each
shiftable appliance is characterized by its length of operation
which is denoted as τsed and it is pre-defined by end users
each day.
3) Elastic appliances: These are also called interruptible
appliances because these are fully controllable in terms of both
usage time and power consumption profile. For example, air
conditioner, refrigerator, water heater, space heater, etc. We
represent elastic appliances by Eed and its power consumption
is denoted by κ. Each elastic appliance eed ∈Eed has power
rating ρeed , power quantity factor λeed, length of operation
τeed , start time αeed and end time βeed . These attributes are
set by the consumer.
B. Energy consumption model
Let A={a1, a2, a3, . . . , am}be the set of appliances
such that a1,a2,a3,· · · ,amare number of appliances that
belong to each category. If t∈T={1,2,3,· · · ,24 }de-
notes the scheduling horizon, then hourly energy consumption
demand of a appliance is given as,
Ea(t) = {Ea
t1+Ea
t2+Ea
t3+. . . +Ea
t24 }(1)
where, Ea
t1,Ea
t2,Ea
t3,· · · ,Ea
t24 denotes energy consumption
demand of each appliance in the respective time slots. The
per day total energy consumption demand for all appliances
is calculated as follows,
ET=
24
X
t=1 A
X
a=1
E(i,t)(2)
C. Energy price model
A number of tariff models are available to define electric
energy prices for a day or for short time duration. Among
these, TOU tariff model is defined for electricity prices depend
on the time of day and are pre-defined in advance. Critical
peak pricing (CPP) is a variant of TOU in which price is
considerably raised in case of emergency situations (e.g. high
demand). RTP based electricity prices can change as often
as hourly, reflecting the utility cost of supplying energy to
customers at that specific time. In our model, we use TOU
with power dependent tariff known as inclined block tariff or
IBR. The energy price at time tis an increasing, piecewise,
linear function of the total energy demand. As E(t)is the total
power consumption of all appliances in a home at each time
slot tand it is calculated as,
E(t) =
24
X
t=1 ν(t) + ∆(t) + κ(t)(3)
To calculate electricity bills, energy price for each unit con-
sumed in each time slot is represented by C(t)and according
to IBR model, it is designed as,
C(t) = 




C1(t) 0 ≤E(t)≤E1
th(t)
C2(t)E1
th(t)≤E(t)≤E2
th(t)
C3(t)E2
th(t)< E(t)
(4)
where, E1
th and E2
th are power consumption thresholds and
C1,C2and C3are costs for these particular cases.

D. Residential users
We design our model for three types of users in residential
area; passive, semi-active and active users.
1) Passive users: They only consume electrical energy of
the grid and does not generate or store electrical energy.
They can only shift there load from high peak to low peak
and reduce their electricity bills. The set of passive users is
represented by P.
2) Semi-active users: They have RESs such as solar panels
and wind turbines. They consume energy both from power grid
and RES to reduce their electricity bills. The set of semi-active
users is represented by S.
3) Active users: They take energy from RES and store it in
storage devices such as batteries as well as also take electrical
energy from grid to fulfill their need. The set of active users
is represented by A.
IV. PROBLEM FORMULATION
In this work, main objectives are to reduce consumer cost by
optimizing the energy consumption patterns of appliances to
maximize the comfort level of end user. Here, we formulate
our scheduling problem by using MKP. MKP is a resource
allocation problem that consists of “M” resources (capacities)
and set of “N” objects [19]. We take “j” number of knapsacks,
and map our scheduling problem in MKP as follows:
•We consider “j” number of knapsacks as power capacities
in each time slot.
•Number of appliances as number of objects.
•The weight of each object as the energy consumed by
appliances in each time slot. Note that it is independent
of “t”.
•The value of object in a specific time slot is the cost of
power consumption of the appliance in that time slot.
•The value of binary variable “χ” can be 0 or 1 depending
on the state of electrical appliance.
The total power consumption for all types of appliances
should not exceed maximum power capacity in each hour
denoted as γ(t), we introduce constraint which limits the
power consumption and depends on load profile and its states.
Constraints show that power consumption is predefined,
24
X
t=1 E(t)×χ(t)≤γ(t)(5)
Here, γ(t)is the power capacity in each hour that is available
from grid and χ(t)∈[0,1] denotes the states of appliances.
Total power consumption in each hour must be limited to this
capacity factor.
A. Objective function and its solution via ACO
The overall objective function of our scheduling problem is
to minimize electricity bill with optimal use of power from
grid and to minimize waiting time (to avoid frustration of
end users). Additionally, optimal integration of RESs is also
a key point to reduce green house gas (GHG) emission. We
formulate our objective function as an optimization function
and is modeled as,
min
24
X
t=1 a1·
A
X
a=1
(Ea(t)×Ca(t))+a2ϕa(t) (6)
where, Cais the electricity cost in each time slot that must be
minimized while keeping waiting time of shiftable appliances
minimized. a1and a2are weights of two parts of objective
function and their values are a1, a2∈[0,1] or a1+a2= 1. It
shows that either a1or a2would be 0 or 1. In this work,
our major concern is with electricity cost reduction with
maximizing comfort level of end users. For this purposed
model, we assume waiting time of each shiftable appliance
not greater than 5, if operation start time of an appliance is
greater than our assumption then utility pays penalty.
Algorithm 1 : Improved Algorithm of ACO-EMC
1: Initialize all parameters (αa,βa,τa,ρa)
2: For all users n ∈N do
3: For all appliances a ∈A do
4: For all time slots t ∈T do
5: Randomly generate ant population
6: while Maximum number of iterations and min error not reached
do
7: For Each individual ant update pheromone refer [21]
8: For Each individual ant evaluate the objective function using
(29)
9: if Ea< E1then
10: calculate electricity bill using C1
11: else {E1< Ea< E2}
12: calculate electricity bill using C2
13: else {Ea> E2}
14: calculate electricity bill using C3
15: end if
16: if C(t)is high peak hour then
17: calculate ϕausing (28)
18: else
19: start an appliance
20: end if
21: local update pheromone for each ant refer [21]
22: choose best solution so far
23: global update pheromone for each ant refer [21]
24: repeat until iteration end
25: using Θ(t)when electricity bill is high
26: if E(t)is high then
27: Θ(t)energy
28: else
29: E(t)
30: end if
31: end while
ACO is a meta-heuristic optimization approach that is used
to solve discrete combinatorial optimization problems. It has
unique properties of self-healing, self-protection and self-
organization [13]. In literature, ACO is used for DSM in many
ways. For-example, authors in [14], investigate congestion
management and cost minimization problems. They formulate
their focused problem as a non-linear programming problem
and electricity bill minimization is achieved using ACO. To
our knowledge, ACO implementation in residential area is not
done before. In our work, we use ACO to evaluate the designed

optimization function to get optimized schedules for home
appliances. Our scheme gives novel idea to implement ACO as
optimization tool for DSM in residential area. In [20], linear
programming is used to designed the optimization function.
Refer to [21], we modified its algorithm for our designed
scenario. Algorithm. 3 gives detailed view of ACO based
EMC (ACO-EMC) model. ACO is used to evaluate objective
function (refer eq. 29) and its constraints (refer eq. 29a to eq.
29i) to get feasible operational time for all appliances. Our
proposed model is applicable for single and multiple homes
in residential areas. The improved ACO algorithm is shown
in algorithm 1.
V. SI MU LATI ON S AN D RE SU LTS
To evaluate different performance metrics of EMC, we
conduct extensive simulations in MATLAB. We use TOU tariff
model of Jemena Electricity Networks (VIC) Ltd [22], [23]
for residential area with IBR. For simulations, we design a
model for residential area in which each home is equipped
with 10 smart appliances and 4 end users. Appliances with
their parametric values that are used in simulations are shown
in table. I, table. II, and table. III, respectively. In table. I, fixed
appliance has only ρaparameter measured in kWh because
these are non-manageable appliances and do not play any role
in load scheduling problem. Whereas, other two categories
TABLE I: Parameters of Fixed Appliances
Appliances ρa(kWh)
Lighting 0.6
Fans 0.75
Clothes iron 1.5
Microwave oven 1.18
Toaster 0.5
Coffee maker 0.8
of appliances; shiftable and elastic appliances are known as
schedulable appliances. As, in table. II, the parameters for
shiftable appliances are αa,βa,ξa,ϕaand ρaare kWh. ϕa
is the unique parameter in shiftable appliance because these
appliances can be interruptible during its length of use. For
elastic appliances, the parameters are αa,βaand ρain kWh
are shown in table. III.
TABLE II: Parameters of Shiftable Appliances
Appliances αa
(hours)
βa
(hours)
ϕa
(hours)
ρa
(kWh)
Washing machine 8 16 5 0.78
Dish washer 7 12 5 3.60
Clothes dyer 6 18 5 4.40
TABLE III: Parameters of Elastic Appliances
Appliances αa
(hours)
βa
(hours)
ρa
(kWh)
Air conditioner 6 24 1.44
Refrigerator 6 24 0.73
Water heater 6 24 4.45
Space heater 6 24 1.50
TABLE IV: ACO parametric list
Parameters Values
Ant quantity 10
Pheromone intensity factor 2
Visibility intensity factor 6
Evaporation rate 5
Trail decay factor 0.5
Stopping criteria Max. iteration
Max. iteration 600
Simulation parameters of ACO-EMC are given in table. IV,
respectively.
A. Electricity bill reduction
The maximum value of electricity bill in unscheduled model
is 266.3492 cent as shown in fig. 3. It is reduced to 114.2536
cent in ACO-EMC. During peak hours (16-22), sufficient
electricity cost reduction is shown for the designed ACO-EMC
model. ACO-EMC acts more effectively than the unscheduled-
EMC BPSO-EMC in achieving our designed objective of
electricity cost reduction due to its characteristics of local and
global exploration.
Fig. 3: Electricity bill (cent)
B. PAR
Performance of the designed model (ACO-EMC) with re-
spect to PAR reduction is shown in fig. 4. It shows that PAR
is significantly reduced for ACO-EMC as compared to the
unscheduled case because these are designed to avoid peak
formation in any hour of a day. Results prove that our proposed
model effectively tackle the peak formation problem. PAR
curves for ACO-EMC describe that power consumption of
appliances is optimally distributed in 24 hours without creating
peak in peak hours (16-22) of a day. We have used combined
model of TOU and IBR for electricity billing to avoid peak
formation via giving information to consumers.
C. Waiting time
User comfort is related to both electricity bill and waiting
time of an appliance. In order to achieve lower electricity
bills, smart users must operate their appliances according
to optimal schedule of EMC. During scheduling horizon of

shiftable appliances, operational time is not fixed due to price
variation in dynamic pricing models. Generally, it is observed
that electricity cost reduction and waiting time show inverse
relationship. By applying waiting time constraints on the
objective function, we have enhanced the performance of EMC
in terms of user comfort and electricity bill reduction. In fig. 5,
it is shown that electricity bill is high if rate of waiting time
is zero and it is low with increase in rate of waiting time for
the proposed model.
Fig. 4: PAR curve
Fig. 5: Possible trade off between electricity cost and waiting
time
VI. CONCLUSION AND FUTURE WO RK
In this paper, we have presented an efficient DSM model
for residential energy management system in order to avoid
peak formations while decreasing the utilities electricity bill
by preserving user comfort level within acceptable limits. We
used ACO to solve our objective function and used combined
pricing models, TOU tariff and IBR model for electricity bill
calculation. From the results, it is clearly justified that our
proposed model works efficiently in terms of electricity bill
reduction, and minimization of PAR while considering user
satisfaction.
In future, we will focus on human behavior to achieve
comfort level of consumer and to minimize frustration cost
and improve security and privacy issues between end user and
utility.
REFERENCES
[1] V. Gungor, D. Sahin, T. Kocak, S. Ergut, C. buccella, C. Cecati and G.
Hancke, “Smart Grid Technologies: Communication Technologies and
Standards”, Industrial Informatics, IEEE Transaction, Vol. 7, No. 4, pp.
529-539, Nov. 2011.
[2] M. Hashmi, S. Hanninen, and K. Maki, “Survey of Smart Grid Concepts,
Architectures and Technological Demonstrations Worldwide”, IEEE PES
Conference, Medellin, Oct. 2011.
[3] L. Gelazanskas, and K. A. A. Gamage, “Demand Side Management in
Smart Grid: A Eeview and Proposals Forfuture Direction”, Sustainable
Cities and Society, Vol. 11, pp. 2230, Feb. 2014.
[4] P. Siano, “Demand Response and Smart Grids A Survey”, Renewable
and Sustainable Energy Reviews, Vol. 30, pp. 461478, Feb. 2014.
[5] A. Molderink, V. Bakker, M. G. Bosman, J. L. Hurink, and G. J. Smit,
“Domestic Energy Management Methodology for Optimizing Efficiency
in Smart Grids”, IEEE PowerTech, Bucharest, pp. 1-7, 28 Jun(2008) - 2
Jul (2009)
[6] T. Sousa, H. Morais, Z. Vale, P. Faria, and J. Soares, “Intelligent
Energy Resource Management Considering Vehicle-to-Grid: A Simulated
Annealing Approach”, IEEE Transaction Smart Grid, Vol. 3, No. 1, pp.
535-542, Mar. 2012.
[7] J. Soares, T. Sousa, H. Morais, Z. Vale, and P. Faria, “An Optimal
Scheduling Problem in Distribution Networks Considering V2G”, in Proc.
IEEE CIASG, Paris, 11-15 Apr. 2011.
[8] K. M. Tsui and S. C. Chan, “Demand Response Optimization for Smart
Home Scheduling Under Real-Time Pricing”, IEEE Transaction Smart
Grid, Vol. 3, No. 4, pp. 1812-1821, Dec. 2012.
[9] D. Maringer, “Portfolio Management with Heuristic Optimization”,
Springer, 2004.
[10] T. Logenthiran, D. Srinivasan, and T. Z. Shun, “Demand Side Man-
agement in Smart Grid using Heuristic Optimization”, IEEE Transaction
Smart Grid, Vol. 3, No. 3, pp. 1244-1252, Sept. 2012.
[11] Z. Zhao, W. C. Lee, Y. Shin and K. Song, “An Optimal Power
Scheduling Method for Demand Response in Home Energy Management
System”, IEEE Transaction Smart Grid, Vol. 4, No. 3, pp. 1390-1400,
Sept 2013.
[12] M. A. Khan, N. Javaid, A. Mahmood, Z. A. Khan and N. Alrajeh, “A
Generic Demand-Side Management Model for Smart Grid”, International
Journal of Energy Research, Vol. 39, No. 7, pp. 954964, Jun. 2015.
[13] T. Dethlefs, T. Preisler and W. Renz, “Ant-Colony based Self-
Optimization for Demand-Side-Management”, Conference: SmartER Eu-
rope, Essen, Feb. 2015.
[14] B. Liu, J. Kang, N. Jiang and Y. Jing, “Cost Control of the Transmission
Congestion Management in Electricity Systems based on Ant Colony
Algorithm”, Energy and Power Engineering, Vol. 3, No. 1, pp. 17 - 23,
Feb. 2011.
[15] N. Kumaraguruparan, H. Sivaramakrishnan and S. Sapatnekar, “Residen-
tial task scheduling under dynamic pricing using the multiple knapsack
method”, IEEE Conference, Washington, DC, pp. 1-6, Jan. 2012.
[16] O. A. Sianaki, O. Hussian and A.R. Tabesh, “A Knapsack Problem
Approach for Achieving Efficient Energy Consumption in Smart Grid
for End-user Life Style”,IEEE conference, Waltham, MA, Sept. 2010.
[17] C. Ogwumike, M. Short and M. Denai, “Near-Optimal Scheduling of
Residential Smart Home Appliances using Heuristic Approach”, IEEE
International Conference on Industrial Technology, Seville, Spain, 2015.
[18] A. Barbato and A. Capone, “Optimization Models and Methods for
Demand-Side Management of Residential Users: A Survey”, Sept. 2014
[19] H. Kellerer, U. Pferschy, and D. Pisinger, “Knapsack Problems”.
Springer, 2004.
[20] I. K. Yu and Y. H song, “A Novel Short-term Generation Scheduling
Technique of Thermal Units using Ant Colony Search Algorithms”,
International Journal of Electrical Power and Energy Systems, Vol. 23,
No. 6, pp. 471479, Aug. 2001.
[21] S. Rahim, S. A. Khan, N. Javaid, N. Shaheen, Z. Iqbal and G. Rehman,
“Towards Multiple Knapsack Problem Approach for Home Energy Man-
agement in Smart Grid”, 8th IEEE International Conference on Network-
Based Information Systems, Taipei, Taiwan, 2015.
[22] http://jemena.com.au/supply-interruptions/electricity(Last accessed: sep
20, 2015)
[23] “Jemena Electricity Networks (VIC) Ltd - Network Tariffs For The 2015
Calendar Year (Exclusive of GST)”