Modeling,Analysis and Validation of Friendship Paradox in Evolving Networks

Friendship paradox states that individuals are likely to have fewer friends than their friends do,on average.Despite of its wide existence and appealing applications in real social networks,the mathematical understanding of friendship paradox is very limited.Only few works provide theoretical evidence of single-step and multi-step friendship paradoxes,given that the neighbors of interest are onehop and multi-hop away from the target node.However,they consider non-evolving networks,as opposed to the topology of real social networks that are constantly growing over time.We are thus motivated to present a first look into friendship paradox in evolving networks,where newly added nodes preferentially attach themselves to those with higher degrees.Our analytical verification of both single-step and multistep friendship paradoxes in evolving networks,along with comparison to the non-evolving counterparts,discloses that“friendship paradox is even more paradoxical in evolving networks”,primarily from three aspects:1)we demonstrate a strengthened effect of single-step friendship paradox in evolving networks,with a larger probability(more than 0.8)of a random node’s neighbors having higher average degree than the random node itself;2)we unravel higher effectiveness of multi-step friendship paradox in seeking for influential nodes in evolving networks,as the rate of reaching the max degree node can be improved by a factor of at least Θ(t^(2/3))with t being the network size;3)we empirically verify our findings through both synthetic and real datasets,which suggest high agreements of results and consolidate the reasonability of evolving model for real social networks.

Modeling and Comprehensive Review of Signaling Storms in 3GPP-Based Mobile Broadband Networks:Causes,Solutions,and Countermeasures

Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.

Learning the parameters of a class of stochastic Lotka-Volterra systems with neural networks

In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.

Predicting outcomes using neural networks in the intensive care unit

Patients in intensive care units(ICUs)require rapid critical decision making.Modern ICUs are data rich,where information streams from diverse sources.Machine learning(ML)and neural networks(NN)can leverage the rich data for prognostication and clinical care.They can handle complex nonlinear relation-ships in medical data and have advantages over traditional predictive methods.A number of models are used:(1)Feedforward networks;and(2)Recurrent NN and convolutional NN to predict key outcomes such as mortality,length of stay in the ICU and the likelihood of complications.Current NN models exist in silos;their integration into clinical workflow requires greater transparency on data that are analyzed.Most models that are accurate enough for use in clinical care operate as‘black-boxes’in which the logic behind their decision making is opaque.Advan-ces have occurred to see through the opacity and peer into the processing of the black-box.In the near future ML is positioned to help in clinical decision making far beyond what is currently possible.Transparency is the first step toward vali-dation which is followed by clinical trust and adoption.In summary,NNs have the transformative ability to enhance predictive accuracy and improve patient management in ICUs.The concept should soon be turning into reality.

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

As an optical processor,a diffractive deep neural network(D2NN)utilizes engineered diffractive surfaces designed through machine learning to perform all-optical information processing,completing its tasks at the speed of light propagation through thin optical layers.With sufficient degrees of freedom,D2NNs can perform arbitrary complex-valued linear transformations using spatially coherent light.Similarly,D2NNs can also perform arbitrary linear intensity transformations with spatially incoherent illumination;however,under spatially incoherent light,these transformations are nonnegative,acting on diffraction-limited optical intensity patterns at the input field of view.Here,we expand the use of spatially incoherent D2NNs to complex-valued information processing for executing arbitrary complex-valued linear transformations using spatially incoherent light.Through simulations,we show that as the number of optimized diffractive features increases beyond a threshold dictated by the multiplication of the input and output space-bandwidth products,a spatially incoherent diffractive visual processor can approximate any complex-valued linear transformation and be used for all-optical image encryption using incoherent illumination.The findings are important for the all-optical processing of information under natural light using various forms of diffractive surface-based optical processors.

Application of virtual reality technology improves the functionality of brain networks in individuals experiencing pain

Medical procedures are inherently invasive and carry the risk of inducing pain to the mind and body.Recently,efforts have been made to alleviate the discomfort associated with invasive medical procedures through the use of virtual reality(VR)technology.VR has been demonstrated to be an effective treatment for pain associated with medical procedures,as well as for chronic pain conditions for which no effective treatment has been established.The precise mechanism by which the diversion from reality facilitated by VR contributes to the diminution of pain and anxiety has yet to be elucidated.However,the provision of positive images through VR-based visual stimulation may enhance the functionality of brain networks.The salience network is diminished,while the default mode network is enhanced.Additionally,the medial prefrontal cortex may establish a stronger connection with the default mode network,which could result in a reduction of pain and anxiety.Further research into the potential of VR technology to alleviate pain could lead to a reduction in the number of individuals who overdose on painkillers and contribute to positive change in the medical field.

Unlocking the future:Mitochondrial genes and neural networks in predicting ovarian cancer prognosis and immunotherapy response

BACKGROUND Mitochondrial genes are involved in tumor metabolism in ovarian cancer(OC)and affect immune cell infiltration and treatment responses.AIM To predict prognosis and immunotherapy response in patients diagnosed with OC using mitochondrial genes and neural networks.METHODS Prognosis,immunotherapy efficacy,and next-generation sequencing data of patients with OC were downloaded from The Cancer Genome Atlas and Gene Expression Omnibus.Mitochondrial genes were sourced from the MitoCarta3.0 database.The discovery cohort for model construction was created from 70% of the patients,whereas the remaining 30% constituted the validation cohort.Using the expression of mitochondrial genes as the predictor variable and based on neural network algorithm,the overall survival time and immunotherapy efficacy(complete or partial response)of patients were predicted.RESULTS In total,375 patients with OC were included to construct the prognostic model,and 26 patients were included to construct the immune efficacy model.The average area under the receiver operating characteristic curve of the prognostic model was 0.7268[95% confidence interval(CI):0.7258-0.7278]in the discovery cohort and 0.6475(95%CI:0.6466-0.6484)in the validation cohort.The average area under the receiver operating characteristic curve of the immunotherapy efficacy model was 0.9444(95%CI:0.8333-1.0000)in the discovery cohort and 0.9167(95%CI:0.6667-1.0000)in the validation cohort.CONCLUSION The application of mitochondrial genes and neural networks has the potential to predict prognosis and immunotherapy response in patients with OC,providing valuable insights into personalized treatment strategies.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

The Immense Impact of Reverse Edges on Large Hierarchical Networks

Hierarchical networks are frequently encountered in animal groups,gene networks,and artificial engineering systems such as multiple robots,unmanned vehicle systems,smart grids,wind farm networks,and so forth.The structure of a large directed hierarchical network is often strongly influenced by reverse edges from lower-to higher-level nodes,such as lagging birds’howl in a flock or the opinions of lowerlevel individuals feeding back to higher-level ones in a social group.This study reveals that,for most large-scale real hierarchical networks,the majority of the reverse edges do not affect the synchronization process of the entire network;the synchronization process is influenced only by a small part of these reverse edges along specific paths.More surprisingly,a single effective reverse edge can slow down the synchronization of a huge hierarchical network by over 60%.The effect of such edges depends not on the network size but only on the average in-degree of the involved subnetwork.The overwhelming majority of active reverse edges turn out to have some kind of“bunching”effect on the information flows of hierarchical networks,which slows down synchronization processes.This finding refines the current understanding of the role of reverse edges in many natural,social,and engineering hierarchical networks,which might be beneficial for precisely tuning the synchronization rhythms of these networks.Our study also proposes an effective way to attack a hierarchical network by adding a malicious reverse edge to it and provides some guidance for protecting a network by screening out the specific small proportion of vulnerable nodes.

Source localization in signed networks with effective distance

While progress has been made in information source localization,it has overlooked the prevalent friend and adversarial relationships in social networks.This paper addresses this gap by focusing on source localization in signed network models.Leveraging the topological characteristics of signed networks and transforming the propagation probability into effective distance,we propose an optimization method for observer selection.Additionally,by using the reverse propagation algorithm we present a method for information source localization in signed networks.Extensive experimental results demonstrate that a higher proportion of positive edges within signed networks contributes to more favorable source localization,and the higher the ratio of propagation rates between positive and negative edges,the more accurate the source localization becomes.Interestingly,this aligns with our observation that,in reality,the number of friends tends to be greater than the number of adversaries,and the likelihood of information propagation among friends is often higher than among adversaries.In addition,the source located at the periphery of the network is not easy to identify.Furthermore,our proposed observer selection method based on effective distance achieves higher operational efficiency and exhibits higher accuracy in information source localization,compared with three strategies for observer selection based on the classical full-order neighbor coverage.

A Review of Computing with Spiking Neural Networks

Artificial neural networks(ANNs)have led to landmark changes in many fields,but they still differ significantly fromthemechanisms of real biological neural networks and face problems such as high computing costs,excessive computing power,and so on.Spiking neural networks(SNNs)provide a new approach combined with brain-like science to improve the computational energy efficiency,computational architecture,and biological credibility of current deep learning applications.In the early stage of development,its poor performance hindered the application of SNNs in real-world scenarios.In recent years,SNNs have made great progress in computational performance and practicability compared with the earlier research results,and are continuously producing significant results.Although there are already many pieces of literature on SNNs,there is still a lack of comprehensive review on SNNs from the perspective of improving performance and practicality as well as incorporating the latest research results.Starting from this issue,this paper elaborates on SNNs along the complete usage process of SNNs including network construction,data processing,model training,development,and deployment,aiming to provide more comprehensive and practical guidance to promote the development of SNNs.Therefore,the connotation and development status of SNNcomputing is reviewed systematically and comprehensively from four aspects:composition structure,data set,learning algorithm,software/hardware development platform.Then the development characteristics of SNNs in intelligent computing are summarized,the current challenges of SNNs are discussed and the future development directions are also prospected.Our research shows that in the fields of machine learning and intelligent computing,SNNs have comparable network scale and performance to ANNs and the ability to challenge large datasets and a variety of tasks.The advantages of SNNs over ANNs in terms of energy efficiency and spatial-temporal data processing have been more fully exploited.And the development of programming and deployment tools has lowered the threshold for the use of SNNs.SNNs show a broad development prospect for brain-like computing.

Hybrid millimeter wave heterogeneous networks with spatially correlated user equipment

In this paper,we analyze a hybrid Heterogeneous Cellular Network(HCNet)framework by deploying millimeter Wave(mmWave)small cells with coexisting traditional sub-6GHz macro cells to achieve improved coverage and high data rate.We consider randomly-deployed macro base stations throughout the network whereas mmWave Small Base Stations(SBSs)are deployed in the areas with high User Equipment(UE)density.Such user centric deployment of mmWave SBSs inevitably incurs correlation between UE and SBSs.For a realistic scenario where the UEs are distributed according to Poisson cluster process and directional beamforming with line-of-sight and non-line-of-sight transmissions is adopted for mmWave communication.By using tools from stochastic geometry,we develop an analytical framework to analyze various performance metrics in the downlink hybrid HCNets under biased received power association.For UE clustering we considered Thomas cluster process and derive expressions for the association probability,coverage probability,area spectral efficiency,and energy efficiency.We also provide Monte Carlo simulation results to validate the accuracy of the derived expressions.Furthermore,we analyze the impact of mmWave operating frequency,antenna gain,small cell biasing,and BSs density to get useful engineering insights into the performance of hybrid mmWave HCNets.Our results show that network performance is significantly improved by deploying millimeter wave SBS instead of microwave BS in hot spots.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

A Novel Approach to Energy Optimization:Efficient Path Selection in Wireless Sensor Networks with Hybrid ANN

In pursuit of enhancing the Wireless Sensor Networks(WSNs)energy efficiency and operational lifespan,this paper delves into the domain of energy-efficient routing protocols.InWSNs,the limited energy resources of Sensor Nodes(SNs)are a big challenge for ensuring their efficient and reliable operation.WSN data gathering involves the utilization of a mobile sink(MS)to mitigate the energy consumption problem through periodic network traversal.The mobile sink(MS)strategy minimizes energy consumption and latency by visiting the fewest nodes or predetermined locations called rendezvous points(RPs)instead of all cluster heads(CHs).CHs subsequently transmit packets to neighboring RPs.The unique determination of this study is the shortest path to reach RPs.As the mobile sink(MS)concept has emerged as a promising solution to the energy consumption problem in WSNs,caused by multi-hop data collection with static sinks.In this study,we proposed two novel hybrid algorithms,namely“ Reduced k-means based on Artificial Neural Network”(RkM-ANN)and“Delay Bound Reduced kmeans with ANN”(DBRkM-ANN)for designing a fast,efficient,and most proficient MS path depending upon rendezvous points(RPs).The first algorithm optimizes the MS’s latency,while the second considers the designing of delay-bound paths,also defined as the number of paths with delay over bound for the MS.Both methods use a weight function and k-means clustering to choose RPs in a way that maximizes efficiency and guarantees network-wide coverage.In addition,a method of using MS scheduling for efficient data collection is provided.Extensive simulations and comparisons to several existing algorithms have shown the effectiveness of the suggested methodologies over a wide range of performance indicators.

Anomalous node detection in attributed social networks using dual variational autoencoder with generative adversarial networks

Many types of real-world information systems, including social media and e-commerce platforms, can be modelled by means of attribute-rich, connected networks. The goal of anomaly detection in artificial intelligence is to identify illustrations that deviate significantly from the main distribution of data or that differ from known cases. Anomalous nodes in node-attributed networks can be identified with greater precision if both graph and node attributes are taken into account. Almost all of the studies in this area focus on supervised techniques for spotting outliers. While supervised algorithms for anomaly detection work well in theory, they cannot be applied to real-world applications owing to a lack of labelled data. Considering the possible data distribution, our model employs a dual variational autoencoder (VAE), while a generative adversarial network (GAN) assures that the model is robust to adversarial training. The dual VAEs are used in another capacity: as a fake-node generator. Adversarial training is used to ensure that our latent codes have a Gaussian or uniform distribution. To provide a fair presentation of the graph, the discriminator instructs the generator to generate latent variables with distributions that are more consistent with the actual distribution of the data. Once the model has been learned, the discriminator is used for anomaly detection via reconstruction loss which has been trained to distinguish between the normal and artificial distributions of data. First, using a dual VAE, our model simultaneously captures cross-modality interactions between topological structure and node characteristics and overcomes the problem of unlabeled anomalies, allowing us to better understand the network sparsity and nonlinearity. Second, the proposed model considers the regularization of the latent codes while solving the issue of unregularized embedding techniques that can quickly lead to unsatisfactory representation. Finally, we use the discriminator reconstruction loss for anomaly detection as the discriminator is well-trained to separate the normal and generated data distributions because reconstruction-based loss does not include the adversarial component. Experiments conducted on attributed networks demonstrate the effectiveness of the proposed model and show that it greatly surpasses the previous methods. The area under the curve scores of our proposed model for the BlogCatalog, Flickr, and Enron datasets are 0.83680, 0.82020, and 0.71180, respectively, proving the effectiveness of the proposed model. The result of the proposed model on the Enron dataset is slightly worse than other models;we attribute this to the dataset’s low dimensionality as the most probable explanation.

Correcting Climate Model Sea Surface Temperature Simulations with Generative Adversarial Networks:Climatology,Interannual Variability,and Extremes

Climate models are vital for understanding and projecting global climate change and its associated impacts.However,these models suffer from biases that limit their accuracy in historical simulations and the trustworthiness of future projections.Addressing these challenges requires addressing internal variability,hindering the direct alignment between model simulations and observations,and thwarting conventional supervised learning methods.Here,we employ an unsupervised Cycle-consistent Generative Adversarial Network(CycleGAN),to correct daily Sea Surface Temperature(SST)simulations from the Community Earth System Model 2(CESM2).Our results reveal that the CycleGAN not only corrects climatological biases but also improves the simulation of major dynamic modes including the El Niño-Southern Oscillation(ENSO)and the Indian Ocean Dipole mode,as well as SST extremes.Notably,it substantially corrects climatological SST biases,decreasing the globally averaged Root-Mean-Square Error(RMSE)by 58%.Intriguingly,the CycleGAN effectively addresses the well-known excessive westward bias in ENSO SST anomalies,a common issue in climate models that traditional methods,like quantile mapping,struggle to rectify.Additionally,it substantially improves the simulation of SST extremes,raising the pattern correlation coefficient(PCC)from 0.56 to 0.88 and lowering the RMSE from 0.5 to 0.32.This enhancement is attributed to better representations of interannual,intraseasonal,and synoptic scales variabilities.Our study offers a novel approach to correct global SST simulations and underscores its effectiveness across different time scales and primary dynamical modes.

Regulatable Orthotropic 3D Hybrid Continuous Carbon Networks for Efficient Bi-Directional Thermal Conduction

Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task.Herein,an orthotropic three-dimensional(3D)hybrid carbon network(VSCG)is fabricated by depositing vertically aligned carbon nanotubes(VACNTs)on the surface of a horizontally oriented graphene film(HOGF).The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy.After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsi-loxane(PDMS),VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained.The highest in-plane and through-plane thermal conduc-tivities of the composites are 113.61 and 24.37 W m^(-1)K^(-1),respectively.The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance.In addition,the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3%compared to that of a state-of-the-art thermal pad.This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Falcon Optimization Algorithm-Based Energy Efficient Communication Protocol for Cluster-Based Vehicular Networks

Rapid development in Information Technology(IT)has allowed several novel application regions like large outdoor vehicular networks for Vehicle-to-Vehicle(V2V)transmission.Vehicular networks give a safe and more effective driving experience by presenting time-sensitive and location-aware data.The communication occurs directly between V2V and Base Station(BS)units such as the Road Side Unit(RSU),named as a Vehicle to Infrastructure(V2I).However,the frequent topology alterations in VANETs generate several problems with data transmission as the vehicle velocity differs with time.Therefore,the scheme of an effectual routing protocol for reliable and stable communications is significant.Current research demonstrates that clustering is an intelligent method for effectual routing in a mobile environment.Therefore,this article presents a Falcon Optimization Algorithm-based Energy Efficient Communication Protocol for Cluster-based Routing(FOA-EECPCR)technique in VANETS.The FOA-EECPCR technique intends to group the vehicles and determine the shortest route in the VANET.To accomplish this,the FOA-EECPCR technique initially clusters the vehicles using FOA with fitness functions comprising energy,distance,and trust level.For the routing process,the Sparrow Search Algorithm(SSA)is derived with a fitness function that encompasses two variables,namely,energy and distance.A series of experiments have been conducted to exhibit the enhanced performance of the FOA-EECPCR method.The experimental outcomes demonstrate the enhanced performance of the FOA-EECPCR approach over other current methods.

Rao Algorithms-Based Structure Optimization for Heterogeneous Wireless Sensor Networks

The structural optimization of wireless sensor networks is a critical issue because it impacts energy consumption and hence the network’s lifetime.Many studies have been conducted for homogeneous networks,but few have been performed for heterogeneouswireless sensor networks.This paper utilizes Rao algorithms to optimize the structure of heterogeneous wireless sensor networks according to node locations and their initial energies.The proposed algorithms lack algorithm-specific parameters and metaphorical connotations.The proposed algorithms examine the search space based on the relations of the population with the best,worst,and randomly assigned solutions.The proposed algorithms can be evaluated using any routing protocol,however,we have chosen the well-known routing protocols in the literature:Low Energy Adaptive Clustering Hierarchy(LEACH),Power-Efficient Gathering in Sensor Information Systems(PEAGSIS),Partitioned-based Energy-efficient LEACH(PE-LEACH),and the Power-Efficient Gathering in Sensor Information Systems Neural Network(PEAGSIS-NN)recent routing protocol.We compare our optimized method with the Jaya,the Particle Swarm Optimization-based Energy Efficient Clustering(PSO-EEC)protocol,and the hybrid Harmony Search Algorithm and PSO(HSA-PSO)algorithms.The efficiencies of our proposed algorithms are evaluated by conducting experiments in terms of the network lifetime(first dead node,half dead nodes,and last dead node),energy consumption,packets to cluster head,and packets to the base station.The experimental results were compared with those obtained using the Jaya optimization algorithm.The proposed algorithms exhibited the best performance.The proposed approach successfully prolongs the network lifetime by 71% for the PEAGSIS protocol,51% for the LEACH protocol,10% for the PE-LEACH protocol,and 73% for the PEGSIS-NN protocol;Moreover,it enhances other criteria such as energy conservation,fitness convergence,packets to cluster head,and packets to the base station.