Content uploaded by Bara'a A. Attea

Author content

All content in this area was uploaded by Bara'a A. Attea on May 02, 2015

Content may be subject to copyright.

1 23

Wireless Personal Communications

An International Journal

ISSN 0929-6212

Volume 81

Number 2

Wireless Pers Commun (2015)

81:819-838

DOI 10.1007/s11277-014-2159-3

A Multi-objective Disjoint Set Covers for

Reliable Lifetime Maximization of Wireless

Sensor Networks

Bara’a A.Attea, Enan A.Khalil, Suat

Özdemir & Oktay Yıldız

1 23

Your article is protected by copyright and all

rights are held exclusively by Springer Science

+Business Media New York. This e-offprint is

for personal use only and shall not be self-

archived in electronic repositories. If you wish

to self-archive your article, please use the

accepted manuscript version for posting on

your own website. You may further deposit

the accepted manuscript version in any

repository, provided it is only made publicly

available 12 months after official publication

or later and provided acknowledgement is

given to the original source of publication

and a link is inserted to the published article

on Springer's website. The link must be

accompanied by the following text: "The final

publication is available at link.springer.com”.

Wireless Pers Commun (2015) 81:819–838

DOI 10.1007/s11277-014-2159-3

A Multi-objective Disjoint Set Covers for Reliable

Lifetime Maximization of Wireless Sensor Networks

Bara’a A. Attea ·Enan A. Khalil ·Suat Özdemir ·

Oktay Yıldız

Published online: 12 November 2014

© Springer Science+Business Media New York 2014

Abstract An important challenge facing many large-scale surveillance applications is how

to schedule sensors into disjoint subsets to maximize the coverage time span. Due to its

NP-hard complexity, the problem of ﬁnding the largest number of disjoint set covers (DSC)

of sensors has been addressed by many researchers. Majority of these studies employs the

Boolean sensing model where a sensor covers a target if it lies within its sensing range. In

reality, however, the sensing reliability may be affected by several parameters, e.g., strength

of the generated signals, environmental conditions and the sensor’s hardware. To the best of

our knowledge, improving coverage reliability of Wireless Sensor Networks (WSNs) has not

been explored while solving DSC problem. This paper addresses the problem of improving

coverage reliability of WSNs while simultaneously maximizing the number of DSC. Thus, in

the context of WSNs design problem, our main contribution is to turn the deﬁnition of single-

objective DSC problem into a multi-objective problem (MOP) by adopting an additional

conﬂicting objective to be optimized. Speciﬁcally, we investigate the performance of two

multi-objective evolutionary algorithms in terms of diversity and quality of the Pareto optimal

set for the modeled MOP. The simulation results indicate that multi-objective approach results

in achieving reliable coverage and large number of DSC compared to a single-objective

approach.

B. A. Attea (B)

Department of Computer Science, Baghdad University, Baghdad, Iraq

e-mail: baraaali@yahoo.com

B. A. Attea

e-mail: baraali@scbaghdad.edu.iq

E. A. Khalil ·S. Özdemir ·O. Yıldız

Department of Computer Engineering, Gazi University, Ankara, Turkey

e-mail: enanameen@yahoo.com

S. Özdemir

e-mail: suatozdemir@gazi.edu.tr

O. Yıldız

e-mail: oyildiz@gazi.edu.tr

123

Author's personal copy

820 B. A. Attea et al.

Keywords DSC ·MOO ·Non-dominated solution ·NP-hard ·Probabilistic coverage ·

Reliability ·WSNs

1 Introduction

The Wireless Sensor Network (WSN) paradigm is an emerging and fast growing technolog-

ical platform in myriad working environments. To name just a few, WSNs can be used in

military and agriculture applications, harsh environment monitoring, emergency search-and-

rescue operations. One of the important characteristics of WSNs is their ability to densely

deploy in ad-hoc manner. For successful operation of WSNs, sensors should effectively cover

the required region of interest for a long period of time. Energy-aware sensing and commu-

nication mechanisms have been substantially pursued by the research community in order to

prolong the lifespan of WSNs. Energy saving techniques can generally be classiﬁed in the

following categories; (1) Energy-efﬁcient data aggregation, gathering and routing; (2) power

management by adjusting the transmission and/or sensing range of sensor nodes; and (3)

sensor wake-up scheduling to alternate between active and idle state.

In this paper, we consider the third approach to achieve energy-efﬁcient WSN that monitors

all the targets at all times. In this approach, sensors are divided into disjoint sets of covers

(DSC) such that every set completely covera set of targets being located with known locations.

We assume that the lifetime of a WSN is divided into intervals and at each interval only one

set is active with while the remaining set covers are in the low-energy sleep mode. The sensors

from the active set are in active state, monitoring all targets within their sensing ranges. Once

the active set cover runs out of energy, another set cover will be selected to enter the active

mode and provide the functionality continuously. As all targets should be monitored by every

set cover, the goal of this approach is to determine a maximum number of DSC. The more

set covers we can ﬁnd, the longer sensor network lifetime is prolonged. It has been proven

that this problem (also called the SET k-cover problem) is a generalization of the minimum

cover problem [1] and proves its NP-completeness [2,3].

Many attempts in the literature have been made to solve DSC problem in WSNs using

either heuristic or meta-heuristic methods (like genetic algorithms). Different scheduling

rules determine when sensors change to be active or sleep mode. In localized and distributed

realizations, sensors periodically investigate their neighborhood and decide whether to change

their operation modes [4–11].

In [2], a heuristic approach called the “most constrained-minimally constraining covering

(MCMCC)” is proposed to select and successively activate mutually exclusive sets of covers,

where every set completely covers the entire monitored area. This method gives priority

to sensors which cover a high number of uncovered ﬁelds, cover sparsely covered ﬁelds

and do not cover ﬁelds redundantly. This method achieves energy savings by increasing the

number of disjoint covers. Also, the DSC problem and its extension to the maximum set

cover (MSC) problem have been solved in [12]and[3] using integer programming, linear

programming, and greedy heuristics. In [12], the DSC problem is reduced to a maximum

ﬂow problem and solved using mixed integer programming. By a branch and bound method,

the maximum covers based on mixed integer programming algorithm (MC-MIP) acts as an

implicit exhaustive search to guarantees ﬁnding the optimal solution.

The deﬁnition of DSC problem has been re-formulated in [3,13], and [14] to include

additional coverage constraints. The deﬁnition of DSC problem has been generalized in [3]

to a maximum set covers (MSC) problem and solved it using linear programming and greedy

techniques. The extended problem in MSC lets the sensors to participate in multiple sets. In

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 821

[13], the DSC problem has been extended to include connectivity constraint as well. Then,

the Connected Set Covers (CSC) problem has as objective ﬁnding a maximum number of set

covers such that each sensor to be activated should be connected to the base station. In [14],

DSC problem has been extended to include sensor coverage-failure probability. Each sensor

is associated with sensor’s failure probability (comes from several facts, e.g., manufacture,

weather in the monitoring area, interferences to the sensors, or unexpected accidents). The

proposed Maximum Reliability Sensor Covers (MRSC) problem has been solved in [14]

using a heuristic greedy algorithm to compute the maximal number of set covers that satisfy

a user speciﬁed coverage-reliability threshold.

The works in [15–17] also provide solutions to the DSC problem in WSNs by employing

the meta-heuristic framework of evolutionary and genetic algorithms. Like the previous

mentioned heuristic methods, the single-objective genetic algorithms proposed in [15–17]

assume simple and common isotropic (i.e., disc) sensing model. Each sensor in this model is

associated with a sensing area which is represented by a circle with the same radius. According

to [18], the upper bound, ub, of the maximum number of disjoint complete set covers depends

on the size of the target area, the total number of sensors, the sensors’ locations, and their

sensing ranges.ub can be estimated as the minimum number of sensors covering the most

sparsely covered target, and thus can be computed by polynomial-time algorithms. It has

been shown that for the same deployment of sensors and targets, ub can be increased by

enlarging the sensing radius of each sensor [15–18]. In reality, however, the sensing region

of a sensor could be irregular, resulting in imprecise target coverage. The coverage in this

case could be expressed in probabilistic terms [19–21]. In probabilistic sensing model, there

is a measure of uncertainty in sensor signal-detection being expressed by a value from 0 to

1. For reliable coverage with threshold cth, the detection uncertainty of each target should

not exceed 1 −cth. This in turn should effect on the number of sensors reliably covering

the most sparsely covered target. As more reliability degree to cover a target is required,

ub becomes smaller. Thus, there should be a trade-off between the coverage reliability (also

denoted throughout this paper as covers reliability)andub.

Like many other sensor network design problems, maintaining reliable coverage while

maximizing the number of DSC (i.e., extending network lifetime) often require optimiz-

ing two conﬂicting decision variables. Due to the conﬂicting nature of many sensor net-

work design problems, multi-objective optimization (MOO) has, recently, attracted several

researchers in formulating multi-objective optimization problems (MOPs). In MOO, a set of

alternative solutions (called non-dominated solutions) can simultaneously be obtained pro-

viding the decision maker with an optimal tradeoff between the conﬂicting objectives. As

multi-objective evolutionary algorithms (MOEAs) possess several interesting characteristics

for tackling MOPs, there are many MOEA approaches for solving different sensor design

problems. For organizing energy efﬁcient WSNs, the literature provides a collection of MOO

schemes in which sensing coverage and network lifetime are the main design issues to be

optimized. However, all of these methods fall in one of the ﬁrst two categories; data aggre-

gation, routing, and sensor clustering [22–25], or sensors’ power management [26–29]. For

the reliable DSC design problem in WSNs, our work in [30] formulates a single objective

evolutionary algorithm to tackle it. To the best of our knowledge, however, MOO concept

has not been exploited. The contributions of this paper are as follows:

1. The paper turns the de-facto deﬁnition of single-objective DSC in WSN design problems

to a multi-objective DSC. The goal of which becomes to cope with contradictory objec-

tives. The formulated optimization problem will be directed to effectively maintaining

reliable coverage with large number of cover sets in WSNs.

123

Author's personal copy

822 B. A. Attea et al.

2. The paper presents two MOEAs with a new heuristic perturbation operator (instead of

the traditional bi-perturbation of crossover and mutation operators) to solve the modeled

problem. The results show that the Pareto-optimization can provide the decision maker

with a set of non-dominated solutions that effectively render the tradeoff between the

two conﬂicting objectives (i.e., network lifetime and coverage probability).

The rest of this paper is outlined as follows. Section 2describes the traditional formulation

of DSC problem in WSNs as well as the new formulation of multi-objective DSC by adding

probabilistic coverage means to the original problem. Section 3provides the preliminaries to

the concept of multi-objective optimization and introduces the formulation of the proposed

perturbation operator. The results of multi-objective DSC optimizations are then compared

with a related work of single-objective genetic algorithm in Sect. 4. Finally, Sect. 5concludes

the current work and hints some further ramiﬁcations.

2 Problem Deﬁnition

2.1 System Model and Assumptions

In order to model the system, we assume that the investigated WSNs have 2D sensing area

Awith known size(Xmax,Ymax ). We also assume that Ahas a set T(i.e., target set) of n

targets with known locations, i.e., T={

(xt1,yt1),(xt2,yt2),...,(xtn,ytn)}.Therearem

homogenous sensors S={

(xs1,ys1),(xs2,ys2),...,(xsm,ysm)}having the same sens-

ing range rs. All the sensors are dropped randomly in A(1≤∀i≤m|(xsi,ysi)=

([0,Xmax],[0,Ymax ])). Depending on the sensing range rs, each sensor is responsible for

sensing and covering a part of A. We consider a probabilistic sensing model [20,21]todeﬁne

the notion of the probabilistic coverage of a target Tj=xtj,ytjby a sensor si.

Coverage si,tj=⎧

⎨

⎩

0if r

s+ru≤d(si,tj)

e−λaβif r

s−ru<d(si,tj)

1if r

s−ru≥d(si,tj)

<rs+ru(1)

where ruis a measure of the uncertainty in sensor detection. dsi,tjis the Euclidean distance

(xsi −xtj)2+(ysi −ytj)2between sensor siand target tj.a=d(si,tj)−(rs−ru),and

λand βare probabilistic detection parameters to measure detection strength when a target

point lies within the interval {rs−ru,rs+ru}. It causes coverage value to exponentially

decrease as the distance increase. All points that lie within a distance of rs−rufrom the

sensor are said to be 1-covered. Beyond the distance rs+ru, all the points have 0-coverage

by this sensor.

To save energy and prolong WSN’s lifetime, sensors in the sensor set Sshould be divided

into duty-cycling sensor cover (also called set cover) subsets, each of which can cover all

the interested targets in T. Thus, in the traditional Boolean sensing model, the deﬁnition of

the sensor cover could be formulated as:

Deﬁnition 1 (Sensor Cover). Given a WSN consists of target set Tand sensor set S,where

each sensor si∈Scan be represented as a subset Ti⊂T, such that tj ∈Tiif and only if

Coverage si,tj=1. Any subset Si⊂Sthat can completely cover all the target set Tis

termed as a sensor cover.

However, considering probabilistic sensing model, the deﬁnition of the traditional sensor

cover needs to be re-formulated as:

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 823

Deﬁnition 2 (Reliable Sensor Cover). Given a WSN consists of target set Tand sensor set

S, where each sensor si∈Scan be represented as a subset Ti⊂T, such that tj ∈Tiif

and only if Coverag e si,tj≥cth. Any subset Si⊂Sthat can satisfy a user coverage

constraint cth to cover all the targets in Tis termed as a reliable sensor cover or reliable set

cover.

Now, the problem of ﬁnding the maximum number of disjoint set covers (DSC) could be

turned into the problem of ﬁnding the maximum number of disjoint reliable sensor covers

(DRSC), and can be formulated as:

Deﬁnition 3 (Disjoint Reliable Sensor Covers Problem—DRSC). Given a collection Sof

reliable subsets of a ﬁnite set T, ﬁnd the maximum number of disjoint reliable covers for

T. Every cover Siis a subset of S,Si⊆S, such that every element tj of Tbelongs to at

least one member of Si, and for any two covers Siand Sj,Si∩S

j=∅. Now, the upper bound

ub of the maximum number of disjoint reliable covers is determined by the most sparsely

covered target and can be calculated as:

ub =min

i=1,2,...,n(|Si|)(2)

where CS =Si,|Si|=ub denotes the set of sensors (called Critical sensors Set) covering

target ti with certainty equal to or larger than a user speciﬁed threshold cth.Asthemost

sparsely covered target only covered by ub. Sensors, the maximum number of disjoint reliable

covers Nis no larger than ub i.e., N≤ub).

2.2 Problem Formulation

In this section, we formulate the problem of getting high coverage percentage with maximum

number of DSC as multi-objective Disjoint Reliable Sensor Covers Problem:

Given:

A: 2-D plane area with size(Xmax,Ymax).

T:setofntargets being uniformly distributed in A.

S:setofmsensors with probabilistic sensing capability, being uniformly distributed in

A.

rs: sensing range.

ru,λand β: uncertainty-parameters adjusted according to the physical properties of the

sensor.

Decision (Design) variables of a solution:

The scheduling sets of sensors in S, i.e., {S1,S2,...,Sm}|Si∈[1,ub].

Objective:

Two objectives are considered as optimization functions. The ﬁrst objective is to maximize

the number of scheduling sets of the sensors in S, such that each scheduling set Sican form

a complete reliable sensor cover (see Eq. 3). Thus, Eq. 3computes the number of reliable

covers (i.e., without and coverage holes) being formed by a particular solution. Detection of

coverage holes is formulated in Eq. 4. The second objective is to maximize the reliability

of the whole disjoint sensor covers (see Eq. 5). In each sensor cover, we consider only the

highest coverage of the sensors belong to this cover to each target in set T.

max DRSC =Si∈[1,ub]Cover(Si,T)(3)

123

Author's personal copy

824 B. A. Attea et al.

where:

Cover (Si,T)=1if ∀t∈T→∃s∈Si|Coverage (s,t)≥cth

0otherwise (4)

max Reliability =

Si|Cover(Si,T)=1

Coverage(Si,T)(5)

where:

Coverage (Si,T)=t∈Tmax

s∈SiCoverage (s,t)

n(6)

3 Multi-objective Evolutionary Algorithms for DRSC Problem

3.1 Preliminaries

The general formalization of MOP is deﬁned as [31,32]: ﬁnding a vector X∗=

[x∗

1,x∗

2,...,x∗

n]Toptimizing (in terms of domination) the vector function F(X)=

[f1(X),f2(X),...,fk(X)]Twhere X=[x,

1x2,...,xn]Tis the decision variables vector.

Optimizing F(X), here, considers the domination concept. Let us consider two solution U

and Vfrom the solution space P. Then, solution Uis said to dominate Vif and only if the

following two conditions hold:

1. The solution Uis no worse than Vin all objectives, or fi(U)fi(V)for all i=

1,2,...,k. For example in maximization, the word “no worse” means fi(U)≮fi(V).

2. The solution Uis strictly better than Vin at least one objective, or fi(U)fi(V)for at

least one i∈1,2,...,k. For example in maximization, the word “strictly better” means

fi(U)>fi(V).

The notation (ij)is used to denote that solution iis better than solution jregardless of the

type of the optimization problem at hand (maximization or minimization). Also, the notation

(ij)is used in the same way to express that solution jis better than solution i. Hence, a

dominated set can be deﬁned as: among a set of solutions P, the non-dominated solutions

set ´

Pare those that are not dominated by any member of the set P.

In this paper, we consider two multi-objective evolutionary algorithms (MOEAs). These

are: multi-objective evolutionary algorithm with Tchebycheff decomposition (MOEA/D) and

non-dominated sorting genetic algorithm (NSGA-II). In what follows, we only present these

two algorithms focusing on the proposed perturbation operator. We refer interested readers to

[31–35] for more detailed description of the general framework of MOEA/D and NSGA-II.

3.2 The Proposed Meta-heuristic Framework

As MOEA/D and NSGA-II are population-based optimization algorithms, let us consider

a population ρof Ksolutions. The choice of a good solution representation is a critical

issue for the applicability and performance of evolutionary algorithm. Solution representa-

tion is highly problem dependent and related to the evolution operations. In our algorithm

design, each individual solution P1≤i≤K∈ρis represented as a ﬁxed-length vector of size

m, where each element (i.e., gene) value indicates the index of the set cover that the corre-

sponding sensor joins, specifying that the index does not exceed the upper limit ub. Thus,

∀i∈{1,...,N}and ∀j∈[1,m]:Pi=(Pi1,Pi2,...,Pim)s.t.Pij ∈[1,ub]. Then, each of

the implemented MOOs can be described as a process formulated in an iterative evolution

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 825

function :{ρ,EP}→{ρ,EP}with (ρi)=ρi+1,whereiis the iteration index and

ρiis the population in iteration i.EP is an external archive for the generated non-dominated

solutions. The population starts with an initial random population ρ0and continues until a

maximum number of iterations maxihas been reached. Each iteration iconsists of a three

main operators: parents selection, heuristic perturbation, and EP update.

Based on the chromosome representation, we adopted an intuitive and fast random ini-

tialization mechanism, where each gene can take a random value that does not exceed the

upper limit ub. Formally speaking:

(∀i∈{1,...,N},∀j∈[1,m]):Pij ∼[1,ub](7)

where ∼[1,ub]means a uniform random integer number between 1 and ub.

For selection operator, we imitate similar functions to that found in the implementation

of the traditional MOEA/D and NSGA-II. For the perturbation function, we proposed one

evolution operator that provides heuristic for improving a solution coverage reliability

or number of disjoint covers. The process of the proposed heuristic perturbation operator

is presented next (see Algorithm 1). It takes as input two parent individuals P1,P2being

selected from ρby the selection operator and perturbs them with probability pper =1.0to

return one child Cwith its decoded set covers C1,C2,...,Ck. For each child, the proposed

123

Author's personal copy

826 B. A. Attea et al.

heuristic will be directed (with equal probability) either towards maximizing the reliability of

the generated set covers or towards maximizing the number of sensor covers k. Thus, for each

child Ci,1≤i≤K, the heuristic procedure also takes as input a ﬂag Findicating whether to

prefer maximizing reliability or maximizing number of sensor covers. The proposed heuristic

also takes as input the set of the critical sensors CS.

The proposed heuristic recursively builds sensor covers in the child. For each cover i,

the set S(in line 6) collects sensors from both parents that have an index value equal to i.

The sensors in Scan then participate in creating the cover iin the child. When sensors in

Scan cover all the targets without any coverage hole (in line 8), then (and according to the

ﬂag F), the procedure will select from Sthose sensors having the highest contribution to the

heuristic (line 12–18). In order to maximize number of sensor covers towards its upper limit

ub, a heuristic process is maintained in line 15. Note that this process is guided to restrict

the choice of sensors, for the current sensor cover i , to those that do not belong to the set of

critical sensors (i.e., s /∈CS) or at least bias the choice in their support. The biasing depends

on the number of targets being covered by each sensor s/∈CS. However, if there is still

coverage hole in the current cover i, the heuristic process turns the selection to the critical

sensors s∈CS. The remaining sensors can then contribute in the next covers (line 20). They

will migrate to the last set cover kand used again (line 23) when there is a coverage hole

(line 21) while forming a new cover i. Finally, the last cover (line 25) may form a complete

set cover or incomplete one. The generated child Cmay modify the contents of the external

archive EP according to the non-domination condition described previously.

4 Simulation Results and Discussion

In this section, we evaluate the performance of the proposed MOO algorithms in terms of

number of set covers obtained and coverage reliability. The results are obtained after setting

WSNs and algorithm parameters into the most commonly used in the related literature. The

simulation area is square-shaped with side length Xmax = 500 m of 10 randomly distributed

targets. Unless otherwise stated, the simulation is mainly divided into ﬁve groups according

to ﬁve different settings of sensor density: 50, 60, 70, 80, and 90. For each group, we vary the

sensing range of the sensor nodes Rsto three different values {100,200,300},togetadifferent

test instance. Each test instance includes 10 random WSNs with different conﬁgurations. Thus

the overall simulation examines a total of 150 random networks. As we have random WSN

conﬁgurations, we may get different value for the upper bound of set covers ub,forthe

same parameter settings. Thus in each test instance, the presented results also indicate the

average number of upper bound of set covers (denoted by ub). Uncertainty level Ruis set

to Rs∗0.5 units, both λand βare set to 0.5, and cth is set to 0.001. The setting of the

probabilistic coverage parameters also inﬂuences the overall network’s coverage reliability.

Since studying the impact of varying these parameters is out of the scope of this paper, we

ﬁxed these parameters to one setting and evaluate the average coverage reliability (denoted

by ¯r) of all network conﬁgurations in each test instance. Population size is set to 50 and will

be allowed to evolve 500 times. Perturbation probability is ﬁxed to 1.0. For MOEA/D, the

size of neighboring solutions that participate in the evolution of each individual solution is

ﬁxed to 5.

Both MOEA/D and NSGA-II have been compared with Genetic Algorithm for Maximum

Disjoint Set Covers (GAMDSC). GAMDSC has been proposed in [15] to extend the lifetime

of WSNs. GAMDSC is single-objective genetic algorithm that use integer representation

for chromosome representation, traditional uniform crossover, creep mutation, and a scatter

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 827

operator to evolve their chromosome solutions. The proposed ﬁtness function in GAMDSC

has been devoted to maximize number of complete set covers in each chromosome. The per-

formance of GAMDSC has been compared in [15] against the most constrained-minimum

constraining heuristic (MCMCC) [2] and the exhaustive heuristic of Maximum Covers using

Mixed Integer Programming (MCMIP) [12] for solving the DSC problem in WSNs. Simu-

lation results in [15] show that GAMDSC can get near-optimal solutions and improve the

performance of MCMCC by 16% in terms of the obtained sensor covers. As compared with

the exhaustive search of MCMIP, GAMDSC can get results with acceptable computation

time.

4.1 Comparison of Multi-objective Versus Single-objective DSC

First, results are presented in Tables 1and 2to compare the quality of results obtained by

GAMDSC, MOEA/D, and NSGA-II. Table 1presents number of set covers being obtained

by the three algorithms. Table 2presents the coverage reliability being obtained by the

algorithms. Also, to examine the quality of solutions provided by the three algorithms, we

present ub and ¯ras reference values in Tables 1and 2, respectively.

For both MOEA/D and NSGA-II, Tables 1and 2present the two extreme non-dominated

solutions (in terms of number of set covers and reliability, respectively). The solution pro-

viding the closest value to ub in each test instance in Table 1has been presented in bold.

Also, the solution providing the maximum reliability in each test instance in Table 2has been

bolded. Note that in Table 1, closest solutions to ub do not necessary imply best solutions. In

terms of the algorithm’s independent single-objective measure of solution’s quality, closest

solutions to ub should result in high quality solutions. That is GAMDSC provides more

sensor covers in four test instances while NSGA-II provides more sensor covers in almost all

of the remaining test instances. However, seeking for tradeoff solutions that balance between

the sensor covers and coverage reliability (see Table 2), the performance of GAMDSC in

these four test instances is not good enough. The coverage reliability of GAMDSC gives the

lowest score while both MOEA/D and NSGA-II outperform GAMDSC in all test instances.

Similarly, in the third and tenth test instances (referred with asterisk), GAMDSC gives equal

values of sensor covers to NSGA-II or MOEA/D, respectively (as presented in Table 1), how-

ever, both NSGA-II MOEA/D outperform GAMDSC in terms of reliability (as presented in

Tabl e 2). Thus, the combined results of Tables 1and 2signify the importance of utilizing

the two objectives as optimizing criteria rather than maximizing only the number of sensor

covers. Moreover, in all test instances, Table 2presents that NSGA-II performs better than

MOEA/D even in the case of providing an equal number of set covers as in the sixth test

instance, referred with asterisk in Table 1.

Figure 1compares the performance of GAMDSC, MOEA/D, and NSGA-II in terms

of average number of disjoint sensor covers obtained while ﬁxing sensing radius. In this

simulation, we ﬁxed sensing range Rsto 500 and vary number of sensors from 50 to 90 with an

incremental value of 5. Each test instance of this simulation includes 10 random networks, and

thus the total simulation is experimented under test-bed of 90 different network topologies.

This simulation clariﬁes the impact of varying sensing ranges, of a given ﬁxed number and

ﬁxed locations of sensors, on the total number of disjoint sensor covers. The results of this

simulation summarize that for a ﬁxed sensing radius, the number of sensor covers increases

with increasing number of sensors. Also, from the ﬁgure we can that NSGA-II provides more

number of sensor covers than both MOEA/D and GAMDSC.

On the other hand, Fig. 2clariﬁes the impact of varying sensing range Rswhile ﬁxing

number of sensors. In this simulation, the number of sensors is set to 70 and let Rsto vary

123

Author's personal copy

828 B. A. Attea et al.

Tab l e 1 Comparison of the maximum number of the generated set covers for 10 WSNs in each test case

Test instance No. of sensors Rsub GAMDSC MOEA/D NSGA-II

1 50 100 5.00 4.80 4.70 4.60

1.10 1.30

2 200 17.30 15.80 15.10 15.00

6.80 5.90

3 300 23.10 21.20 21.10 21.20∗

9.50 8.20

4 60 100 6.50 5.50 5.60 5.60

1.30 1.80

5 200 22.30 18.90 19.20 19.60

8.90 7.30

6 300 30.00 25.80 26.30 26.30∗

13.40 9.90

7 70 100 7.70 6.70 6.70 6.80

1.80 1.80

8 200 23.80 20.80 20.60 20.90

10.10 8.30

9 300 32.10 28.10 29.00 29.40

14.60 11.10

10 80 100 9.50 8.30 8.30∗8.20

2.10 1.80

11 200 31.20 25.80 25.90 26.50

13.70 10.60

12 300 41.00 34.10 36.10 36.40

18.50 14.50

13 90 100 9.10 8.50 8.40 8.30

3.00 3.40

14 200 30.80 27.10 26.50 26.40

14.80 11.40

15 300 42.10 36.30 36.70 37.90

20.40 16.20

For MOEA/D and NSGA-II, results are presented in terms of max and min DRSC solutions in EP

from 100 to 500 with an incremental value of 50. Also, in this simulation, each test instance

includes 10 random networks with a total of 90 different network topologies. The results of

the ﬁgure indicates that increasing sensing radius have a positive impact on the number of

sensor covers, even when ﬁxing the number of sensors to a certain value. Also, we can see

that NSGS-II provides more number of sensor covers than both MOEA/D and GAMDSC.

4.2 Quality and Diversity of Pareto Front Solutions

Let us now turn to quantitatively compare the performance of MOEA/D and NSGA-II.

Here, the comparison will be according to the quality of the non-dominated solutions set

being obtained by each algorithm. The performance of MOEA/D and NSGA-II can also be

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 829

Tab l e 2 Comparison of the maximum covers reliability provided for 10 WSNs in each test case

Test instance No. of sensors Rs¯rGAMDSC MOEA/D NSGA-II

1 50 100 0.1867 0.3932 0.6971 0.7027

0.4038 0.4052

2 200 0.2114 0.3365 0.6447 0.7542

0.3463 0.3489

3 300 0.3216 0.4805 0.8049 0.9000

0.4783 0.4933

4 60 100 0.1731 0.3295 0.6066 0.6168

0.3661 0.3584

5 200 0.2000 0.3175 0.6069 0.7062

0.3273 0.3187

6 300 0.3206 0.4533 0.7501 0.8784

0.4545 0.4708

7 70 100 0.1754 0.3020 0.6275 0.6531

0.3502 0.3482

8 200 0.2090 0.3367 0.6265 0.7340

0.3357 0.3422

9 300 0.3156 0.4644 0.7706 0.8932

0.4701 0.4768

10 80 100 0.1888 0.3245 0.6221 0.6753

0.3620 0.3711

11 200 0.2072 0.3220 0.5968 0.7229

0.3422 0.3365

12 300 0.3267 0.4799 0.7665 0.8895

0.4764 0.4857

13 90 100 0.1972 0.3796 0.6549 0.6787

0.4263 0.4336

14 200 0.2214 0.3683 0.6163 0.7521

0.3695 0.3910

15 300 0.3384 0.5168 0.7822 0.8772

0.4999 0.5176

For MOEA/D and NSGA-II, results are presented in terms of max and min Reliability extreme solutions in EP

veriﬁed visually by depicting the Pareto Front EP. According to [36], if Aand Bare two

non-dominated sets resulted from two MOEAs Aand B, respectively, then, the set coverage

quality metric (C-metric) will express the fraction of solutions in one non-dominated solution

set that are dominated by those solutions of the second algorithm. The C-metric is deﬁned

as:

C(A,B)=|b∈B|∃a∈A:ab|/|B|(8)

where reads dominate. Note that:

•C(A,B)= 1−C(B,A), and

•Ais better than Bif C(A,B)is found to be higher than C(B,A)over many trials.

123

Author's personal copy

830 B. A. Attea et al.

50 55 60 65 70 75 80 85 90

0

10

20

30

40

50

60

70

Number of Sensors

Avg. Number of Sensor Covers

NSGA-II

MOEA/D

GAMDSC

Fig. 1 Average number of sensor covers for 90 networks with Rs=500 and number of sensors=

{50,55,...,90}. In each group of bars:left,middle,andright bar corresponds to NSGA-II, MOEA/D,

and GAMDSC results, respectively

100 150 200 250 300 350 400 450 500

0

5

10

15

20

25

30

35

40

45

50

Sensing Redius

Avg. Number of Sensor Covers

NSGA-II

MOEA/D

GAMDSC

Fig. 2 Average number of sensor covers for 90 networks with number of sensors =70andRs=

{100,150,...,500}. In each group of bars:left,middle,andright bar corresponds to NSGA-II, MOEA/D,

and GAMDSC results, respectively

The second measure is the domination metric Dom which is deﬁned as:

Dom (A,B)=d(A,B)

d(A,B)+d(B,A)(9)

where d(X,Y)=x∈X|{y∈Y|xy}|, is known as the domination factor. Mutually

non-dominating pairs are ignored in calculating the dominance factor d(A,B). If each solu-

tion in Adominates every solution in B,then Dom (A,B)=1. Thus, Dom (A,B)=

1−Dom(B,A).Table3presents these two metrics when comparing the quality of non-

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 831

Tab l e 3 Comparison of coverage set and domination metric of MOEA/Dversus NSGA-II for 10 WSNs in

each test case

Test instance No. of sensors RsC(A,B)C(B,A)Dom(A.B)Dom(B,A)

1 50 100 0.4897 0.4100 0.5168 0.4832

2 200 0.3895 0.4998 0.4466 0.5534

3 300 0.2609 0.6408 0.3059 0.6941

4 60 100 0.4450 0.3226 0.5386 0.4614

5 200 0.3137 0.5704 0.3595 0.6405

6 300 0.2330 0.6198 0.2844 0.7156

7 70 100 0.3185 0.5356 0.4022 0.5978

8 200 0.2277 0.6786 0.2632 0.7368

9 300 0.2327 0.5813 0.3387 0.6613

10 80 100 0.3829 0.4071 0.4981 0.5019

11 200 0.3152 0.4757 0.4468 0.5532

12 300 0.1732 0.6750 0.2125 0.7875

13 90 100 0.2883 0.6171 0.2994 0.7006

14 200 0.3394 0.4477 0.4597 0.5403

15 300 0.2394 0.5576 0.2664 0.7336

2 2.5 3 3.5 4 4.5 55.5 6

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

DRSC

Reliability

Fig. 3 Pareto solutions of MOEA/D(black ball)andNSGA-II (+), for one network with number of sensors

=50 and Rs=100

dominated set obtained by MOEA/D (denoted as A)against those of NSGA-II (denoted

as B). Also, here best results are given in bold.

From the results, we can consider that on overall, NSGA-II performs better than MOEA/D,

except for two test instances (i.e., test instance 1 and 4) where there is a slight difference

between the solutions quality attained by the two algorithms.

For the purpose of illustration, Figs. 3and 4depict the non-dominated solution sets

provided by the both algorithms for two WSNs belong to the two extreme test instances

experimented in our simulations (i.e. test instance 1 and 15, respectively). x,y−coordinates

123

Author's personal copy

832 B. A. Attea et al.

15 20 25 30 35 40 45

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

DRSC

Reliability

Fig. 4 Pareto solutions of MOEA/D(black ball)andNSGA-II (+), for one network with number of sensors

=90andRs=300

in the ﬁgures correspond to number of set covers (DRSC) and total coverage reliability. In the

ﬁrst test instance, the average number of upper bound of sensor covers ub is 5.00. Projection

in Fig. 3shows the cardinality and quality of both MOEA/D’s and NSGA-II’s Pareto Fronts.

The number of non-dominated solutions being obtained by both algorithms is similar (i.e.,

|A|=|B|=5). Also, we can see that both Aand Bhave nearly equal quality.

However, the dissimilarity in the quality and number of solutions in Aand Bbecomes

more apparent while increasing ub to its extreme in the last test instance (i.e., 42.10). For

this test instance, Fig. 4clariﬁes that NSGA-II discovers more non-dominated solutions

(|B|=24 against |A|=12). Also, we can see that more than 70 % of solutions in Bare

with better quality than those in A. On the other hand, about 25 % of MOEA/D solutions are

with better quality than those obtianed by NSGA-II.

Figures 5and 6also compare the quality and diversity (or width) of Pareto Front solutions

of both NSGA-II and MOEA/D in terms of the extremes solutions found there (i.e., minimum

and maximum values). Here, 9 simulations examine 90 different WSNs (each simulation with

10 networks) with the same sensing radius setting (Rs=500), but with different number

of sensor nodes ({50,55,...,90}). Thus, each simulation carries out a couple of extremes

averaged over 10 different networks with certain number of sensors and ﬁxed value of Rs.

Figure 5depicts the extremes in terms of number of sensor covers, while Fig. 6depicts the

corresponding extremes’ coverage reliability (covers reliability). For complete illustration,

we also present the best results delivered by GAMDSC in both ﬁgures. Moreover, for more

clarity, the overall statistics of NSGA-II, MOEA/D and GAMDSC are presented in Table 4.

According to the tradeoff between the two optimization objectives (i.e., number of sensor

covers and covers reliability), an extreme solution (in Fig. 5) which is dedicated on maxi-

mizing the number of sensor covers is connected to the extreme solution (in Fig. 6)thatis

dedicated to the minimum coverage reliability and vice versa.

From the results of both ﬁgures, we can see that NSGA-II provides a wider Pareto Front

than MOEA/D and with better quality. The detailed results of Fig. 5clariﬁes that the aver-

age distance between the extremes of NSGA-II is about 28.26 sensor covers, while for the

extremes of MOEA/D is 22.68 sensor covers. Also, the results reveals that the maximum

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 833

50 55 60 65 70 75 80 85 90

15

20

25

30

35

40

45

50

55

60

65

Number of Sensor Nodes

Number of Sensor Covers

GAMDSC

NSGA-II (Max)

MOEA/D (Max)

NSGA-II (Min)

MOEA/D (Min)

Fig. 5 Pareto extreme solutions (in terms of number of sensor covers) of MOEA/D(+)andNSGA-II (ﬁlled

circle). GAMDSC’sbest solutions (empty circle) are also included in the ﬁgure. The simulation is experimented

under 90 networks with Rs=500 and number of sensors ={50,55,...,90}

50 55 60 65 70 75 80 85 90

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Numebr of Sensors

Covers Reliability

GAMDSC

MOEA/D (Max)

NSGA-II (Max)

MOEA/D (Min)

NSGA-II (Min)

Fig. 6 Pareto extreme solutions (in terms of covers reliability) of MOEA/D(+)andNSGA-II (ﬁlled circle).

GAMDSC’s best solutions (empty circle) are also included in the ﬁgure. The simulation is experimented under

90 networks with Rs=500 and number of sensors ={50,55,...,90}

number of sensor covers provided by MOEA/D ranges from 34.8to61.8 with an average

of 49.12. On the other hand, NSGA-II provides more number of sensor covers ranges from

35.2to63.9 with average of 50.34. Both MOEA/D and NSGA-II gain more sensor covers

than GAMDSC. In Fig. 5, we can see that GAMDSC can provide from 33.8to60.6 with

average of 47.91 sensor covers.

Similarly, Fig. 6shows that NSGA-II provides wider Pareto Front than MOEA/D. Also, in

Fig. 6we can see that all algorithms have nearly equal reliability performance represented by

min extremes of MOEA/D and NSGA-II and by the best results of GAMDSC. Knowing that

123

Author's personal copy

834 B. A. Attea et al.

Tab l e 4 Overall statistics of Pareto extremes of MOEA/D and NSGA-II and the best solutions of GAMDSC

giveninFigs.5and 6

Objective Algorithm Extreme max min average

No. of sensor covers GAMDSC – 60.633.847.91

MOEA/Dmax 61.834.849.12

min 34.518.126.44

NSGA-II max 63.935.250.34

min 28.716 22.08

Covers relaibility GAMDSC – 0.6737 0.6217 0.644

MOEA/Dmax 0.8913 0.853 0.8726

min 0.6602 0.6077 0.6364

NSGA-II max 0.949 0.9211 0.9403

min 0.6699 0.6156 0.6456

these reliability results are associated with the max extremes (in terms of number of sensor

covers) of MOEA/D and NSGA-II and with the best results of GAMDSC in Fig. 5,wecan

then realize that NSGA-II facilitate more qualitative sensor covers. In contrast, GAMDSC is

incurred by the lowest number of sensor covers. This reﬂects the positive impact of the pro-

posed heuristic perturbation operator over the combined collaboration of crossover, mutation,

and the scattering operators of GAMDSC algorithm.

4.3 Comparison of Worst Case Time Complexity

We also compare the worst-case computational complexity of the single-objective GAMDSC

algorithm and the multi-objective MOEA/D and NSGA-II algorithms for solving Disjoint

Reliable Sensor Covers Problem (DRSC). Due to optimizing multiple objectives instead of

only one objective, multi-objective evolutionary algorithms, in general, are more expensive

than single-objective algorithms. Without loss of generality, the computational complexity of

single-objective genetic algorithms, such as GAMDSC is O(maxi×K)where Kis the size

of solutions to be evolved, via certain evolution operators, for maxiiterations. On the other

hand, the general computational complexity of an MOEA/D is O(maxi×2×K×Kneighbor)

(where 2 means number of objective functions and Kneighbor <Kmeans size of neighboring

solutions for each individual solution) [35]. The computational complexity of NSGA-II is

O(maxi×2×K2)[32,33].

Now, let us consider the computation time needed for the most critical parts of the above

algorithms when applied for solving DRSC problem. It is stated in [15] that in each generation

of GAMDSC, the ﬁtness function is the most critical part which represents the computation

time bottleneck. The evaluation of the ﬁtness function is linearly related to the number of

sensors and the number of targets. Thus, the worst-case time complexity of GAMDSC is:

O(GAMDSC)=maxi×K×|n|×|m|(10)

where |n|is the number of targets and |m|is the number of sensors. On the other hand, for

MOEA/D and NSGA-II, the proposed heuristic perturbation operator (Algorithm 1) costs

the most computation time and in the worst-case time it linearly related to the maximum

number of sensors and targets, and upper bound of sensor covers ub. Thus, the worst-case

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 835

time complexity of MOEA/D and NSGA-II are, respectively, as:

O(MOEA/D)=maxi×2×K×Kneighbor ×|n|×|m|×|ub|(11)

O(NSGA-II)=maxi×2×K2×|n|×|m|×|ub|(12)

5 Conclusions

Maximum DSC is a well-known WSN design which is NP-hard. Unlike all of the existing

work that rely on the traditional single-objective deﬁnition, this paper introduces a multi-

objective Disjoint Reliable Sensor Covers Problem (DRSC). The formulated problem is then

tackled by two well-known and competitor multi-objective evolutionary algorithms, namely

MOEA/D and NSGA-II. Instead of the traditional use of two perturbation operators (i.e.,

crossover and mutation), one heuristic operator is proposed that involves the incorporation

of problem-speciﬁc knowledge in its mechanism. The proposed heuristic operator is proved

to be of positive effect on the overall performance of the implemented MOEAs. The results

over 150 different WSN topologies signiﬁes the importance of utilizing the two contradictory

criteria of getting large number of disjoint sensor covers and more coverage reliability and

optimizing them simultaneously rather than optimizing only number of disjoint sensor covers.

Good overall performance of the multi-objective algorithms for the modeled DRSC highlights

that it may be motivated to consider another WSN’s design criterion while solving disjoint

sensor covers problem. As an example, we can include communication constraints (e.g.,

sensor-sink connectivity) to the multi-objective deﬁnition of disjoint sensor covers. Also, by

satisfying the sensor energy constraints, a sensor can participate in multiple sensor covers

and the deﬁnition of DRSC could be reformulated to satisfy a multi-objective non-disjoint

sensor covers (nDRSC) problem.

Acknowledgments This work is partially supported by TUBITAK under Grant No. 113E328.

References

1. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability. A guide to the theory of NP-

completeness. New York: Freeman.

2. Slijepcevic, S., & Potkonjak, M. (2001). Power efﬁcient organization of wireless sensor networks. In

Proceedings of IEEE international conference communications, Vol. 2. Finland, pp. 472–476.

3. Cardei, M., Thai, M., Li, Y., & Wu,W. (2005). Energy-efﬁcienttarget coverage in wireless sensor networks.

In IEEE INFOCOM 2005, Mar. 2005, pp. 1976–1984.

4. Tian, D., & Georganas, N. D. (2002). A coverage-preserving node scheduling scheme for large wireless

sensor networks. In Proceedings of 1st association computing machinery international workshop wireless

sensor networks and applications, pp. 32–41.

5. Wang, X., Xing, G., Zhang, Y., Lu, C., Pless, R., & Gill, C. (2003). Integrated coverage and connectivity

conﬁguration in wireless sensor networks. In Proceedings of 1st international conference on embedded

network sensor systems, Los Angeles, CA, pp. 28–39.

6. Liu, Y., & Liang, W. (2005). Approximate coverage in wireless sensor networks. In Proceedings of IEEE

conference on local computing network, 30th anniversary, pp. 68–75.

7. Gupta, H., Zhou, Z., Das, S. R., & Gu, Q. (2006). Connected sensor cover: Self-organization of sensor

networks for efﬁcient query execution. IEEE, Association for Computing Machinery Transactions on

Networking,14(1), 55–67.

8. Ai, J., & Abouzeid, A. A. (2006). Coverage by directional sensors in randomly deployed wireless sensor

networks. Journal of Combinatorial Optimization,11(1), 21–41.

9. Funke, S., Kesselman, A., Kuhn, F., Lotker, Z., & Segal, M. (2007). Improved approximation algorithms

for connected sensor cover. Wireless Networks,13(2), 153–164.

123

Author's personal copy

836 B. A. Attea et al.

10. Zhou, Z., Das, S. R., & Gupta, H. (2009). Variable radii connected sensor cover in sensor networks.

Association Computing Machinery Transactions on Sensor Networks, 5(1, article 8), 1–36.

11. Martins, F. V. C., Carrano, E. G., Wanner, E. F., Takahashi, R. H. C., & Mateus, G. R. (2009). A dynamic

multiobjective hybrid approach for designing wireless sensor networks. In Proceedings on IEEE congress

on evolutionary computation, pp. 1145–1152.

12. Cardei, M., & Du, D.-Z. (2005). Improving wireless sensor network lifetime through power aware orga-

nization. Wireless Netwoks,11(3), 333–340.

13. Cardei, I., & Cardei, M. (2008). Energy-efﬁcient connected-coverage in wireless sensor networks. Inter-

national Jounal on Sensor Networks, 3(3), 201–210.

14. He, J., Xiong, N., Xiao, Y., & Pan, Y. (2010). A reliable energy efﬁcient algorithm for target coverage

in wireless sensor networks. In IEEE 30th international conference on distributed computing systems

workshops (ICDCSW), 2010, pp. 180–188.

15. Lai, C., Ting, C., & Ko, R. (2007). An effective genetic algorithm to improve wireless sensor network

lifetime for large-scale surveillance applications. In IEEE congress on evolutionary computation, 2007.

CEC 2007. IEEE, 2007.

16. Hu, X. M., Zhang, J., Yu, Y., Chung, H. H., Li, Y. L., Shi, Y. H., et al. (2010). Hybrid genetic algorithm using

a forward encoding scheme for lifetime maximization of wireless sensor networks. IEEE Transactions

on Evolutionary Computation,14(5), 766–781.

17. Gil, J. M., & Han, Y. H. (2011). A target coverage scheduling scheme based on genetic algorithms in

directional sensor networks. Sensors 11,11(2), 1888–1906.

18. Huang, C.-F.,& Tseng, Y.-C.(2005). The coverage problem in a wireless sensor network. Mobile Networks

and Applications,10(4), 519–528.

19. Elfes, A. (1987). Sonar-based real-world mapping and navigation. IEEE Journal of Robotics and Automa-

tion,RA–3(3), 249–265.

20. Ghosh, A., & Das, S. K. (2006). Coverage and connectivity issues in wireless sensor networks. In Mobile,

wireless, and sensor networks: Technology, applications, and future directions, pp. 221–256.

21. Hossain, A., Biswas, P. K., & Chakrabarti, S. (2008). Sensing models and its impact on network coverage

in wireless sensor network. In IEEE region 10 and the third international conference on Industrial and

information systems, 2008. ICIIS 2008, (pp. 1–5). IEEE.

22. Rajagopalan, R. (2010). A multi-objective optimization approach for data fusion in mobile agent based

distributed sensor networks. In Instrumentation and measurement technology Conference (I2MTC), 2010

IEEE, pp. 208–212.

23. Rajagopalan, R., Mohan, C. K., Varshney,P., & Mehrotra, K. (2005). Multi-objective mobile agent routing

in wireless sensor networks. In The 2005 IEEE congress on evolutionary computation, 2005, Vol. 2, pp.

1730–1737.

24. Özdemir, S., Attea, B. A., & Khalil, Ö. A. (2012). Multi-objective clustered-based routing with cov-

erage control in wireless sensor networks. Soft computing, (pp. 1–12). Berlin: Springer. doi:10.1007/

s00500-012-0970-x.

25. Özdemir, S., Attea, B. A., & Khalil, Ö. A. (2012). Multi-objective evolutionary algorithm based on decom-

position for energy eefﬁcient coverage in wireless sensor networks. Wireless personal communications.

Berlin: Springer. doi:10.1007/s11277-012-0811-3.

26. Konstantinidis, A. (2009). Multiobjective deployment and power assignment in wireless sensor networks

using metaheuristics. University of Essex.

27. Jia, J., Chen, J., Chang, G., Wen, Y., & Song, J. (2009). Multi-objective optimization for coverage control

in wireless sensor network with adjustable sensing radius. Computers and Mathematics with Applications,

57(11), 1767–1775.

28. Konstantinidis, A., Yang, K., Zhang, Q., & Zeinalipour-Yazti, D. (2009). A multi-objective evolutionary

algorithm for the deployment and power assignment problem in wireless sensor networks. Computer

Networks,54(6), 960–976.

29. Konstantinidis, A., & Yang, K. (2011). Multi-objective energy-efﬁcient dense deployment in wireless

sensor networks using a hybrid problem-speciﬁc MOEA/D. Applied Soft Computing,11(6), 4117–4134.

30. Abdulhalim, M. F., & Attea, B. A. (2014). Multi-layer genetic algorithm for maximum disjoint reliable

set covers problem in wireless sensor networks. Accepted in Wireless Personal Communications. Berlin:

Springer.

31. Coello Coello, C. A., Van Veldhuizen, D. A., & Lamont, G. B. (2002). Evolutionary algorithms for solving

multi-objective problems.NewYork:Kluwer.

32. Srinivas, N., & Deb, K. (1994). Multi-objectivefunction optimization using non-dominated sorting genetic

algorithms. Evolutionary Computation,2(3), 221–248.

33. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2000). A fast and elitist multi-objective genetic

algorithm: NSGA-II. In Proceedings parallel problem solving from nature VI, pp. 849–858.

123

Author's personal copy

A Multi-objective Disjoint Set Covers for Reliable Lifetime 837

34. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester: Wiley.

35. Zhang, Q., & Li, H. (2007). MOEA/D: A multi-objective evolutionary algorithm based on decomposition.

IEEE Transactions on Evolutionary Computation,11(6), 712–731.

36. Zitzler, E. (1999). Evolutionary algorithms for multi-objective optimization: Methods and applications.

Doctoral dissertation, Zurich: Swiss Federal Institute of Technology.

Bara’a A. Attea (a.k.a. Baraa A. Atiyah) received the BS and MS

degrees in computer science from University of Baghdad, Baghdad,

Iraq in 1993 and 1996, respectively, and the PhD degree in computer

science from University of Technology, Baghdad in 2002. She is an

associate professor in Computer Science Department - University of

Baghdad. She was a visiting researcher in Gazi University, Ankara,

Turkey from 2011 to 2012. Her main research interests are computa-

tional intelligence, evolutionary algorithms, data mining, and applica-

tions of bio-inspired algorithms in wireless sensor networks.

Enan A. Khalil received the BS, and MS in computer science from

University of Baghdad, Baghdad, Iraq in 2008 and 2011, respectively.

He is currently a PhD student in Computer Engineering Department -

Gazi University, Ankara, Turkey. His main interests are computational

intelligence, evolutionary algorithms, and wireless sensor networks.

Suat Özdemir has been with the Computer Engineering Department

in Gazi University, Ankara, Turkey. He received his MSc degree from

Syracuse University and PhD degree from Arizona State University

in 2001 and 2006, respectively. Dr. Ozdemir’s research areas mainly

include wireless and sensor networks, network security, and data min-

ing. He is a member of IEEE and currently serving as editorial board

or TPC member for various leading IEEE and ACM journals and con-

ferences.

123

Author's personal copy

838 B. A. Attea et al.

Oktay Yıldız received his M.Sc. degree in Institute of Science from

Gazi University, in 2004 and Ph.D. degree in Institute of Information

Sciences from Gazi University, in 2012. He has been with the Com-

puter Engineering Department at Gazi University, Ankara, Turkey since

2009. His research interests include machine learning, data mining and

bioinformatics.

123

Author's personal copy