a biologically inspired energy-efficient duty cycle design...

Research ArticleA Biologically Inspired Energy-Efficient Duty Cycle DesignMethod for Wireless Sensor Networks

Jie Zhou

College of Information Science and Technology, Shihezi University, Shihezi, China

Correspondence should be addressed to Jie Zhou; [email protected]

Received 4 February 2017; Revised 30 March 2017; Accepted 26 April 2017; Published 28 June 2017

Academic Editor: Gabriele Cazzulani

Copyright © 2017 Jie Zhou. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The recent success of emerging wireless sensor networks technology has encouraged researchers to develop new energy-efficientduty cycle design algorithm in this field. The energy-efficient duty cycle design problem is a typical NP-hard combinatorialoptimization problem. In this paper, we investigate an improved elite immune evolutionary algorithm (IEIEA) strategy to optimizeenergy-efficient duty cycle design scheme andmonitored area jointly to enhance the network lifetimes. Simulation results show thatthe network lifetime of the proposed IEIEAmethod increased compared to the other twomethods, which means that the proposedmethod improves the full coverage constraints.

1. Introduction

Recent technological advances in sensing, nanosystems tech-nologies, and communication have made it possible to equipinexpensive small, low-cost, vulnerable, and fast responsesensing units [1]. Wireless sensor networks (WSNs) are com-posed of some sensors having limited sensing, computing,communication, and self-organizing abilities [2]. Each sensornode consists of five modules: the computation module, thedata acquisition module, the RF module, the data storagemodule, and the powermodule [3].Wireless sensor networkshave applications in many areas such as military surveillance,traffic avoidance, intelligent family, preventing forest fire loss,building monitoring and control, and advanced health caredelivery [4].

The energy-efficient duty cycle design problem hasrecently attracted the attention of many researchers in thefield of wireless sensor networks [5]. Limited by their size,small wireless sensors are equipped with restricted sensingcapacity [6]. To have a long network lifetime, energy-efficientduty cycle scheme should be designed properly. However,finding the ideal energy-efficient duty cycle design is an NP-hard problem. For large-scale wireless sensor networks, theexhaustive search cannot be used to get the ideal duty cycledesign in real time [7].

Due to its computational complexity, many heuristics areproposed to get near-optimal solutions in reasonable time.In [8], an energy-efficient duty cycle design technique thatenables trade-offs between computation cost and networklifetime is investigated. It provides a wider search spaceby randomly selecting energy-efficient duty cycle designsolutions when each one in the population gets updated.However, the reference does not take into considerationfactors such as sensing radius. A research effort to the energy-efficient duty cycle design for the wireless sensor networksbased on the genetic algorithm (GA) can be found in [9].The work therein focused on an energy-efficient duty cycledesign optimization with many constraints. But it suffersfrom premature convergence and low convergence rate whenthe number of nodes is high. A particle swarm optimization(PSO) is developed by employing a refined fitness evaluationtechnique [10]. In the work therein, the authors maximizethe network lifetime without considering the fact that theenergy of a battery is limited. PSO approach has a problemof algorithm convergence and complexity.

Elite computing and immune theory have alwaysattracted attention of the scholars of artificial intelligence [11].Besides that, the superior performance of evolutionary theoryfor combinatorial optimization problems is demonstrated in[12, 13]. In particular, in this paper, an improved elite immune

HindawiJournal of SensorsVolume 2017, Article ID 3089402, 9 pageshttps://doi.org/10.1155/2017/3089402

https://doi.org/10.1155/2017/3089402

2 Journal of Sensors

evolutionary algorithm (IEIEA) is investigated to effectivelyrepresent the individuals to explore the search space witha small group and to exploit the global optimal solutionin the search space within a few iterations, respective-ly.

We first formulate an optimization problem as inte-ger programming that is proven to be NP-complete. Thenadvanced evolutionary algorithm is used to solve the prob-lem.Moreover, immune clone operator is adopted to enhanceglobal search ability. The immune clone strategy helps toavoid local optima, and the improved stopping criterion auto-matically finds the best solution. Extensive simulations areconducted which compare IEIEA with SA and PSO. Sim-ulation results show that the proposed IEIEA algorithmoutperforms, regarding network lifetime, SA and PSO withthe same computational complexity. Furthermore, IEIEA hasbetter robustness.

The rest of this paper is briefed as follows. In Section 2,we describe the full mathematical model of energy-efficientduty cycle design. In Section 3, IEIEA for energy-efficientduty cycle design as well as its detailed implementation ispresented. In Section 4, we evaluate the performance ofthe proposed algorithm and show the simulation resultsand comparisons. We also analyze the characteristics ofIEIEA. Finally, in Section 5, concluding remarks are pre-sented.

2. System Model

In this section, we build the systemmodel to demonstrate theenergy-efficient duty cycle design problem concerning theconstraints of the energy of a battery and sensing radius. In[14], the authors propose a set of inequalities for modelingthe energy efficiency. Later in [15], the authors showed asimilar model by a fewer number of sensors and targets.The model proposed in [16] is more flexible than the modelproposed in [14]. In this work, a similar set of inequalities formaximizing the network lifetime is employed to model theenergy-efficient duty cycle design inWSNs. Consider a WSNsystem with 𝐹 sensors and 𝐸 targets in the monitoring area.The monitoring relationship can be shown as

𝑄 =

[[[[[[[[[[[[[[

𝑞1,1 𝑞1,2 ⋅ ⋅ ⋅ 𝑞1,𝐸−1 𝑞1,𝐸𝑞2,1 𝑞2,2 ⋅ ⋅ ⋅ 𝑞2,𝐸−1 𝑞2,𝐸... 𝑞𝑓,𝑒 ...𝑞𝐹−1,1 𝑞𝐹−1,2 ⋅ ⋅ ⋅ 𝑞𝐹−1,𝐸−1 𝑞𝐹−1,𝐸𝑞𝐹,1 𝑞𝐹,2 ⋅ ⋅ ⋅ 𝑞𝐹,𝐸−1 𝑞𝐹,𝐸

]]]]]]]]]]]]]](𝑞𝑓,𝑒 ∈ {0, 1}) ,

(1)

where 𝑞𝑓,𝑒 is the monitoring relationship between the 𝑒thtarget and 𝑓th sensor; 𝑞𝑓,𝑒 = 1 means that the 𝑒th target iswithin the monitoring range of the 𝑓th sensor and 𝑞𝑓,𝑒 = 0otherwise. Due to the limited battery capacity of the sensor

nodes, the maximum length of work time is assumed to 𝐾rounds. The duty cycle of the WSN can be shown as

𝐷 =[[[[[[[[[[

𝑑1,1 𝑑1,2 ⋅ ⋅ ⋅ 𝑑1,𝐹−1 𝑑1,𝐹𝑑2,1 𝑑2,2 ⋅ ⋅ ⋅ 𝑑2,𝐹−1 𝑑2,𝐹... 𝑑𝑖,𝑓 ...𝑑𝐹𝐾−1,1 𝑑𝐹𝐾−1,2 ⋅ ⋅ ⋅ 𝑑𝐹𝐾−1,𝐹−1 𝑑𝐹𝐾−1,𝐹𝑑𝐹𝐾,1 𝑑𝐹𝐾,2 ⋅ ⋅ ⋅ 𝑑𝐹𝐾,𝐹−1 𝑑𝐹𝐾,𝐹

]]]]]]]]]]

(𝑑𝑖,𝑓 ∈ {0, 1}) ,

(2)

where 𝑑𝑖,𝑓 = 1 means that the 𝑖th sensor node is active inround 𝑖 and 𝑑𝑖,𝑓 = 0 otherwise. The monitoring cycle of thewhole network can be shown as

𝐷𝑄

=

[[[[[[[[[[[[[[[[[[[[[

𝐹

∑𝑓=1

𝑑1,𝑓𝑞𝑓,1 ⋅ ⋅ ⋅𝐹

∑𝑓=1

𝑑1,𝑓𝑞𝑓,𝐸−1𝐹

∑𝑓=1

𝑑1,𝑓𝑞𝑓,𝐸𝐹

∑𝑓=1

𝑑2,𝑓𝑞𝑓,1 ⋅ ⋅ ⋅𝐹

∑𝑓=1

𝑑2,𝑓𝑞𝑓,𝐸−1𝐹

∑𝑓=1

𝑑2,𝑓𝑞𝑓,𝐸... d

... ...𝐹

∑𝑓=1

𝑑𝐹𝐾−1,𝑓𝑞𝑓,1 ⋅ ⋅ ⋅𝐹

∑𝑓=1

𝑑𝐹𝐾−1,𝑓𝑞𝑓,𝐸−1𝐹

∑𝑓=1

𝑑𝐹𝐾−1,𝑓𝑞𝑓,𝐸𝐹

∑𝑓=1

𝑑𝐹𝐾,𝑓𝑞𝑓,1 ⋅ ⋅ ⋅𝐹

∑𝑓=1

𝑑𝐹𝐾,𝑓𝑞𝑓,𝐸−1𝐹

∑𝑓=1

𝑑𝐹𝐾,𝑓𝑞𝑓,𝐸

]]]]]]]]]]]]]]]]]]]]]

, (3)

where the element∑𝐹𝑓=1 𝑑𝑗,𝑓𝑞𝑓,𝑒 = 1 is positive and representsthe fact that the 𝑒th target is monitored by at least one sensornode in round 𝑗 and ∑𝐹𝑓=1 𝑑𝑗,𝑓𝑞𝑓,𝑒 = 0 otherwise. Whenthe WSN maintains a full coverage in the 𝑗th round, all theelements in the 𝑗th row must be positive. Thus, from top tobottom, the previous row number of the first zero elementis the network lifetime. Thus, the mathematical model of theduty cycle design problem can be shown as follows:

Objective is

𝑓 (𝐷) = zero row (𝐷𝑄) − 1 (4)

subject to

𝐹𝐾

∑𝑖=1

𝑑𝑖,𝑓 ≤ 𝐾, 𝑓 = 1 ⋅ ⋅ ⋅ 𝐹, (5)

where zero row is the row number of the first zero elementwhich occurs from row 1 to row 𝐹𝐾 in matrix.The constraint∑𝐹𝐾𝑖=1 𝑑𝑖,𝑓 ≤ 𝐾means that the maximum lifetime of node is𝐾.

3. Energy-Efficient Duty Cycle Design Basedon IEIEA for Wireless Sensor Networks

An evolutionary algorithm (EA) is a search method thatmimics the mechanism of Darwinian’s evolutionary theorysuch as genetic recombination and survival of the fittest. EA

Journal of Sensors 3

is used for a large number of multiobjective optimizationproblems which is confirmed to be suitable for locating thebest and near-optimal answers. The EA has good searchingability. However, the algorithm is often not suitable for large-scale complex problems. In many cases, the algorithm fallsinto local optima.

In recent times, elite computing and immune theoryimpressed strategic methods are getting evolved. They areconfirmed to be very successful while looking for bettersolutions, targeting not only more efficient convergence butalso solving combinatorial optimization problems. In thispaper, we propose an improved elite immune evolutionaryalgorithm (IEIEA), which is amodification of EA, for energy-efficient duty cycle design in wireless sensor networks. InIEIEA, based on the concept and principles of elite computingand immune theory, new evolutionary theory techniques aregetting developed, which can achieve an increased balance inexploitation of the solution space and receive better resultscompared with the standard EA. In such a hybrid technique,search ability of elite evolutionary strategy and immuneclone operator are involved to generate faster and efficientconvergence. It operates parallel exploration in complicatedsearch regions.

Throughout each generation, IEIEA gets a different popu-lation out of the current population by using genetic oper-ators, such as selection, crossover, and mutation. Addition-ally, suggested elite evolutionary strategy is using the eliteidea, and the provided immune clone operator is using theimmune idea to improve the global search capability ofIEIEA.

3.1. Initialization. In IEIEA, a solution is represented by achromosome (individual). We select a string as a chromo-some to symbolize a solution to the energy-efficient dutycycle design problem. Each chromosome within the popu-lation can signify a group of randomly selected duty cycles.The energy-efficient duty cycle design problem is acquiring achromosomewithin prospective solution regionsmaking useof IEIEA. Therefore, if matrix (2) is arranged in rows, a fea-sible solution could be presented as a binary sequence. So weuse theway of binary coding for each chromosome. Each genein the chromosome is mapped to a binary number, and thegene valuemeans that the sensor is in active or sleepmode. Inother words, the binary chromosome is made up of Booleanvariables implying whether the sensor is active or not.

The number of binary solution genesmatches the numberof sensor nodes and the maximum rounds. As an example,consider a system with three sensor nodes and four rounds.Binary coding representation with 36 binary numbers isaccurate and reliable as it covers up to the entire solutionspace, and, besides, the string size is the number of sensornodes square times the maximum rounds of the duty cycle.For ten sensor nodes with the highest lifetime of 20 rounds,the total string length is 2000. Here, the search space is thespace of all matrices that satisfy (5). The total amount of allpossible solutions is very large.

IEIEA solves optimizing challenges by using a popu-lation of a preset number, named the population size, ofsolutions. IEIEA maintains a number of such solutions. The

initialization design applied by this algorithm is as follows.The algorithm starts out by constructing an initial populationof random candidate solutions. The original population wasbuilt randomly expecting to search globally to find somesolutions. In each solution, a previously chosen number ofrandom bits in the chromosome are set to 1. The rest bitsin the chromosome are set to 0. By doing this, the initialpopulation contains randomly produced chromosomes. Eachsolution in the population will be initialized to a binarynumber randomly selected from the uniform distributionover the set [0, 1]. A large number of low fitness solutionsare constructed via utilizing the discrete random values inthe initialization step. If a solution owns a low fitness value,random bits are determined from the set [0, 1] to renew thesolution. After obtaining the genes for each chromosome, theinitial population is generated. The process is applied overand over unless all the chromosomes in the population getfeasible. There are 𝑃 size individuals in the population ofIEIEA.The population in the initialization process carries onrandomly to ensure that the diversity is well kept.

3.2. Selection and Crossover. For every generation, childrenare generated by mixing the characteristics of two parentindividuals. The selection operator picks a solution comingfrom themost recent population for the next population withpossibility proportional to its fitness value.

Solutions in the current population are evaluated for theirmerit to survive in the following population. Every solutioninside population is associated with a figure of benefit as wellas a fitness value. Every time a set of two parent solutions areto be selected from a current population for developing anoffspring by a crossover operation. The fitness value of eachsolution within the current population is calculated as theobjective function by (4).

Picking out parents is based on random and selectiveapproaches. At each iteration, couples of parents are selectedby fitness, whereby every parent is chosen as the best ofthose randomly selected among the best candidates. In theselection step, fitter individuals are more regularly used togenerate offspring than less fit individuals, which tends toraise the average fitness as the algorithm continues. Becausethe objective is to maximize the network lifetime, a solutionstring with a practically significant number of cycles musthave comparatively high fitness value. So the solutions thatare better will have a greater chance to be chosen. The selec-tion operation mimics relatively neutral selection in real life.

The RWPS (roulette wheel proportionate selection) isused for choosing the solutions from the latest population.Better solutions have a relatively higher possibility to beselected for reproduction making use of the RWPS. The ideaof RWPS is simple. The selection possibility of each solutionis defined by the roulette wheel selection utilizing the linearscaling. By using the scaling, the probability of choosingthe relevant solution for reproduction is proportional to theamount of scaled fitness.

In each step, two parents are picked out first accordingto the roulette wheel rule. This process will likely be appliedrepeatedly except when the whole set of child individuals inthe population turns into feasible. In this way, all child strings


in the population were split into several pairs, with every pairestablishing two children in the crossover operation. Whenall the parents were selected, their properties will be passedto their offspring.Thepreviouslymentioned selection processpermits efficient constraint raising the quality of solutions byselecting the child chromosomes from high fitness districts.

In a crossover, the genes of the parent are replicated toits offspring. It signifies the mixing up of information fromboth parents to construct the children. We use a crossoveroperator to each of the selected pairs of parent solutions. Incrossover operation, a couple of offspring are produced by theselected pair of parent solutions. In thisway, twonew childrenare manufactured by the randommixture of the properties oftheir parents. The crossover procedure is done between twochromosomes in their binary form. In a binary crossover, twonew child chromosomes are created while using the intervalbetween the two parents.

Standard crossover operator switches the segments ofselected strings through the crossover points with a proba-bility. The crossover place is randomly selected. One-pointcrossover specifies the point of crossover of the two par-ent chromosomes. Therefore, in single-point crossover, onecrossover suggests that a child gets the left side of the binarystring coming from the first parent and the right side com-ing from the second parent. For the second child, the cross-over is accomplished by combining other parts of childchromosomes of the parents. The second child from thisunion obtains the complementary substances not taken bythe first child, that is, receives the right section from the firstparent and the left side from the second parent, having thesame crossover location. Two-point crossover indicates thatthe first child gets both right and left sections from the firstparent. Meanwhile, the first child also gets the middle sectionfrom the second parent. The crossover point is randomlychosen.

It is often known that uniform crossover works moreefficiently at solving combinatorial optimization issues thanjust one-point or two-point crossover. In this case, we presenta binary execution of uniform crossover. The crossoveroperation is done in the mating pool to build children. Inuniform crossover, every one of these couples produces twochildren utilizing an adaptive number of crossovers. Binarystrings are changed between the two parents to generatetwo children. Despite establishing the crossover point in theconventional crossover, we use the random binary number asthe mask to form the binary uniform crossover.

In binary uniform crossover operation, a probability termis set to manage the rate of crossover. We generate a randomdecimal between 0 and 1. Then choose each gene with anequal chance from two child strings and recombine the genesto create a new offspring. Exchange positions in the twochromosomes are selected arbitrarily. Once the decimal isover the probability term, no change takes place, and thecorresponding bit in solutions one and two is passed on tochild one and child two, respectively. Otherwise, the cross-over operation is carried out. If the bit in the mask is equal toone, the related bit in solutions one and two is distributed tochild two and child one, respectively, if the crossover oppor-tunity term is below the probability term. For this reason, in

a binary uniform crossover, each pair of parents has a prob-ability term chance of using uniform crossover operator.Thisprocess should be implemented continually except in caseswhere all the child strings become feasible. All elements ofgenes handed down from the parents ought to keep the orderas they are available in their parents. So, there have been childindividuals soon after the crossover has been carried out.

Observe that since binary encoding is applied, the tiniestunit that is exchanged in binary uniform crossover could bea bit. It allows developing the offspring positioned accordingto the parents. Crossover creates a designed yet randomizedexchange of genetic elements between strings. Hence theoffspring contains the properties received from each of itsparents. Moreover, using uniform crossover can mix thegenes from two solutions with a more consistent way.

3.3. Mutation and Recombination. The content of this por-tion is kept in the mutation procedure. In IEIEA, ran-dom mutation is conducted to the offspring to prevent thepremature convergence. This is executed by using randomadjustments to a ratio of the children generated. In thispaper, mutation operation is established by randomly pickingout any chromosomes utilizing prespecified possibilities. Inthis way, plenty of random mutations are exercised to addsome diversity to the population. For the duty cycle designproblem, this means replacing some genes with new randomfigures. Selected genes in a single individual are randomlychosen to carry out the mutation.

In IEIEA, thinking of a sufficiently large, diverse initialpopulation where zeros and ones are available for every bitwithin the chromosomes, full convergence could conceivablybe obtained without having mutations at all because anypractical solutions can be manufactured from some blendof the initial population. Nevertheless, the initial populationdimension is limited, and the tiniest gene that may bechanged in a crossover is binary. Recognize thatmutations arean essential method for IEIEA; we need to apply a mutationoperator to develop new solutions.

Subsequent mutations of the offspring apply diversityto the population and investigate different locations of thesearching space. Offspring experience a constraint amount ofmutations completed, and so the offspring are then scored forfitness. Each and every gene in chromosomes is mutated asmentioned above applying a probability, labeled as mutationprobability. The chances that a certain gene is mutated areoperated by the mutation rate. In this paper, an initialmutation rate of 5%means that each gene has a 5% possibilityof being replaced with a new value. We employ reversemutation in IEIEA. The reverse mutation is an importantoperation for preserving diversity in the population to beable to stay away from local optima. It will be shown in thesimulation section that this mutation assists in reachingmoreefficient solutions.

For stopping the premature convergence of the algorithm,we employed dynamic mutation operators to diversify thepopulation to be able to result in making the strings inthe population dissimilar to each other. Dynamic mutationfunction is an iteration based function that determinesthe mutation rate. Smaller mutation levels indicate a more


local search, while larger mutation levels are more efficientfor introducing diversity. In case the constructed variablesconverge at the low objective value, the degree of mutationcan be higher. If a solution has a superior fitness value, a lowermutation rate is picked. In this way, the convergence length ofIEIEA is reduced.

As in natural reproduction, there exists a likelihood ofillegal mutation during the mutation process. The solutionsthat comply with constraints (5) are classified as legal strings;otherwise, they are recognized as illegal chromosomes. Inillegal strings, a fully new random legal individual will becreated to replace the illegal one.

Following using the crossover operator and the mutationoperator, there have already been 𝑃 size chromosomes inthe population that consisted of 𝑃 size parent strings and𝑃 size offspring solutions. More advanced than the executionin EA, the selection and recombination processes in IEIEAare blended to manufacture a much better population. Therecombination technique is a sort of uniform crossover whichselects one offspring from two strings. After recombination,the new offspring fitness will be estimated depending on thefitness function.

3.4. Evaluation andElite CloneOperation. In the examinationprocedure, the values of fitness for each string are assessed.Each chromosome in the population is linked to a figureof merit (fitness value) following the value of the functionto be optimized. These individuals are scored, with the bestperformers probably going to be parents for the next iteration.Individuals with the greatest scores are implemented to beparents. In this paper, the aim is to increase the networklifetime. Within the current context, the fitness value of achromosome would depend upon the entire duty cycle. Thefunction values (fitness values) linked to the duty cycle arethen assessed. The duty cycle design problem can be adaptedswiftly to suit the full coverage constraints by mapping theduty cycle to the chromosomes and defining a fitness functionto evaluate the potential fitness computation function forsolution strings by the chromosome.

Here, we intend to identify the formulation of examiningthe level of chromosomes. To be able to calculate the level ofeach solution string in the population, formula (4) associatesa fitness function. We determine fitness as the amountof network lifetime that can be shown by a combinationof duty cycles; thus, fitness is an integer value from 0 tomaximum rounds. The function value denoted by networklifetime is calculated by delivering binary individuals into theobjective function. The solutions are then decoded into theirmatrix equivalent and examined for constraints violation.The fitness function is going to be scaled to avoid prematureconvergence. Through this definition, the fitness value ismore effective when it is larger.

This procedure will be used for Max gen times exceptfor the solution that becomes feasible before Max gen times.In this way, the algorithm ends till the fitness of the highestquality string converges to the maximum rounds. If it doesnot reach this value, the final chromosome distribution isadopted as the fittest individual (demonstrating the opti-mized network lifetime) following the Max gen generations.

In this way, the IEIEA is terminated, and the fittest string inthe population is taken as the final solution.

The individuals in the elite collection demonstrate thepromising zones to seek out the suitable solution. The stringin the elite group was harvested over all the generations.The population of the next generation includes the certainpercentage of solutions from the elite group and most fromoffspring. The percentage between 2 kinds of individualsinside the new generation is defined by the probabilities ofthe alternative. The activity repeats for Elite num times, and,as a consequence, a new population is constructed.

The IEIEA commences with the building of an initialpopulation, normally by spreading random binary numberswithin investigated space. First, all individuals in a populationare rated in lowering the order of fitness. The first 10% pointsare selected for cloning. Individuals with higher fitness willhavemore clones.The clones, not the original individual, thenundergo the clonal mutation progress. The clonal mutationonly performs on the cloned chromosomes to conserve theinformation. By doing this, the benefits of using the clonalmutation provide a neighboring exploration throughout theoriginal chromosome, while the utilization of the chaoticmutation provides a global survey surrounding the string.Following that, strings are evaluated on the fitness function,and merely the best of each clone can successfully pass to thepopulation, preserving an equal scale of the population.Withthis type of alternative, the diversity is conserved, and newfields of looking region tend to be quite possibly explained.

4. Simulation and Discussion

In this section, we compare the proposed IEIEAmethod withthe simulated annealing algorithm (SA) and PSO methodfor energy-efficient duty cycle design in WSN. Simulationsare performed to validate and test the performance of theproposed IEIEA approach to the energy-efficient duty cycledesign problem in WSN. To examine the applicability forpractical implementation, we evaluate the performance of theschemes on a PC with Intel Core i5, 4G RAM, WIN-10 OS,and MATLAB software. The fitness function in Section 2 isused to evaluate the IEIEA efficiency. Then we generate theposition of sensors and targets randomly specified withina 500 × 500m square area. We assume that each sensornode has the same energy consumption per unit time. Weplaced 70, 80, 90, and 100 sensors, respectively. The sensingrange of all sensor nodes is 300 meters. IEIEA has been usedto solve this problem, and the generations obtained havebeen compared with SA and PSO. The maximum numberof generations of IEIEA, SA, and PSO is 100. In all threemethods, a population size of 100 individuals (solutions) isused. In SA, the initial temperature is set to 500 degreesand the annealing temperature coefficient is set to 0.98. InIEIEA, crossover and mutation probabilities are 0.9 and 0.05,respectively. In PSO, the dynamic range of the particle hasbeen set to 0.4, the maximum velocity is 4, and the cognitiveand social parameters are 𝑐1 = 𝑐2 = 0.5.

Figure 1 presents the network lifetime obtained by IEIEA,SA, and PSO on the energy-efficient duty cycle designproblem with 100 sensors and 10, 20, 30, and 40 targets,


IEIEAPSOSA

0 8020 40 60 100

Iteration

75

80

85

90N

etw

ork

lifet

ime (

roun

d)

(a)

IEIEAPSOSA

68

70

72

74

76

78

80

Net

wor

k lif

etim

e (ro

und)

20 40 60 80 1000

Iteration

(b)

IEIEAPSOSA

20 40 60 80 1000

Iteration

60

62

64

66

68

70

72

Net

wor

k lif

etim

e (ro

und)

(c)

IEIEAPSOSA

20 40 60 80 1000

Iteration

52

54

56

58

60

62

64N

etw

ork

lifet

ime (

roun

d)

(d)

Figure 1: Network lifetime with 100 sensors and 10 targets (a), 20 targets (b), 30 targets (c), and 40 targets (d).

respectively. For each method, the fitness of the best indi-vidual at each generation is recorded. The results are theaverage of 30 time runs with three different methods to showthe convergence difference. So there is a certain differencebetween the result of Figure 1 and the average value in Table 1.

From Figure 1, we can see that the network lifetime ofIEIEA is better than those obtained by SA and PSO methodsand it provides improvement of network lifetime after the100 iterations. In the beginning, the value of network lifetimeincreased with the growth of the generations, as shown in thefigure. After 50 iterations, IEIEA still has a fast convergencerate, but PSO and SA can only slowly converge to a lowervalue than IEIEA. As a result, diverse population leading tobetter solutions is maintained, so IEIEA is prevented from

Table 1: Network lifetime with different targets and 100 sensors.

Number of targets IEIEA PSO SA10 89.32 86.49 83.5820 80.24 77.39 74.4830 71.75 68.89 65.5440 63.06 60.19 57.28

premature convergence. Over 100 iterations, IEIEA providesa longer network lifetime than PSO and SA, and IEIEAconverges with a faster rate. Similar results can be obtainedwith 90 sensors in Figure 2.


IEIEAPSOSA

0 8020 40 60 100Iteration

70

75

80

85N

etw

ork

lifet

ime (

roun

d)

(a)

IEIEAPSOSA

64

66

68

70

72

74

76

Net

wor

k lif

etim

e (ro

und)

20 40 60 80 1000Iteration

(b)

IEIEAPSOSA

20 40 60 80 1000Iteration

56

58

60

62

64

66

68

Net

wor

k lif

etim

e (ro

und)

(c)

IEIEAPSOSA

20 40 60 80 1000Iteration

48

50

52

54

56

58

60N

etw

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lifet

ime (

roun

d)

(d)

Figure 2: Network lifetime with 90 sensors and 10 targets (a), 20 targets (b), 30 targets (c), and 40 targets (d).

Figure 3 presents the obtained results of IEIEA, SA, andPSO approaches after 100 iterations with 100, 90, 80, and 70sensors and 10, 20, 30, and 40 targets, respectively. All theresults were averaged over 100 runs. Table 1 shows the resultsof Figure 3(a) with 100 sensor nodes and 10, 20, 30, and 40targets, respectively. It can be seen that, after 100 iterations,the average network lifetime of IEIEA is 89.32, 80.24, 71.75,and 63.06 rounds, respectively. However, PSO cannot alwaysobtain the optimal solution within the predefined iterationsand the network lifetimes obtained by the PSO are 86.49,77.39, 68.89, and 60.19, respectively. On the other hand,the SA shows quite slower convergence and the networklifetimes obtained by the SA are 83.58, 74.48, 65.54, and 57.28,

respectively, hence proving the superior reliability of IEIEA.Similar results can be obtained with 90, 80, and 70 sensors.

5. Conclusion

In this paper, we use an improved elite immune evolutionaryalgorithm (IEIEA) to solve the energy-efficient duty cycledesign problem in WSN. In this work, we first propose anovel formulation of the objective function to maximizethe network lifetime to satisfy the full coverage constraints.Simulations are conducted by using the IEIEA and theenergy-efficient duty cycle designmethods based on SA, PSO,and GA. Simulation results show that the proposed IEIEA


IEIEAPSOSA

20 30 4010Number of targets

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Figure 3: Network lifetime with different targets and 100 sensors (a), 90 sensors (b), 80 sensors (c), and 70 sensors (d).

provides longer network lifetime compared with previousSA, PSO, and GA. Besides that, the network lifetime of theproposed IEIEA is much higher than those of GA and SA. Sothe proposed method significantly enhanced the monitoringresults.

Conflicts of Interest

The author declares that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

This paper is supported by the National Natural ScienceFoundation of China (no. 61662063) and High-Level TalentResearch Project of Shihezi University (no. RCZX201530).

References

[1] G. Y. Li, Z. Xu, C. Xiong et al., “Energy-efficient wireless com-munications: tutorial, survey, and open issues,” IEEE WirelessCommunications, vol. 18, no. 6, pp. 28–34, 2011.

[2] X. Zhao, Y. Zhuang, and J. Wang, “Local adaptive transmitpower assignment strategy for wireless sensor networks,” Jour-nal of Central SouthUniversity, vol. 19, no. 7, pp. 1909–1920, 2012.

[3] N. Sun, Y.-S. Jeong, and S.-H. Lee, “Energy efficient mechanismusing flexible medium access control protocol for hybrid wire-less sensor networks,” Journal of Central South University, vol.20, no. 8, pp. 2165–2174, 2013.

[4] D. Feng, C. Jiang, G. Lim, L. J. Cimini Jr., G. Feng, and G. Y. Li,“A survey of energy-efficient wireless communications,” IEEECommunications Surveys & Tutorials, vol. 15, no. 1, pp. 167–178,2013.


[5] A. A. Kumar Somappa, K. Øvsthus, and L. M. Kristensen, “Anindustrial perspective on wireless sensor networks—a surveyof requirements, protocols, and challenges,” IEEE Communica-tions Surveys & Tutorials, vol. 16, no. 3, pp. 1391–1412, 2014.

[6] D. Dong, X. Liao, K. Liu, Y. Liu, andW. Xu, “Distributed cover-age in wireless ad hoc and sensor networks by topological graphapproaches,” Institute of Electrical and Electronics Engineers.Transactions on Computers, vol. 61, no. 10, pp. 1417–1428, 2012.

[7] W.-C. Ke, B.-H. Liu, and M.-J. Tsai, “Constructing a wirelesssensor network to fully cover critical grids by deployingminimum sensors on grid points is NP-complete,” Institute ofElectrical and Electronics Engineers. Transactions on Computers,vol. 56, no. 5, pp. 710–715, 2007.

[8] K. Han, J. Luo, L. Xiang, M. Xiao, and L. Huang, “Achievingenergy efficiency and reliability for data dissemination in duty-cycled WSNs,” IEEE/ACM Transactions on Networking, vol. 23,no. 4, pp. 1041–1052, 2015.

[9] X. Hu, J. Zhang, Y. Yu et al., “Hybrid genetic algorithm using aforward encoding scheme for lifetime maximization of wirelesssensor networks,” IEEE Transactions on Evolutionary Computa-tion, vol. 14, no. 5, pp. 766–781, 2010.

[10] E. R. Dosciatti, W. Godoy Junior, and A. Foronda, “TQ/PSO - Anew scheduler to optimize the time frame with PSO inWiMAXnetworks,” IEEE Latin America Transactions, vol. 13, no. 1, pp.365–376, 2015.

[11] T. Back, U. Hammel, and H.-P. Schwefel, “Evolutionary com-putation: Comments on the history and current state,” IEEETransactions on Evolutionary Computation, vol. 1, no. 1, pp. 3–17,1997.

[12] Z.-J. Zhang, J. Huang, and Y. Wei, “Frequent item sets miningfrom high-dimensional dataset based on a novel binary particleswarm optimization,” Journal of Central South University, vol.23, no. 7, pp. 1700–1708, 2016.

[13] S. Sarafijanovic and J.-Y. Le Boudec, “An artificial immunesystem approach with secondary response for misbehaviordetection in mobile ad hoc networks,” IEEE Transactions onNeural Networks, vol. 16, no. 5, pp. 1076–1087, 2005.

[14] Z. Lu, W.W. Li, andM. Pan, “Maximum lifetime scheduling fortarget coverage and data collection in wireless sensor networks,”IEEE Transactions on Vehicular Technology, vol. 64, no. 2, pp.714–727, 2015.

[15] O. Demigha, W. Hidouci, and T. Ahmed, “On Energy efficiencyin collaborative target tracking in wireless sensor network: areview,” IEEECommunications Surveys andTutorials, vol. 15, no.3, pp. 1210–1222, 2013.

[16] C.-L. Yang and K.-W. Chin, “Novel algorithms for completetargets coverage in energy harvesting wireless sensor networks,”IEEE Communications Letters, vol. 18, no. 1, pp. 118–121, 2014.

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