Hybrid Chaotic Salp Swarm with Crossover Algorithm for Underground Wireless Sensor Networks

Mariem Ayedi,Walaa H.ElAshmawi and Esraa Eldesouky

1First Department of Computer Science,College of Computer Engineering and Sciences,Prince Sattam Bin Abdulaziz University,Al-Kharj,11942,Saudi Arabia

2MEDIATRON Lab.,SUP’COM,Carthage University,Tunis,2083,Tunisia

3Department of Computer Science,Faculty of Computers and Informatics,Suez Canal University,Ismailia,41522,Egypt

4Faculty of Computer Science,Misr International University,Cairo,Egypt

Abstract: Resource management in Underground Wireless Sensor Networks(UWSNs) is one of the pillars to extend the network lifetime.An intriguing design goal for such networks is to achieve balanced energy and spectral resource utilization.This paper focuses on optimizing the resource efficiency in UWSNs where underground relay nodes amplify and forward sensed data,received from the buried source nodes through a lossy soil medium,to the aboveground base station.A new algorithm called the Hybrid Chaotic Salp Swarm and Crossover(HCSSC)algorithm is proposed to obtain the optimal source and relay transmission powers to maximize the network resource efficiency.The proposed algorithm improves the standard Salp Swarm Algorithm(SSA) by considering a chaotic map to initialize the population along with performing the crossover technique in the position updates of salps.Through experimental results,the HCSSC algorithm proves its outstanding superiority to the standard SSA for resource efficiency optimization.Hence,the network’s lifetime is prolonged.Indeed,the proposed algorithm achieves an improvement performance of 23.6%and 20.4%for the resource efficiency and average remaining relay battery per transmission,respectively.Furthermore,simulation results demonstrate that the HCSSC algorithm proves its efficacy in the case of both equal and different node battery capacities.

Keywords: Underground wireless sensor networks;resource efficiency;chaotic theory;crossover algorithm;salp swarm algorithm

1 Introduction

With the precipitous growth of microelectronics and sensing technologies,Wireless Sensor Networks(WSNs)have been categorized as an intense research arena.The outstanding privileges of such networks,including their easy configuration,mobility,and flexibility,lead to their deployment in many environments.UWSNs are an important extension of WSNs applications for use in the underground world.These underground networks have a broad range of applications including tracking coal mining facilities,soil monitoring,and gas/oil pipeline control.In such networks,buried sensors continuously collect sensitive data regarding the sensed environment and forward it to the base station[1].However,the limited communication range and the energy constraints along with the complex and unpredictable conditions of the underground medium are the primary challenges of UWSNs.Thus,the role of relay nodes is vital in UWSNs because they represent a promising method for achieving high bandwidth and expanding network coverage [2].In UWSNs,communications among nodes come in three distinct channels:UnderGround-to-AboveGround (UG2AG),UnderGround-to-UnderGround (UG2UG),and AboveGround-to-UnderGround(AG2UG)[3].The UG2AG channel connection is mainly used to transmit sensed data from buried sensors to relay nodes or aboveground base stations[3-5].Relay node deployment has been studied in UWSNs [5-8].In [5],an underground coal mine was divided into separate regions and addressed optimal relay node placement to support robust coverage of the network.In [6],Wu targeted controlling the amount of energy used by underground sensors to map water pipelines through optimal relay placement.In the same way,the optimum relay node location was debated for the goal of extending the network’s duration subjected to reducing the load balance and the number of relays [7].In [8],two approximation algorithms for relay node deployment and assignment to sensor nodes were introduced to reduce transmission loss among nodes.Since high throughput and capacity are critically constrained by nodes energy consumption,research work in WSN focus recently on studying the trade-off between spectral efficiency and energy efficiency metrics called the resource efficiency [9-12].The primary objective is to jointly evaluate the efficient use of a limited frequency spectrum along with energy consumption.In UWSNs,this problem was first addressed in [13],where optimal powers used by underground sources and relay nodes for data forwarding to an aboveground base station were computed to maximize the energy and spectral efficiency tradeoff.The work[13]proposes a power allocation algorithm that utilizes the Salp Swarm Algorithm(SSA)[14]to solve the considered problem since the swarm intelligence models are interesting for various computer science fields [15,16].The SSA is suggested in [14]as a recent metaheuristic algorithm which outperforms many other metaheuristic algorithms through tests on 19 different benchmark functions.In nearby research works,SSA proves its efficiency in node localization optimization in WSN[17,18],energy consumption and lifetime optimization in WSN[19].The work[13]proves that the SSA-based scheme offers a better resource efficiency,given similar bandwidth and battery cost resources,compared with the traditional UWSN scheme.In this paper,we propose to further enhance the resource efficiency of the UWSN considered in[13]by modifying and improving the SSA.A novel algorithm called Hybrid Chaotic Salp Swarm with Crossover(HCSSC)is proposed to determine the optimal powers required by the source and relay nodes that enhance the network resource efficiency considering the initial nodes’battery capacities.The proposed algorithm uses chaos theory[20]to generate feasible initial solutions.This can enhance the diversity of solutions due to the randomness and dynamic features of the chaos.Moreover,to compute the final optimal solution,a uniform crossover operator[21,22]is integrated in the exploration phase of the optimization algorithm.This leads to accelerated algorithm convergence due to the wide exploration of the search space.The proposed power optimization scheme is evaluated in terms of its effect on the average relay power and battery remaining per transmission.Since the relay node can have a higher battery capacity than the source node,we propose to study the efficiency of the proposed algorithm under both equal and different node capacities.

The main contributions of this work are listed as follows

1.A new algorithm called HCSSC algorithm is proposed to improve the standard SSA by considering a logistic chaotic map to initialize the population and integrating the uniform crossover operator in the update of salps positions.

2.The resource efficiency performance is ameliorated compared to that obtained in the work[13].

3.The average consumed relay power per transmission is minimized and the average remaining relay battery per transmission is maximized.

4.The efficiency of the proposed algorithm is proved in case of both equal and different node batteries capacities.

This paper is structured as follows.In Section 2,the UWSN system model is presented and the considered problem is formulated.In Section 3,the proposed HCSSC algorithm is detailed.In Section 4,the experimental results and performance analysis are discussed,and finally,Section 5 concludes the paper.

2 System Model and Problem Formulation

The considered UWSN model consists of sensor source nodeSthat gathers and forwards sensory data to an aboveground base stationBthrough a half-duplex Amplify-and-Forward(AF)relay nodeR.The communication link betweenSandRis an UG2UG link,whereas the communication link betweenRandBis an UG2AG link.The mathematical expressions of the path losses for UG2UG and UG2AG,the communication mechanism among nodes,and the optimization problem under consideration are described in this section.

2.1 UG2UG and UG2AG Channel Model

Both source and relay nodes are buried in the soil in UWSNs.Here,the sensor nodes are buried deeper than the relay nodes according to the ground surface.In Fig.1,a two-dimensional plane represents UWSN deployment where the nodes distances in the plane using Cartesian coordinates defined on thexandyaxes with originO.The base station is positioned at the origin ofx-axis whereas the ground surface is represented as the origin ofy-axis.dXGis the node burial depth at positions(xX,yY)for nodeX∈{S,R}.

Figure 1:The topology of UWSN

According to[23],the UG2UG path lossLuuSRis defined as

wheredSR=is the distance in metres betweenSandR.The constantsαandβmeasure the attenuation and phase shifting,respectively.The factorVrepresents the attenuation of the reflection path obtained when the wave is reflected by the ground surface.Hence,the UG2UG communication results from the propagation of the signal in the reflection path and in the direct path between the two sensors [22].The authors in [24]utilize the electromagnetic propagation model to provide the detailed expressions the constantsαandβ.The soil medium dielectric characteristics along with the system operating frequencyq,the sand and clay percentages,the bulk density and the Volumetric Water Content constitute the main features that these constants depend on[25].The soil and air constitute the two media throughout passes the communication betweenRandB.Yet,there is no refraction loss from under to aboveground transition due to the perpendicular propagation of signal from higher to lower density medium[3,26].Then,based on[3,26],the path lossLuaRBof the channel betweenRandBis the result of adding the path losses for both underground and aboveground portions as in Eq.(2)

wheredORrepresents the horizontal distance betweenRand the originO,dOBis the height of the aboveground base stationBandηis the attenuation coefficient on air[26].

2.2 UWSN System Model

Here,the uplink communication procedure among the trio link is presented.The Time Division Multiple Access (TDMA) scheme is considered to mitigate the signal interference.Each nodeX∈{S,R}has a limited battery with power capacityCX.At each packet transmission,t,nodeXconsumes a powerPXt∈[PXmin,PXmax].The communication process at each transmissiont∈[1,τ]needs two phases.

In the first phase,the source nodeStransmits a data packetdtto the relay nodeR.The resulting

such thathtSRrepresents the gain of the UG2UG channel between the two nodesSandR,which obeys to the Rayleigh distribution[23]with the underground path lossLuuSRcalculated in Eq.(1)andis the zero-mean complex Additive White Gaussian Noise(AWGN)vector with varianceN0.Hence,the Signal-to-Noise Ratio(SNR)betweenSandRdesignated by,resulting of the communication betweenSandRat transmissiont,is as follows

Wherebdenotes the channel bandwidth in Hz,which is equal to the operating frequencyqwhen TDMA is applied.In the second phase,the signalis amplified and forwarded byRtoB.

Consequently,the received signalatBis calculated as follows.

Withis the UG2AG Rayleigh distributed channel betweenRandB[23]with the underground path lossLuaRBcalculated in Eq.(2),is the zero-mean complex AWGN vector andis the amplification factor.Thus,the SNR,denoted by,of the transmission betweenRandBis computed as follows.

With respect to Eqs.(4) and (6),the total SNRand the maximum data ratefor the trio link are given respectively by

2.3 Problem Formulation

The overall paper objective is to determine the power allocation vectorallowing an efficient balance between two competing metrics:the energy efficiencyEEtand spectral efficiencySEtat each transmissiont.Indeed,EEt.is the total bits generated per unit energy whereasSEtrepresents the total delivered bits per unit bandwidth of link(S-R-B)at transmissiont.Their expressions are respectively as follows

As discussed in[9],the resource efficiency metricREtis capable to exploit the trade-off betweenEEtandSEt.It is given by

where the weighted factorωis computed aswithis a constant andPtot=PSmax+PRmaxis the total power budget allocated to the link(S-R-B)at each transmission.Since,SEtis practically smaller thanEEt,this weighted factorωis utilized to achieve the balance betweenEEtandSEt.In fact,it solves the inconsistence of adding two metrics with different units since the unit ofEEtis bits/Joule while the unit ofSEtis bits/s/Hz.Then,the unit ofREtis equivalent toEEtwhich is still bits/Joule.Besides,maximizingREtis simply maximizingEEtif=0 andSEtif=∞.The selection of this constant value in the UWSN model is described in[13].

For each nodeX,optimizing the powerat each transmissiontis a mandatory requirement because it depends on the limited battery capacity CXof the buried node,the spent powers for transmissions[P1X,...,]and the allowed power limitation range at each transmission[PXmin,PXmax].

Then,the proposed optimization problem is stated as

In Eq.(12),the maximization problem presented is considered a NP-hard problem that requires an efficient optimization algorithm to solve it.Therefore,a hybrid meta-heuristic algorithm based on SSA is proposed to obtain optimal values of nodes powers considering the resource efficiencyREto be maximized.

3 The Proposed HCSSC for Resource Efficiency

In this section,the main structure of the standard Salp Swarm Algorithm(SSA)is first reviewed.Then,the detailed steps of the proposed Hybrid Chaotic Salp Swarm with Crossover(HCSSC)scheme for maximizing the resource efficiency in the considered UWSN are addressed.

3.1 Salp Swarm Algorithm(SSA)

The Salp Swarm Algorithm(SSA)is one of the recent swam algorithms proposed in 2017[14]and widely used in solving many optimization problems[27,28].SSA emulates the motion of Salpidae that have a transparent barrel-shaped body and live-in deep oceans[29].Salps are organized in a form of swarm called salp chain.Mathematically,the salp chain is divided into two groups:leader (i.e.,the first salp of the chain and followers (i.e.,the remaining salps of the chain which follow the leader).Researchers viewed that their searching for food is an indicator to their behavior[30].

The leader in the swarm updates its position relative to the food sourceFaccording to Eq.(13)

Whereis the position of the leader in thejthdimension,lbjandubjare the lower and the upper bound of thejthdimension,respectively,andFjis the position of food source in thejthdimension.The parameterc1balances the scale between exploration and exploitation and is computed according to Eq.(14).The coefficientsc2andc3are random numbers between [-1,1].Also,c3determines the direction of moving the leader towards a positive infinity or negative infinity.

wherelis the current iteration andLis the maximum number of iterations.

The remaining of the salps in the chain (i.e.,followers) update their positions based on the Newton’s law of motion as in Eq.(15)

Withx1jis theithsalp in thejthdimension,tis the time,v0is the initial speed.

In the optimization problems,the time is considered as an iteration where the conflict between iterations is equal to 1 andv0is set to 0.Then,Eq.(15)can be reformulated in Eq.(17)for updating the positions of followers.

While the global optimal solution of any optimization problem is unknown,the best solution can be obtained by moving the leader,followed by the followers,towards the food source.As a result,the salp chain moves towards the global optimum.The overall steps of the SSA are described below.

Algorithm 1:Salp Swarm Algorithm(SSA)Input:initial population:initialize the number of salps N in the population randomly in the range[lbj,ubj],xi j,i={1,...,n},j={1,...,m}Steps:1.Each salp in the population is evaluated according to a fitness function and the global best fittest one is assigned to F (i.e.,food source).2.The parameter c1 is updated according to Eq.(14).3.The position of the leader(i.e.,i=1)and the followers(i.e.,i ≥2)are updated according to Eq.(13)and(17),respectively.4.The steps from 1 to 4 are repeated until a termination condition,as reaching a maximum number of iterations,is satisfied.Output:Report the global best final solution F

3.2 Hybrid Chaotic Salp Swarm with Crossover(HCSSC)Algorithm for RE

This subsection discusses the main steps of the proposed HCSSC algorithm to find the optimal source and relay nodes powers for maximizing the resource efficiencyREtat each packet transmissiontin the UWSN.Assuming thatBhas perfect Channel State Information(CSI)awareness,the proposed HCSSC algorithm is implemented atBwhich will send the obtained powers values to source and relay nodes prior to their packets’transmissions.The hybrid algorithm uses a logistic chaotic map to generate a feasible initial population at random.Furthermore,improving the solution during the number of iterations through the uniform crossover operator and chaotic map can guarantee that the optimal solution is the final solution.The steps of the proposed HCSSC are discussed in detail as follows.

3.2.1 Initial Population

Each salp(i.e.,xi,i={1,...,n})in the HCSSC populationNcorresponds to a possible solution for the resource efficiency optimization problem.Moreover,each salp consists of many variables(i.e.,var(j),j={1,...,m})that affect the optimization of the resource efficiency as shown in Fig.2.This paper considers a salpxconsists of two variables which arePSandPR.An illustrative example of a salpxis shown in Fig.3.The value for each variable can be generated within the lowerPXminand upperPXmaxbounds,respectively.

Figure 2:HCSSC population

Figure 3:An illustrative example of salp x

The diversity of the initial population has a great impact on spreading effectively in the search space.Therefore,for generating an effective initial population,a chaotic map is used in the proposed algorithm.One of the simplest maps is the logistic map that appears in the nonlinear dynamics of a biological population that evidences the chaotic behavior[31]and it is represented mathematically by Eq.(18).

whereckis the chaotic value at each independent runk(i.e.,ck∈(0,1)),ris the growth rate that controls the behavior of chaotic value at a certain time(r=4).To be more specific,the generated random value of resources at any given time(round)is a function of the growth rate parameter and the previous time step’s resource’s value.Consequently,the initial populationNof the proposed HCSSC algorithm is generated according to the following pseudo code.

Pseudo code 1:Initial population N generation using logistic chaotic map For i=1 to n For j=1 to m xij=lbi+ck(ubj-lbj)End For xi=(xi1,xi2,...,xi m)End For

Each variable is bounded within lower and upper values[lbj,ubj],ckis the chaotic sequence that is generated by logistic chaotic map.The integration of chaotic maps with salp swarm algorithm leads to produce a proper distribution through the characteristic of random and stochasticity of chaos.

3.2.2 Evaluation of Salps

The resource efficiency optimization can be modelled as an optimization problem with a maximized objective function.Therefore,each individual(i.e.,salp)in the population is evaluated according to Eq.(12)and the fittest one is assigned toF.

3.2.3 Updating Salps

The first salp in the population is called the leader which is responsible for guiding the salp chain and is continuously updating its position towards the direction of the source food.The rest salps in the population are called the followers because they follow the leader in updating their positions.Leader’s and followers’updates are illustrated below.

• Leader’s update

Since the leader updates its position in a positive direction,we ignore the negative direction.Also,the random numbersc2andc3are replaced by a chaotic sequencesc1kandc2kcomputed according to Eq.(18) whilec1is calculated according to Eq.(14).Thus,Eq.(13) is modified and represented in Eq.(19)

• Follower’s updates

Each followerxij;i≥2 in the population updates its position based on how far the current position from the best salp’s position.To achieve a better follow to the leader,we mate the best individual with the current individual through the uniform crossover [21,32].The uniform crossover proves its efficiency compared to other crossover operators[20].An illustrative example of uniform crossover is shown in Fig.4.

Figure 4:An illustrative example of uniform crossover

In the process of crossover,two parents(aandb)are selected and a binary mask consists of 1/0 digits is generated randomly with the same length of the individual.The result of this operation is generating two offsprings(and)based on the corresponding digit in the binary mask.For the first offspring(),if the digit in a mask is 1,then the digit it is taken from(a)otherwise from(b).Regarding the generation offspring,the complementary of mask is used.The two obtained offspringsandare considered as two new salps in the population.Each offspring∈{,}is a vector of two variables=[PtS,Pt R].Then,the objective function,which is the resource efficiency at each transmission,t,REtof each offspring∈{,}denoted byREt()is evaluated as follows

Further,REt()andREt()are compared.IfREt()＞REt(),then,is chosen to bexucross,else,is chosen to bexucross.Therefore,each follower in the salp chain updates its position as follows

3.2.4 Test the Termination Condition

The leader and followers are updating their positions iteratively until reaching a maximum number of iterations.Once the HCSSC algorithm reached the termination condition,the global best salp is returned as the best solution so far for the resource efficiencyREtat each packet transmissiont.The overall steps of the HCSSC algorithm for optimizing the resource efficiency in UWSN are described in the Fig.5.

Figure 5:Flowchart of the proposed HCSSC algorithm

4 Experimental Results and Analysis

This section presents the numerical results illustrating the performance of the proposed HCSSC based power optimization scheme.Simulations are done using MATLAB-R2015a running on Windows 7 with 2 GB RAM memory.Simulation results are obtained by averaging over 1000 channel iterations.We assume that source and relay nodes have equal batteries power capacitiesC(i.e.,C=CX)and equal maximum allowed powersPXmax=Pmax.Authors in [13]determine the mathematical computation of UG2UG and UG2AG path losses.Tab.1 summarizes the set of the system parameters and their corresponding values.

Table 1:Simulation parameters

The improvement of the resource efficiency using the proposed HCSSC algorithm,REHCSSC,against the resource efficiency,which uses the standard SSA,RESSA,is computed as follows:

In order to demonstrate the effectiveness of chaos theory for generating the initial population,a set of experiments have been conducted with various number of individuals,as shown in Fig.5,for the standard SSA(i.e.,with random initial salp positions)and SSA using chaotic map for initial positions generation with power capacityC=3wand maximum transmission powerPmax=50mw.

Fig.6 illustrates the convergence of the resource efficiencyREobtained using both algorithms for different number of salp.Clearly,the generation of initial population using chaotic map has achieved better results in maximizing the resource efficiency compared to the standard SSA,during the number of iterations,due to the better exploration of the search space.The improvement is increased with the increase ofN.Indeed,forN=5,the SSA with chaotic initial positions gains 4.9%better than standard SSA while atN=40,it gains 7%better.

Figure 6:Convergence curves of the standard SSA and SSA using chaotic initial positions

To demonstrate the efficiency of using the chaos theory and the crossover operator to achieve a maximum resource efficiency,the proposed HCSSC algorithm has been tested for different number of salpsN∈{5,10,20,40} atC=3wandPmax=50mw,as shown in Fig.7.The figure depicts the convergence of resource efficiency as a function of iterations numbers obtained using the proposed HCSSC algorithm in the nodes powers.

Figure 7:Convergence curve of the resource efficiency using the HCSSC algorithm

From the figure,the convergence of the proposed algorithm is rapidly obtained for various number of salps to reach the optimalREvalues.Also,the increase in the number of salps enhances the computation accuracy of the optimalRE.Therefore,the proposed algorithm can be efficiently implemented with acceptable cost of computational complexity.

For a fair comparison,the individuals number involved in the swarm population and the maximum number of iterations are equal for both standard SSA and the proposed HCSSC algorithms.Tab.2 illustrates the maximum(Max.),minimum(Min.),Average(Avg.)and Standard deviation(Std.)ofREat variousNand variousPmaxatC=3w.The best results are shown in bold.

Table 2:Statistical results of RE(Mbits/Joule)for C=3w

Table 2:Continued

In comparison with the traditional SSA based optimization scheme,the proposed HCSSC outperforms it in all evaluated performance measurements.According to Tab.2,forN=5 andPmax=300mw,the average value of theREbased HCSSC reaches 166.576 (Mbits/Joule) and the average value of theREbased SSA reaches 146.8785 (Mbits/Joule).Hence,the gain is about 13%.While forN=40 andPmax=50mw,the average value ofREbased HCSSC is 681.45(Mbits/Joule)while the average value of theREbased SSA equals 592.1117(Mbits/Joule).So,the gain reaches 15%.

Fig.8 shows the convergence behavior of the resource efficiency using the proposed algorithm HCSSC against the standard SSA,in nodes power optimization,with different number of salpsN∈{5,20,40}atC=3wandPmax=50mw.

Figure 8:Convergence curve of HCSSC against standard SSA

With different number of salps,the proposed HCSSC obtains a betterREconvergence than standard SSA for different number of iterations.The amelioration is raising with the increase ofN.AtN=5,20 and 40 theREof HCSSC is raising up to 9%,15%and 16%,respectively.

Furthermore,Fig.9 illustrates the effect of the maximum power permitted for a single transmissionPmaxon resource efficiency for both HCSSC and SSA with respect to different power capacityC∈{2,3,4}wandN=20.

Figure 9:Resource efficiency of HCSSC and SSA vs.the maximum allowed power Pmax

Once more,compared to the power optimized SSA scheme,the HCSSC achieves a higher resource efficiency at the same power cost.Indeed,the combination of chaotic map and the cross over operations in the proposed power algorithm improves the search of optimal nodes powers considering the power physical limitations.Hence,the resource efficiencyREincreases with the increase of nodes batteries capacity.Notably,the gain gap between HCSSC and SSA schemes is higher asCincreases.In fact,forC=2w,theREimprovement reaches 15.3% atPmax=50mwand reaches 19% atPmax=400mw.While forC=4w,the gain inREis 15.5% atPmax=50mwand is 23.6% atPmax=400mw.Since the increase in the maximum allowed powerPmaxdegrades the energy efficiencyEEand the weighted spectral efficiencyωSEas well,the resource efficiency diminishes whenPmaxincreases.In addition,network designers can regulatePmaxdepending on the accessible power resource of batteries capacities for a given resource efficiency specification.

The average consumed relay power and the average remaining relay battery per transmission for HCSSC and SSAvs.PmaxwithN=20 are shown in Figs.10 and 11,respectively.In Fig.10,The average consumed relay power is shown forC=3w.

Figure 10:Average consumed relay energy per transmission(HCSSC and SSA)

Figure 11:Average remaining relay battery per transmission(HCSSC and SSA)

Clearly,the deployment of HCSSC in nodes powers optimization allows a better relay power conservation since the average consumed relay power per transmission is minimized compared with the standard SSA along withPmaxvalues.In Fig.11,the effect of the HCSSC algorithm on the average remaining relay battery per transmission compared to the SSA is illustrated forC∈{2,3,4}w.The proposed HCSSC based scheme significantly ameliorates the average remaining relay battery per transmission for all battery capacity valueC.AtPmax=350mw,the obtained gain equals 23% atC=2w,it equals 21.6% atC=3wand it reaches 20.4% atC=4w.Thus,the proposed HCSSC based power optimization extends the nodes batteries lifetime and consequently the whole network lifetime.

In Fig.12,we propose to study the resource efficiency performance in the case where the relay node has a higher battery capacity than the source node and can forward packets considering higher maximum allowed power.In fact,the relay node is expected to consume more power than the source node since it collects data from different sources to forward it to the sink node and,possibly,retransmits lost packets.Interestingly,the proposed algorithm proves its efficiency,not only in the case of equal source and relay batteries capacities,but also in the case of different source and relay batteries capacities as clearly shown in Fig.12.We assume thatPRmax=2PSmaxandN=20.The proposed HCSSC based power optimization scheme achieves higher resource efficiency performance than the SSA asCSandCRincrease.AtCS=2wandCR=3w,the HCSSC algorithm achieves a gain of 21%better than the SSA atPsmax=50mw.While atCS=3wandCR=4w,the HCSSC algorithm achieves a gain of 28%better than the SSA atPSmax=200mw.

Figure 12:Resource efficiency of HCSSC and SSA for PRmax=2PSmax for different source and relay batteries capacities

In some applications,the benefit from of sensor nodes in UWSNs is restricteddue to harsh environmental conditions.For agricultural application for example,authors in [4]mention that if the water volume fraction of the mixture is high (passed 25%),the UG2UG communication link is interrupted specially with some particular soil type whose the capacity to hold the bound water is low.Consequently,the UG2UG communication can be interrupted for a long period in case of a rainfall.Also,for underground mine applications,UG2UG communications may be interrupted in many unpredictable situations such as rock falls or explosions.Moreover,we notice that the base station should implement a powerful operating system to support the additional computing complexity of the HCSSC algorithm.

5 Conclusions

This paper proposed a Hybrid Chaotic Salp Swarm with Crossover (HCSSC) algorithm for an UWSN to maximize the network resource efficiency.This last is a global metric that jointly considers the energy and the spectral efficiencies to balance the power consumption and the bandwidth usage.The algorithm improves the standard metaheuristic SSA by the use of logistic chaotic map in the generation of the initial population and the deployment of the uniform crossover operator to compute the final solution.At each packet transmission,the HCSSC is applied to provide the optimal source and relay nodes powers considering the remaining nodes batteries capacities constraints.Simulations showed that the integration of the chaotic map in the population initialization and the use of the crossover method in the positions’updates improved the resource efficiency compared to the standard SSA for different nodes batteries capacities and different maximum allowed powers.Also,the use of the HCSSC algorithm offered a better relay power conservation proved by the minimization of the average consumed relay power per transmission and the maximization of the average remaining relay battery per transmission.Moreover,the efficiency of the proposed algorithm is demonstrated in the case where the relay node has a higher battery capacity than the source node and can forward packets considering higher maximum power.As future work,the efficiency of the proposed HCSSC algorithm in multi-relay UWSN,where many relay nodes cooperate with source nodes to transmit sensory data to the base station,will be addressed.Thus,the impact of the numbers of variables on HCSSC algorithm performance will be effectively studied.Moreover,the impact of the data packet size on the RE performance will be studied.

Funding Statement:The authors received no specific funding for this study.

Conflicts of Interest:The authors declare that they have no conflicts of interest to report regarding the present study.