Research Article An Energy Distribution and Optimization ...downloads.hindawi.com/journals/ijdsn/2013/725869.pdf · data to the sink node a er identifying the sink node. e sensor

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013, Article ID 725869, 8 pageshttp://dx.doi.org/10.1155/2013/725869

Research ArticleAn Energy Distribution and Optimization Algorithm inWireless Sensor Networks for Maritime Search and Rescue

Huafeng Wu,1 Qiannan Zhang,1 Su Nie,1 Wei Sun,1 and Xinping Guan2

1 Merchant Marine College, Shanghai Maritime University, Shanghai 200135, China2 School of Electronic, Information and Electrical Engrineering, Shanghai Jiaotong University, Shanghai 200240, China

Correspondence should be addressed to Huafeng Wu; [email protected]

Received 16 October 2012; Accepted 2 January 2013

Academic Editor: Haigang Gong

Copyright © 2013 Huafeng Wu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Currently, maritime search and rescue (MSR) is mainly depending on the search party, while the searching objects are waitingpassively. Therefore, a new method of MSR which is based on the wireless sensor network (WSN) techniques is proposed in thispaper. WSN could be self-organized into network and transmit nodes information, such as position information, for search partyto accomplish the search and rescue work. However, the application encounters the problems of dynamic adaptability and life cyclelimitation at sea. An energy dynamic distribution and optimization algorithm (EDDO), which is based on genetic algorithm (GA),is presented to handle with these problems. The algorithm satisfies the connectivity and energy saving of the network, and the GAwith elitism-based immigrants approach is put forward to optimize the poor individuals when the positions of some nodes havechanged. Simulation results show that the algorithm can quickly adapt to a dynamic network and reduce energy consumption atthe same time.

1. Introduction

Maritime search and rescue (MSR) generally searches thetargets by the technology of satellite and radar. There aresome new technologies that have been applied to MSR, suchas machine vision. However, the search work is dependenton the effort by the search and rescue party, and the rescuetargets can only passively wait for the search and rescue. Inrecent years, with the development of the wireless sensornetwork (WSN), there are improvements both in computingability and energy consumption of sensor nodes. This willbe helpful for its application in MSR. In MSR-WSN, thesensor nodes were put in the life jackets and can be organizedinto an ad hoc network. The network locates its nodes andtransmits the data of position to the sink nodes whichwere put on the survival craft. The sink nodes transmitthe data to the base station of the SAR ships first, andthen the search and rescue network center can receive theinformation about the targets. By this way, it will be muchmore quickly and accurately for the rescuers to find thetargets.

Wireless sensor networks are suitable for the applicationof maritime search and rescue because of its features suchas self-organization, self-adaptive, multihop, and robustness.In the circumstances of MSR, there is not have any basestation, and nodes are highly dynamic and requires smallersize and longer lifetime. However, related researches do notpay enough attention to the application environment of MSRwhere WSN’s nodes could not be replaced and they aremoving all the time at sea. Therefore, it is crucial for nodesthat their transmit power can adapt to dynamic environmen-tal changes, the network lifetime can be extended, and theconnectivity can meet the requirements at the same time.

Evolution algorithm (EA) is a bionic algorithm based onnature selection in biological evolution theory. EA has a goodadaptability to complex engineering optimization problems.There are many researches about the EAs in topology controland covering algorithm of WSN. In MSR-WSN, the topologywill change and the energy deploymentwill not be suitable forthe topology when the environment changes. The most sim-ple and direct way of energy deployment is to restart the EAsfrom scratch in case that an environmental change is detected.

2 International Journal of Distributed Sensor Networks

But it is more efficient to develop other solutions which makeuse of knowledge gathered from the original environments.Elitism-based immigrant scheme is a representative one indynamic environments.

The remainder of the paper is organized as follows.Section 2 introduces the related topology control and is opti-mized by EAs and energy-based topology control in WSN.Section 3 presents the proposed WSN energy distributionand optimization solution at sea which is based on the geneticalgorithm (GA) in EAs. Section 4 introduces the setup of thesimulation and the results of analysis. Section 5 concludes thispaper and suggests some topics for future research.

2. Related Work

Many studies in MSR research the runaway boat drift modelor the best search area via applying the operations research,fuzzy mathematics, fluid mechanics, simulation theory, andso on. There are also some methods which introduce thenew information techniques into MSR, for instance, thecomputer simulation method based on Monte Carlo. Othersabout multispectral analysis, machine vision, and satelliteremote sensing technology are also explored in MSR [1, 2].A common defect exists in this technology that the targetscan only passively be searched; the searching objects cannotsend their location information to the search and rescueparty.

WSN is capable of real-time monitoring and collectingthe objects information and can send the information togateway nodes. The rapid and self-organization deploymentand network survivability features of WSN will meet theenvironment and application characteristics in MSR. Kimet al. [3] designed a kind of equipment which can sendGPS location information and mayday distress signal to helplocate victims in offshore area; they also referred to WSNtechnology, but the key technical issues, such as how toorganize the network, are not addressed.

An important purpose of wireless sensor networks topol-ogy is to extend the life cycle of the network as possible. InMSR-WSN, the lifetime of the network is also very important.In [4], the optimal coverage problem was taken as a 0/1sequence problem inwhich “0” stands for the nodewas sleep-ing, “1” stands for the node was working, and the evolutionalgorithm was adopted to optimize the 0/1 sequence. Thismethod can save the energy effectively, while in MSR-WSNthere will not be so many nodes to make some of them sleep,andnoone inwater can lose the connectivitywith others; thusthe sleeping mechanism is not the best one. Konstantinidisand Yang [5] defined the dense deployment and powerassignment problem (d-DPAP) inWSNs andproposed amul-tiobjective evolutionary algorithm based on decomposition(MOEA/D) hybridized with a problem-specific generalizedsubproblem-dependent heuristic (GSH). In theirmethod, thed-DPAP is decomposed into a number of scalar subproblems,and the subproblems are optimized in parallel by using neigh-borhoods information and problem-specific knowledge. Butthis method does not take full account of the dynamic of thenodes.

The algorithms DRNG and DLMST were proposed in[6], and they are based on the proximity graph theory.In both algorithms, each node collects the information ofthe surrounding neighbors and then determines their owntransmit power to ensure the connectivity of network. Chenet al. [7] proposed the SPAN protocol in which each nodecan sleep if its two random neighbors can communicate witheach other; otherwise the node must be in working state. Inthe ASCENT [8] protocol of Cerpa and Estrin, the nodescan determine the working state of their own according tothe detected local communication situation and decide thetransmit power according to the packet loss rate.

Glauche et al. [9] defined critical node degree as therequired size of the node degree that can keep network fullconnectivity. On the account that they proposed a distributedalgorithm to ensure that the ad hoc network can communi-cate, the algorithm adjusts nodes’ communication radius toguarantee the satisfaction of the critical node degrees. Jiangand Bruck [10] controlled the network topology by adjustingthe radius of nodes communication and proposed an algo-rithm to ensure that any source node can communicate withthe sink node. But in this paper, the algorithm does not takeaccount of the energy savings and the network lifetime. Liqunet al. [11] proposed a power control method based on contin-uous time slot scheduling and proved the NP-completenessof it. This method requires the network to maintain stricttime synchronization, and the fairness between the nodesis not considered. The application-oriented fault detectionand recovery algorithm (AFDR) [12] is mainly to limit theimpact of critical node failure on coverage and connectivity inwireless sensor and actor networks (WSANS).The algorithmneeds a moving backup actor to detect the critical nodefailure, and then the recovery process is initiated, yet thebackup actor in MSR-WSN is not practicable because sensornodes cannot move by themselves and cannot be replaced.

All of these researches are very helpful for the topologycontrol of our MSR-WSN, but they are mainly for staticwireless sensor networks and have a poor adaptability forMSR-WSN. For instance, the methods in [4, 7] could extendthe lifetime of the network, but sleeping mechanisms is notsuitable for MSR-WSN. Therefore, it is necessary to carryout specific research related to the two requirements thatare higher dynamic adaptability and longer lifetime of MSR-WSN.

3. Model and Algorithm Design

3.1. System Model. In this section, we present our networkmodel and then formulate the problem of energy dynamicdistribution and optimization of nodes in the MSR-WSN.

In the MSR-WSN, there have been a certain numberof homogeneous sensor nodes and a small amount of sinknodes.The sensor nodes are placed in lifejackets with limitedenergy, and the number of them is 𝑁. The sink nodes areplaced in survival crafts with unlimited energy, and they canmove by themselves. Sensor nodes can be organized into anetwork and identify the sink node which has entered theconvergence range of the network. The sensor nodes transfer

International Journal of Distributed Sensor Networks 3

data to the sink node after identifying the sink node. Thesensor nodes are responsible for regularly transmitting theinformation, such as nodes’ location or monitoring data, tothe sink node. Each sensor node communicates to the sinknode directly or in the form of a multihop. The networktopology dynamically changes as the movement of sensornodes and sink nodes. Then the energy distribution shouldchange with the topology, so that the energy can be saved,and consequently the lifetime of network can be extended.

We assume a perfect medium access control, such asSMAC [13], which ensures that there are no collisions at anysensor during data communication, and we adopt the simplebut relevant path loss communicationmodel as in [14]. In thismodel, the transmit power level that should be assigned to asensor 𝑖 to reach a sensor 𝑗 is 𝑃

𝑖= 𝛽 × 𝑑

𝛼

𝑖𝑗, where 𝛼 ∈ [2, 6] is

the path loss exponent and 𝛽 = 1 is the transmission qualityparameter. The energy loss due to channel transmission is𝑑𝛼

𝑖𝑗, 𝑑𝑖𝑗is the Euclidean distance between sensors 𝑖 and 𝑗, and

𝑅𝑖

𝐶= 𝑑𝑖𝑗is sensor 𝑖’s communication range, s.t. 𝑅𝑖

𝐶≤ 𝑅max,

where 𝑅max is a fixed maximum communication distance,which is constrained by themaximumpower that sensors cantransmit, that is, 𝑃max.

The residual energy of sensor 𝑖, at time 𝑡, is calculated asfollows:

𝐸𝑖 (𝑡) = 𝐸

𝑖 (𝑡 − 1) − [(𝑟𝑖 (𝑡) + 1) × 𝑃

𝑖× amp] , (1)

where (𝑟𝑖(𝑡) + 1) is the total traffic load that sensor 𝑖 forwards

towards 𝐻 at 𝑡, 𝑟𝑖(𝑡) is the traffic load that 𝑖 receives and

relays, “+1” is the data packet generated by 𝑖 to forwardits own data information, and amp is the power amplifier’senergy consumption. In EDDO, we assume that the region𝐴

is large and 𝑁 is relatively small. Consequently, the sensorsshould spread and communicate through long transmissiondistances. Thus, the energy consumed by the transceiverelectronics is negligible and can be ignored because thetransmit power is the main factor on sensors’ total energyconsumption [15, 16].

3.2. Problem Formulation. The problem of energy distribu-tion and optimization is given as follows:

(i) 𝐴: a 2D plane, where the sensor nodes are distributed;(ii) 𝑁: the number of the sensor nodes in region 𝐴;(iii) 𝐸: the initial energy of sensor nodes;(iv) 𝑅

𝑐: the maximum communication distance of the

sensor nodes;(v) 𝑃max: the maximum emission energy levels.

Decision variables of a network design 𝑋 as follows:

(i) (𝑥𝑗, 𝑦𝑗): the location of sensor 𝑗;

(ii) 𝑃𝑗: the transmission power level of sensor 𝑗.

Objectives are to maximize connectivity and minimizeenergy consumption of the network.

The network connectivity is defined as the fact thateach node can communicate with the sink node directly or

indirectly, and the network energy consumption is defined asthe sum of all sensor nodes’ emission energy.

Connectivity: for any 𝑐𝑗𝐻

∈ 𝐶(𝑁)

, 1 ≤ 𝑗 ≤ 𝑁, 𝐻 is thesink node, there is 𝑐

𝑗𝐻= 1, 𝐶(𝑁) is the connectivity matrix of

the network, and 𝑐𝑗𝐻

is the connectivity status of a sensor 𝑗,which is denoted as:

𝑐𝑗𝐻

= {1, if 𝑗 is connected;0, otherwise,

(2)

where sensor 𝑗 directly communicates with 𝐻, or if itsustains some neighbors with positive advance towards 𝐻

(i.e., neighbors are closer to 𝐻 than 𝑗 [17]), considering themany-to-one communication nature of WSNs as follows:

Energy consumption : 𝐸min =

min {𝑃1+ 𝑃2+ ⋅ ⋅ ⋅ + 𝑃

𝑗+ ⋅ ⋅ ⋅ 𝑃

𝑁} .

(3)

During the process of EDDO, 𝑐𝑗𝐻

= 0 represents thatsensor 𝑗 is disconnected, then the transmit power 𝑃

𝑖𝑗of 𝑗

should automaticly convert to 𝑃(𝑖+1)𝑗

. This process is repeateduntil 𝑐

𝑗𝐻= 1 or 𝑖 = 𝑛. If 𝑖 = 𝑛 and 𝑐

𝑗𝐻= 0, it means that sensor

𝑗 is not within the scope of cover. In this case, sensor 𝑗 shouldsend information by the transmit power 𝑃

𝑛at intervals until

𝑐𝑗𝐻

= 1.

3.3. Solution Representation and Ordering. In this paper, acandidate solution 𝑋 consists of 𝑁 items which correspond-ing to the 𝑁 sensor nodes. The 𝑗th item of 𝑋 has two parts,which represent the location (𝑥

𝑗, 𝑦𝑗) and the transmit power

𝑃𝑗of sensor 𝑗, respectively.The location (𝑥

𝑗, 𝑦𝑗) is assumed that has been obtained

by the GPS, and it will change with the environmentalconditions. The moving of some nodes may lead to thetransmit power to be reallocated. The location informationin solution 𝑋 will affect the local topology of node 𝑗, and itcan help the objective function to evaluate or select a newsolution. It mainly depends on the value of 𝑃

𝑖𝑗that whether

𝑋 is the optimal solution, the 𝑛th transmit power of sensorsis the selection content of an operator, 𝑃

𝑖𝑗is the 𝑖th transmit

power of sensor𝑗, and it belongs to 𝑛 items which are from𝑃0to 𝑃𝑛, 𝑃0

= 0, 𝑃𝑛

= 𝑃max. 𝑃0 = 0 means that sensor𝑗 isdisconnected. Dividing the transmit power into 𝑛 levels is inorder to operate on the genetic coding conveniently.

3.4. The Energy Distribution Based on Genetic Algorithm. Inrecent years, genetic algorithm (GA) is a popular optimizedmethod which has a parallel search and group optimizationfeatures. GA is a kind of bionic algorithm; this type ofalgorithms can solve many complex engineering problemswithout the mathematical properties of them.

3.4.1. The Algorithm Coding Mapping and Population Initial-ization. According to the real-coded ideological of K. H.Jin, each individual represents a power allocation scheme ofMSR-WSN.The genome of the population of individuals is

𝑔 = {𝐶1, 𝐶2, . . . , 𝐶

𝑁} , (4)


1

3

2

4

Figure 1: Initial solutions 𝑋 of 𝑁 individuals (Pareto charts).

where chromosome𝐶𝑗= 𝑃𝑗, and𝑃

𝑗is the transmission power

of the sensor node 𝑗. If 𝐶𝑗

= 0, then the chromosome isempty which represents that sensor 𝑗 is disconnected. Thegenome can not only indicate node power allocation scheme,but also indicate the number of the activity sensor nodes inthe communication network.

𝑥𝑗(𝑡) is the 𝑗th individual in the population 𝑡, and 𝑥

𝑗(𝑡)

contains 𝑛 genes as follows:

𝑥𝑗 (𝑡) = (𝑥

1𝑗 (𝑡) , 𝑥2𝑗 (𝑡) , . . . , 𝑥𝑛𝑗 (𝑡)) , (5)

where 𝑗 = 1, 2, . . . , 𝑁 and 𝑡 = 1, 2, . . . , 𝑡max. 𝑛 is the numberof the chromosome in the individual and the number ofvariables in the vector, 𝑁 is the population size, 𝑡max is themaximum evolution generation, and gene 𝑥

𝑖𝑗(𝑡) corresponds

to 𝑃𝑖𝑗.

During the population initialization process, each nodedetermines its own transmit power according to the distanceof the sensor and 𝐻 or the distance between sensors. Firstly,the sensors are sorted based on their distance to 𝐻 such asAlgorithm 1 referenced [18], where 1 is the closest and 𝑁 isthe farthest sensor location with respect to 𝐻, respectively.𝑋 is showed in Figure 1, where the transmission power ofeach of the node 𝑗 is proportional to the transmitting radius𝑅𝑗

𝐶, 𝑅𝑗

𝐶≤ 𝑅max. 𝑅

𝑗

𝐶needs to meet the condition that sensor 𝑗

can connect to its closest node 𝑘 (𝑘 < 𝑗), and the𝑋 is initiallygenerated as follows.

Algorithm 1. The representation process for each solution 𝑌

Input:𝐴 solution 𝑌;Output:𝐴 solution 𝑋;Step 1: Calculate the dense-to-spread ordering of𝑌 toget 𝑋;Step 2: for each (𝑥

𝑗, 𝑦𝑗) in 𝑋 do

𝑃𝑖𝑗

=

{{{{{{{

{{{{{{{

{

(𝑑𝑗,𝐻

)𝛼

,

if (𝑥𝐻, 𝑦𝐻) is 𝑗’s closest location, 𝑑

𝑗,𝐻≤ 𝑅max

(𝑑𝑗,𝑘

)𝛼

,

if (𝑥𝑘, 𝑦𝑘) is 𝑗’s closest location, 𝑘 < 𝑗, 𝑃

𝑘̸= 0,

𝑑𝑗,𝑘

≤ 𝑅max.

(6)

This process of topology generating is simple and conve-nient, but it does not have the dynamic adaptability and is not

conducive to the followup topology control. In MAR-WSN,the sink node 𝐻 can move freely, and the sensor nodes willmove with water waves. Therefore, the distribution of nodepower should be optimized constantly as the time goes by, sothat the energy consumption level of each node can adapt tothe network well.

3.4.2. The Selection of the Objective Function. For the givensolution, we need to accurately estimate its quality (fitnessvalue), which is determined by the fitness function. In thispaper, we aim at finding a solution which ensures the nodesthat can communicate with 𝐻 with as little as possible ofthe energy consumption. The quality of solution𝑋(𝑡)mainlydepends on the connectivity and energy consumption.

𝐹(𝐶𝑗) is the fitness value of chromosome 𝐶

𝑗which

represents the transmit energy level of sensor 𝑗, and 𝐹(𝐶𝑗) is

defined as the ratio of sensor 𝑗’s transmit power and the totalpower of all nodes, as follows:

𝐹 (𝐶𝑗) =

𝑃𝑗

∑𝑁

𝑗=1𝑃𝑗

. (7)

In addition, we made the value as the comparisonreference which is the ratio of the average power of all nodesand the total transmits power. The comparison reference iscalculated and simplified as follows:

(∑𝑁

𝑗=1𝑃𝑗) /𝑁

∑𝑁

𝑗=1𝑃𝑗

=1

𝑁. (8)

The fitness function can select out the nodes whosetransmit power is less than the average power in the network.Then the selected nodes will be the cross-object nodes whichinstead of those nodes whose transmit power is more thanaverage power. By this way, the nodes whose transmit poweris overload will be optimized, and they will not be deadquickly.

3.4.3. Selection Mechanism. Select operation can improvethe average quality of the population by selecting high-quality chromosome into the next generation of the popu-lation. Chromosome selection is based on the fitness value.Selection operation selects the chromosomes according tothe constraint environment of each individual (that are thedistances between the sensor and its neighbors), the positiondynamically change information, and the fitness of 𝑋 asfollows:

When 𝐹(𝐶𝑗) > 1/𝑁, then the 𝐶

𝑗will be eliminated.

When 𝐹(𝐶𝑗) ≤ 1/𝑁, then 𝐶

𝑗will be the cross-object.

3.4.4. Crossover and Evolution. The genetic algorithm isbased on two basic genetic operation that are cross-operationand evolution operation. The cross-operation handles thecurrent solution in order to find a better solution. The evolu-tion operation can help theGA to avoid falling into local opti-mal solution [8]. The effect of the genetic algorithm dependson these two steps. In this paper, we crossed the genes


𝑥1𝑗(𝑡), 𝑥2𝑗(𝑡), . . . , 𝑥

𝑛𝑗(𝑡) on the chromosome when the chro-

mosome 𝐶𝑗needs to be evaluated. The cross-objects come

from the solution which is selected by the selection operationand is the immigration solution selected (Section 3.5). Thenwe crossed the binary coding that corresponds to the power.We adopted single-point crossover, and the new chromosomeis updated.

The updating formula after crossover operation is such as

𝑥𝑖𝑗 (𝑡 + 1) = {

ℎ𝑖𝑗 (𝑡 + 1) , 𝑓 (ℎ

𝑖𝑗 (𝑡 + 1) < 𝑓 (𝑥𝑖𝑗 (𝑡)))

𝑥𝑖𝑗 (𝑡) , 𝑓 (ℎ

𝑖𝑗 (𝑡 + 1) ≥ 𝑓 (𝑥𝑖𝑗 (𝑡))) ,

(9)

where ℎ𝑖𝑗(𝑡 + 1) is the new chromosome after the crossover

operation.The new chromosome should be evaluated that it could

communicate with 𝐻, after that the updating operation canbe performed. The evaluation processed as the Algorithm 2.

Algorithm 2. The updating process

Input:The new chromosome ℎ𝑖𝑗(𝑡 + 1);

Output:Theexternal chromosome in this generation.Step 1: Calculate the connectivity status of a sensor 𝑗.

Step 1.1: Generate the 𝐶(𝑁) by the new 𝑃

𝑖𝑗of

ℎ𝑖𝑗(𝑡 + 1).

Step 1.2: Return 𝑐𝑗𝐻

Step 2: If 𝑐𝑗𝐻

= 1.

3.5.TheEnergyDynamicDistribution andOptimization Basedon GA. For dynamic optimization problem, the GAs shouldmaintain a certain level of solution diversity to keep thesolution adapting to the changes in the environment; then theconvergence problem becomes very important. To addressthis problem, the random immigrants approach is a quitenatural and simple way [19, 20]. It was proposed by Grefen-stette with the inspiration from the flux of immigrants thatwander in and out of a population between two generationsin nature. It maintains the diversity level of the populationthrough replacing some individuals of the current populationwith random individuals, called random immigrants, everygeneration. As to which individuals in the population shouldbe replaced, usually there are two strategies: replacing ran-dom individuals or replacing the worst ones [21]. In orderto avoid that random immigrants disrupt the ongoing searchprogress too much, especially during the period when theenvironment does not change, the ratio of the number ofrandom immigrants to the population size is usually set toa small value, for example, 0.2.

However, if the environment of nodes changes slowly,the introduced random immigrants may divert the searchingforce of the GA and hence may degrade the performance.On the other hand, if the environment of nodes only changesslightly in terms of severity of changes, random immigrantsmay not have any actual effect even when a change occursbecause individuals in the previous environment may stillbe quite fit in the new environment. Based on the above

considerations, an immigrants approach, called elitism-basedimmigrants [22], is proposed for GAs to address the energydeployment problem.

For each generation 𝑡, after the normal genetic operations(i.e., selection and recombination), the elite 𝐸(𝑡 − 1) fromprevious generation is used as the base to create immigrants.From 𝐸(𝑡 − 1), a set of 𝑟ei × 𝑁 individuals are iterativelygenerated by mutating 𝐸(𝑡 − 1) with a probability 𝑝

𝑖

𝑚, where

𝑁 is the population size and 𝑟ei is the ratio of the numberof elitism-based immigrants to the population size. Thegenerated individuals then act as immigrants and replace theworst individuals in the current population. It can be seenthat the elitism-based immigrants’ scheme combines the ideaof elitism with traditional random immigrants’ scheme.

The whole energy dynamic distribution and optimiza-tion (EDDO) algorithm is described as Algorithm 3. In thegenetic operation of Algorithm 3, if the mutation proba-bility 𝑝

𝑖

𝑚is satisfied, the elite 𝐸(𝑡 − 1) will be used to

generate the new immigrants by the mutation operation;otherwise, 𝐸(𝑡 − 1) itself will be directly used as the newimmigrants. It uses the elite from previous population toguide the immigrants toward the current environment,which is expected to improve GA’s performance in dynamicenvironments.

Algorithm 3. The energy deployment general framework

Input: network parameters (𝐴,𝑁, 𝑛, 𝐸, 𝑃max, 𝑡max);Output: the external population (EP)Step 0-Setup: Set EP := Φ; 𝑡 := 0; IP

𝑡:= Φ;

Step 1-Initialization: Generate an initial solution asAlgorithm 1: IP

0= {𝑋1, . . . , 𝑋

𝑁};

Step 2: For 𝑖 = 1, . . . , 𝑁 do

Step 2.1-Genetic Operators: Generate a newsolution 𝑌 using the genetic operators.Step 2.2-Perform elitism-based immigration:Generate 𝑟

𝑒𝑖×𝑁 immigrants bymutating𝐸(𝑡−1)

with 𝑝𝑖

𝑚.

Step 2.3-Update Populations:Update the pop-ulation as Algorithm 2.

Step 3-Stopping criterion: If stopping criterion issatisfied, i.e.

4. Simulation and Analysis

4.1. Simulation Setup. In the environment of MSR-WSN, wedesigned the region A which is 1000m × 1000m, and 100sensor nodes are randomly distributed in the region. Themedium access control, such as SMAC, is introduced inSection 3.1, and its parameters were set according to [5]. Inour experimental studies, the parameters of algorithm are setas in [9]. That is, the number of power levels 𝑛 = 40, maxnumber of generations 𝑡max = 300, crossover rate 𝑟

𝑐= 0.9,

mutation rate 𝑟𝑚

= 0.5, tournament size 𝑀 = 10, andneighborhoods size is 2. Moreover, in all simulation studies


the following network parameters are set [23]: 𝑅𝑠/𝑅max =

100/200, 𝐸 = 10 J, 𝑑min = 100m, 𝑎 = 2, and amp =

100 pJ/bit/m2.During the experiment, to imitate the dynamic nature of

the actual environment, we made the nodes move randomlylike

𝑥 (𝑇 + 1) = 𝑥 (𝑇) + 𝜂 cos 𝜃; 𝑦 (𝑇 + 1) = 𝑦 (𝑇) + 𝜂 sin 𝜃, (10)

where 𝜂, 𝜃 were randomly generated number and 0 ≤ 𝜂 ≤ 1,0 ≤ 𝜃 ≤ 2𝜋, 𝑇 represented time and it’s unit was second.

4.2. Simulation Scheme. The simulation experiments wererealized throughMATLAB 7.0 to verify feasibility and validityof the proposed algorithm.

We compared the EDDO algorithms with SGA andRestart GA at first as in Section 4.2.1. After that we comparedthe EDDOwith other algorithms about energy as DRNG andDLMST in Section 4.2.1.

4.2.1. Comparisons with SGA and Restart GA. Figure 2(a)shows that average node power obtained from the proposedEDDO algorithm, the SGA, and Restart GA. We can seethat with the increasing of the population generation, all thealgorithms could achieve the convergence solution. But theEDDO algorithm is faster than the SGA and Restart GAbecause of its elite scheme. And the final average node powerof the algorithm is lower than that of SGA by about 0.3 J inone convergence.

Figure 2(b) shows that the convergence time of the EDDOalgorithm would be much lower than the time of SGAand the Restart GA. It indicates that the EDDO algorithmcan adapt to the dynamic movement of nodes because thealgorithm makes full use of the excellent solution in theoriginal environment and the immigrant also contributes tothe convergence speed. With time goes by, the convergencetime of the algorithm becomes relatively stable and is lowerthan the SGA by about 13.7%.

4.2.2. Comparisons with Other Algorithms. Figure 3 showsthe comparison with the DLMST and DRNG algorithms [4]in which every sensor determines its power based on theinformation of neighbors. We can see that the average powerof three algorithms is almost the same in Figure 3(a) and theaverage power of the whole time of the EDDO algorithmis a little higher than the other two algorithms. However,the running time of these three algorithms is different inFigure 3(b) and the EDDO algorithm is the best one here. Itdues to the algorithm in this paper can seek the optimizationsolution overall the nodes, while in the DLMST and DRNGevery node takes account of itself only. The local informationcould help DLMST and DRNG to adapt the dynamic changeof networks in a certain extent, but it is not very helpful forthe whole network. And the two algorithms’ execution timeis not so stable than that in the EDDO algorithm.

0 50 100 150 200 250 300

0

1

2

3

4

5

6

7

8

9

10

EDDO

SGA

Restart GA

(a) Average node power: generation 0–300

0 5 10 15

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Av

erag

e t

ime o

f a

lgo

rit

hm

s (

s)

EDDO

DLMST

DRNG

(b) Convergence time: time 0–15 seconds

Figure 2: Comparisons with SGA and Restart GA.

5. Conclusion

In this paper, the energy distribution problemofMSR-WSN isdefined as a deployment solution that should take account ofthe connectivity and the lifetime of the network.The problemis modeled in the environment at sea, and the applianceprocess of the network has been described at first. In theprocedure of solving the problem, the dynamic nature andenergy consumption of the nodes is focused on in the harshenvironment of sea. Introducing the genetic algorithms withelitism-based immigrants, we made the energy distributionmethod adapt to the dynamic change of the nodes positionand convergent more quickly. In the future, we will study amore efficient and perfect topology control method of theMSR-WSN.


0 5 10 15

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

EDDO

DLMST

DRNG

(a) Average node power: time 1–15 seconds

0 5 10 15

EDDO

SGA

Restart GA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Co

nv

erg

en

ce t

ime (

s)

(b) Average time of algorithms: time 1–15 seconds

Figure 3: Comparisons with DRNG and DLMST algorithms.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51279099), the Shanghai Natural Sci-ence Foundation (12ZR1412500), the Innovation Programof Shanghai Municipal Education Commission (13ZZ124),and the “Shu Guang” Project supported by the ShanghaiMunicipal Education Commission and Shanghai EducationDevelopment Foundation (12SG40).

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Research Article An Energy Distribution and Optimization ...downloads.hindawi.com/journals/ijdsn/2013/725869.pdf · data to the sink node a er identifying the sink node. e sensor