• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Identifying influential spreaders in social networks: A two-stage quantum-behaved particle swarm optimization with L′evy flight

    2024-01-25 07:14:58PengliLu盧鵬麗JimaoLan攬繼茂JianxinTang唐建新LiZhang張莉ShihuiSong宋仕輝andHongyuZhu朱虹羽
    Chinese Physics B 2024年1期
    關鍵詞:張莉

    Pengli Lu(盧鵬麗), Jimao Lan(攬繼茂), Jianxin Tang(唐建新)1,,?, Li Zhang(張莉),Shihui Song(宋仕輝), and Hongyu Zhu(朱虹羽)

    1Wenzhou Engineering Institute of Pump&Valve,Lanzhou University of Technology,Wenzhou 325100,China

    2School of Computer and Communication,Lanzhou University of Technology,Lanzhou 730050,China

    Keywords: social networks, influence maximization, metaheuristic optimization, quantum-behaved particle swarm optimization,L′evy flight

    1.Introduction

    As the pandemic spread around the world, lifestyles and the ways in which people obtain information were unexpectedly transferred to online mediums.[1]The virtual world has provided essential services, while reducing the distance between individuals.In particular,online social platforms,such as Facebook,WeChat,and TikTok,have promoted the growth of information consumption with the growing number of users and have nourished the emergence of online viral marketing on social networks.

    While online social networks provide convenience to the users, they also offer opportunities to companies to market their products.[3]Generally, companies first select a group of influential individuals as adopters and give them free access to the product in the expectation that they will recommend the product to their family and friends through word of mouth.If there are strong connections among these users to sustain the exponential spread of the message, then the viral marketing campaign will probably be successful and the referral behavior will, partly, influence the final choice of the purchasers.This scenario has applications in practical campaigns, such as rumor restriction,[4]where one would identify the superspreaders of rumors and restrict them to reduce the risk to society.

    Due to the inherent heterogeneity of individuals and the different ways of communication,the influence maximization(IM)problem here refers to the selection of a set of independent individuals that can maximize the coverage of information dissemination through the social relationships among the individuals.

    The IM problem was first proposed by Domingos and Richardson,[5]who suggested that we should consider the consumer market as a social network and model it as a Markov random field.Researchers have since proposed a series of IM algorithms to conduct an in-depth study.Kempeet al.[6]proved that the optimization problem of selecting the most influential nodes is NP-hard under the independent cascade(IC)model and linear threshold (LT) model, and proposed a natural greedy strategy, promising that the obtained solution is approximately within 63% of the optimal based on submodular function analysis.However, to accurately evaluate the marginal gain of influence of each candidate node,thousands of Monte Carlo simulations are required in each round of seed selection.This leads to the high time complexityO(knmR)of the algorithm.In particular,the running time of the algorithm increases exponentially with the increase of the network scale,thereby limiting its application in large-scale social networks.

    Researchers have subsequently tried to directly selectknodes as influential nodes according to the network topology features,such as degree centrality,[7]PageRank,[8]and so on.Alshahraniet al.[9]tried to combine the local influence with global influence of each node by using classical centrality metrics and proposed two algorithms, which are called Max-CDegKatzd-hops and MinCDegKatzd-hops.However, the approach of using network topology centrality fails to provide stable performance guarantees due to the lack of diversity in the selected nodes in different networks.In addition,community-based approaches have been developed to find influential nodes in the network.Bozorgiet al.[10]considered the influence of nodes within communities as a local influence and the influence of communities in the whole network as a global influence, and proposed INICIM to evaluate influential nodes by combining global influence and local influence.Caiet al.[11]explored the community property to improve the efficiency of the algorithm and proposed a communitybased greedy algorithm to identify the seed nodes.The advantage of community-based methods is that they provide a good trade-off between influence propagation and runtime.However, there are two problems: first,there is a lack of effective strategies to reduce the search space when selecting select seed nodes in large networks; and second, some of the algorithms suffer from the community overlap problem.

    In recent years, metaheuristic algorithms have been proposed to efficiently solve the IM problem.Zareieet al.[12]defined the cost function as the influence of nodes and the distance between them,and proposed a population-based gray wolf algorithm to solve the IM problem.Liet al.[13]proposed a discrete crow optimization metaheuristic algorithm to efficiently solve the IM problem.This type of algorithm has a significant improvement in running time when compared with the greedy strategy-based approach.There is also a substantial improvement in the solution accuracy when compared to the centrality-based methods.However, the existing metaheuristic algorithms have some limitations because they may fall into another local optimum when they try to get rid of the local optimum.With this in mind, we develop a discrete twostage metaheuristic optimization(DTMO)algorithm combining QPSO and L′evy flight to efficiently identify the influential nodes in the network.The main contributions of this paper are as follows:

    A new two-stage metaheuristic optimization algorithm framework was formulated to solve the IM problem.

    (i) The evolution rules of the quantum-behaved particle swarm optimization algorithm were modified and a discrete quantum-behaved particle swarm optimization(DQPSO)algorithm with nonlinearly decreasing randomized crossover operation was developed.

    (ii) A discrete L′evy flight (DLF) algorithm with automatic candidate pool selection based on greedy strategy was presented to enhance the performance of the DQPSO.

    (iii) A new method for population diversity calculation was designed and a novel algorithmic transformation strategy was introduced using this method.

    (iv) Our method was compared with other well-known methods on six real-world social networks.The experiments showed that our method can obtain comparable effects to the algorithms based on greedy strategy but with low time complexity.

    The rest of this paper is organized as follows.Section 2 reviews and discusses the related work.The problem description,the fitness assessment function,and the propagation model are given in Section 3.Section 4 presents the original QPSO and L′evy algorithms and describes our proposed framework in detail.The experimental results and analysis are given in Section 5.Finally, this study is summarized and future research directions are proposed in Section 6.

    2.Related work

    The IM problem was first proposed from a network perspective by Domingos and Richardson,[5]where the authors argued that consumers and the individuals around them are interconnected and have an interacting influence, which was modeled through Markov random field theory.Kempeet al.[6]transformed the IM problem into a combinatorial optimization problem.They adopted the Monte Carlo simulation mechanism to evaluate the influence of candidate nodes and introduced a greedy algorithm that was based on a hill-climbing search strategy to find the influential nodes.To reduce the expensive computational cost that arose from the Monte Carlo simulations,Leskovecet al.[14]developed an improved greedy algorithm that was scalable to large-scale social networks.Their experiments showed that it is 700 times faster than the simple greedy algorithm, while the results are nearly optimal.Subsequently, Goyalet al.[15]proposed a superior version called CELF++, which is 35%–55% faster than CELF.Following this seminal work, Zhanget al.[16]introduced a residual-based algorithm RCELF that can achieve good time efficiency, low memory consumption, and approximate quality of the results.Compared with the original greedy algorithm, the improved greedy algorithm has a certain degree of improvement in terms of time cost.However,some algorithms need to record the states during propagation to reduce the number of Monte Carlo simulations.Meanwhile,some algorithms increase the memory consumption,which means that they cannot be scaled to real large-scale social networks.

    Several heuristic algorithms have been put forward to tackle IM variations.Chenet al.[17]gave a more accurate discount value to the neighbors of the nodes selected as seeds and proposed the DegreeDiscount under the IC model with small propagation probability.Their experiments showed that the fine-tuned heuristic can provide a truly scalable solution to the IM problem with satisfactory propagation range and greater efficiency.Zareieet al.[18]proposed a special hierarchical measure to provide sufficient information about the topological position of the nodes,which ranks the influence of nodes more accurately than other state-of-the-art measures.Wanget al.[19]introduced a new metric, which they called node key degree,to measure the importance of nodes,and proposed the IT¨O algorithm to balance the conflict between exploration and exploitation.More recently, considering the dynamic nature and local aggregation factors on diffusion,Liet al.[20]adopted various entropy calculations to obtain the cohesion between neighboring nodes and then identify whether the node has the ability to become a propagable pioneer of other nodes.Menget al.[21]combined H-index,K-shell iteration factor,and clustering coefficient to attach weights to connected edges,which were in turn combined with the neighborhood, position and topology of nodes in the network to identify influential nodes.Liet al.[22]combined an improved gravity model with the community detection method to identify influence propagators in the network by finding bridge nodes in the network’s topology.Compared with traditional centrality methods, the methods combining the node characteristics can achieve a certain degree of improvement in accuracy.However,there is also a high time complexity,which makes it difficult to apply these methods to large-scale networks.In addition, some methods only measure the local structure of the network without diversity,and therefore lack solution stability when dealing with the IM problem.

    Some recent research interest has focused on the use of metaheuristic algorithms,broadly referring to the construction of low computational cost influence evaluating models and the utilization of appropriate evolutionary optimization strategies to view the IM problem as a fitness optimization problem.Jianget al.[23]were the first to use the fitness evaluation function, named expected diffusion value (EDV), as an influence evaluation measurement and proposed a simulated annealing algorithm to optimize EDV to identify a set of influential seed nodes.Their experimental results showed that the proposed algorithm runs 2–3 orders of magnitude faster than the state-of-the-art greedy algorithm,while improving the optimal solution accuracy.Gonget al.[24]proposed a discrete particle swarm optimization algorithm to map candidate seeds to particles in the population and established a novel evaluation function called local influence estimation (LIE), which can be evaluated more accurately under the IC model with lower time complexity.A metaheuristic discrete bat algorithm based on the collective intelligence of individual bats from the population was proposed by Tanget al.[25]This algorithm combines the evolutionary rules of the original bat algorithm and designs a seed node candidate pool to enhance the search capability of the algorithm, and finally achieves satisfactory experimental results.By analyzing the efficiency of the greedy algorithm,Cuiet al.[26]proposed a degree-descending search strategy and developed a more efficient evolutionary algorithm,named degree-descending search evolution(DDSE),through the operations of mutation,crossover,and greedy selection.Singhet al.[27]extended EDV to a two-hop area to realize a more accurate evaluation of seed nodes and proposed a variant of discrete particle swarm optimization(DPSO)based on the mechanism of learning automata.To maximize the distance between the seed nodes and ensure that different parts of the network are reached,Zareieet al.[12]solved the IM problem by optimizing the influence of nodes and the distance between them via the gray wolf optimization algorithm, which performed well in experimental results and had lower computational cost.Wanget al.[28]developed an influence evaluation model based on the total valuation and valuation differences of neighboring nodes.The authors developed an evolutionary strategy with local crossover and variation on natural moth evolutionary rules.Their experiments showed that the method is effective and robust in dealing with the IM problem.After conducting extensive experiments, Weskidaet al.[29]showed computationally that evolutionary algorithms not only overcome the limitations of greedy algorithms but also have several advantages, such as the transferability of their parameters.However,a reasonable discrete evolutionary mechanism can provide a balanced trade-off in terms of solution accuracy,time consumption,and even memory management.Therefore,the design of more effective influence evaluation mechanisms and more reasonable evolution mechanisms deserves further discussion.

    Quantum-behaved particle swarm optimization, as a swarm intelligence algorithm, was proposed by Sunet al.[30]from a quantum mechanical perspective by combining some features of the original particle swarm optimization(PSO)algorithm.Due to its efficiency and robustness, this algorithm has recently been applied to solve problems in various fields.For example, a hybrid inversion method based on the quantum particle swarm optimization method was introduced to solve the electromagnetic inverse problem by Yanget al.[31]Bajajet al.[32]proposed a discrete quantitative particle swarm optimization to improve the efficiency of test case prioritization.There are many other studies and applications of QPSO,such as path planning and the design of mobile robots in the workspace,[33]the constrained portfolio selection problem,[34]and the network clustering problem.[35]The results of these studies show that the QPSO algorithm provides strong robustness and solution efficiency thanks to its excellent evolutionary rules.

    QPSO has attracted the attention of many researchers due to the simplicity of the evolution equation,few control parameters, and fast convergence, but it also suffers from problems such as premature convergence.As a random wandering strategy,L′evy flight is mainly adopted by combinatorial optimization algorithms to effectively solve intractable optimization problems, such as the green scheduling problem of the flexible manufacturing cell.[36]However,the use of combinatorial algorithms based on QPSO and L′evy flight for the IM problem has not yet been reported in the literature.Therefore, exploring reasonable evolutionary mechanisms based on QPSO and L′evy flight to effectively identify influential nodes is worth further investigation.

    3.Preliminary information

    3.1.Influence maximization

    In the study of IM,a social network can be abstracted as a graphG=(V,E),whereV={v1,v2,...,vn}is the set of vertices, representing the individuals or organizations in the social network, andE={e1,e2,...,em}is the set of connected edges, indicating the existence of connections and cooperation between individuals or organizations in the social network.Note thatnandmdenote the number of vertices and the number of connected edges in the network,respectively.

    For a given graphG,a set ofk(k ?n)influential nodes are selected and ignited.The number of nodes activated by the seed set in the graph is expected to be maximized under a specific propagation model.This problem can be formalized as

    whereσ(·) is a measure of influence spread,Srepresents a candidate seed set withknodes andS?denotes the optimal seed set that maximizes the influence spread.

    3.2.Influence estimation function

    In the IM problem, the influence evaluation methods are divided into two main categories: (i) in the first category, a Monte Carlo simulation evaluates the propagation outcomes of the influential nodes;and(ii)in the second category,information based on the neighborhood structure characteristics of the nodes is utilized to estimate the diffusion effect of the seed nodes.

    Although the Monte Carlo simulation method can achieve high accuracy, it is not well satisfied with practical scenarios due to its tremendous computational complexity.Therefore,to reduce computational cost, Jianget al.[23]proposed an influence evaluation function based on the direct adjacent neighbors of its corresponding seed nodes.Inspired by the principle of two-degree theory on influence spreading,[37]Gonget al.[24]proposed a LIE function, which approximates the expected influence spread based on the two-hop neighbors area of the influential nodes,

    3.3.Influence propagation model

    Currently, there are three widely spreading models for simulating influence propagation in the IM problem: the IC model,the LT model,and the weighted cascade model.Based on the influence estimator, we employ the classical IC model to simulate the spread of influence in given networks.In the IC model, nodes have two states: active and inactive.The node can only be converted from the inactive state to the active state during the propagation process, and vice versa.In the diffusion process,when a node is activated at timet,it has a single chance at timet+1 to activate its direct inactive neighbors with probabilityp.When a new node is activated, it repeats the previous step until no new node is activated,the propagation ends,and all nodes in the active state are returned.

    4.Algorithm

    4.1.Quantum-behaved particle swarm optimization

    PSO, one of the most widely used swarm intelligence algorithms, was originally proposed by Kennedy and Eberhart.[38]PSO is often used to solve optimization problems due to its effectiveness and robustness.The original updating rules for PSO can be described as follows:

    wherewis the inertia weight,c1is the individual learning factor,c2is the social learning factor, andr1andr2are random numbers drawn uniformly from[0,1].Xi=(x1,x2,...,xd)andVi=(v1,v2,...,vd)represent the position vector of theith particle in thedth dimension and its corresponding velocity vector,respectively.Pbestidenotes the historical best position of particleiand Gbest is defined as the best position in the whole population.More specifically,the first partwVtiin Eq.(4)reflects the effect of the particle’s velocity at timeton its new velocity at timet+1,and the second partc1r1(Pbesti?Xti)and the third partc2r2(Gbest?Xti) imply that the particle learns information from its corresponding historical optimal position and global optimal position of the population,respectively.

    In recent years, many strategies have been proposed to enhance the performance of PSO, such as L′evy flight,[39]multi-swarm cooperative approach,[40]and fitness landscape features.[41]Inspired by quantum mechanics theory and trajectory analysis,[42]the ideology of quantum parallel mechanics is introduced into the framework of PSO to improve the performance of the algorithm,termed the quantum particle swarm optimisation algorithm,which outperforms traditional PSO in terms of exploration capability but with fewer control parameters.In QPSO,the position of theith particle is updated according to the following equations:

    where Pbestiand Gbest denote the historical best position and the global best position of theith particle, respectively.Piis defined as a local attractor.According to Eq.(6), it can be seen that the local attractorPiis located in a hyper-rectangle with Pbestiand Gbest as vertices.?anduare random numbers in the interval(0,1),βis a contraction-expansion factor,and mbest is the average of the best positions of all particles.Ifu <0.5, then the minus symbol “?” is selected in Eq.(7),otherwise the plus sign“+”will be selected.The framework of QPSO is given in Algorithm 1.

    Algorithm 1 The framework of QPSO.Initialize each particle’s position,Pbest,Gbest while T <Tmax do for each particle do Calculate local attractor Pi using Eq.(6)Compute particle’s position using Eq.(7)Update Pbest and Gbest end for end while Return the best position Gbest.

    4.2.L′evy flight

    In nature,most animals generally combine frequent shortdistance wandering with occasional long-distance travel when foraging food.As a random walk process,L′evy flight mainly consists of frequent local exploitation and occasional global exploration of the search space.The application of this mechanism to swarm-based intelligence algorithms can enhance the global search capability of the metaheuristics and prevent them from falling into premature convergence.By combining the characteristics of L′evy flight, some researchers have introduced hybrid swarm intelligence optimization algorithms[36]with promising results.The following are the rules to calculate the inherent step lengths of L′evy flight:

    wherelrepresents the random step.For the parameter setting,1<m ≤3,andμ~N(0,σ2μ),υ~N(0,σ2υ).υandυare random numbers obeying Gaussian distribution,whileσμandσυsatisfy the following equations:

    where Γ(·)denotes Gamma function.Figure 1 shows the trajectory of an individual wandering randomly in the search space under the L′evy flight mechanism.

    Fig.1.The trajectory of an individual after flying 1000 steps under theL′evy flight in two dimensions.

    4.3.Proposed algorithm

    The whole framework of the proposed algorithm for IM is outlined in Algorithm 2.The algorithm is divided into three main stages: (i) initialize the particles in the population; (ii)update the positions of the particles in the population according to the rules of DQPSO;and(iii)apply the L′evy flight strategy on the Gbest and finally output the optimal solution.

    Algorithm 2 The framework of the proposed algorithm.Input Graph G=(V,E),size of particle swarm n,size of seed set k,number of iterations Tmax and the contraction-expansion coefficient β1 and β2.Initialize particle position vectors X and Pbest Initialize historical diversity value HDV ←0 Initialize stages of algorithm evolution Stage ←1 Initialize iterator T ←0 Compute the shortest path length matrix M for graph G Compute fitness(X)and fitness(Pbest)Select out the initial global best position vector Gbest while T <Tmax do Update the stage of the evolution Stage and identify the algorithm to be selected Algorithm switch Algorithm do case Algorithm==“DQPSO”do Apply the DQPSO algorithm to update X Update Pbest and Gbest end case case Algorithm==“DLF”do Apply the DLF algorithm to update Gbest end case end switch T ←T+1 end while Output Output the best position Gbest as the seed set S.

    4.3.1.Initialization

    During the initialization phase,a degree-based initialization strategy similar to that of DPSO is employed.First, all particles in the population select the topknodes with the greatest degree in the graphG.At the same time,to guarantee the diversity of the population, a random replacement operation on the nodes in each particle is performed,i.e.,when the random value is greater than 0.5,the corresponding node will be replaced by any node in the graphGthat has not been selected as a candidate node in that particle.The same approach is utilized when initializing Pbest.The detailed initialization procedure is given in Algorithm 3.

    Algorithm 3 Initialization.Input Graph G=(V,E),the size of particle swarm n,size of seed set k.for each i ≤n do Xi ←degree(G,k)for each element xij ∈Xi do if random>0.5 then xij ←replace(xij,N)end if end for end for Output The initial position vector X.

    4.3.2.Discrete quantum-behaved particle swarm optimization algorithm

    The original QPSO algorithm is only applicable to solve optimization problems with continuous space.Therefore, the update rules are redesigned in discrete form to solve the IM problem.The new evolutionary mechanism of DQPSO is defined as

    whereuis a random value between 1/e and 1,Xtiis the position vector of theith particle at iterationt,βrepresents contraction-expansion coefficient, andβln(1/u) is redefined as the crossover probability, as described by the following equation:

    forβ1=1,β2=0.5.Tmaxrepresents the maximum number of iterations.From Eqs.(10) and (11), it is obvious thatβgenerally varies nonlinearly from 1 to 0.Whenβreaches a large value in the first few steps, the crossover ability of the particles becomes stronger,which indicates that the particles have stronger exploration ability.In the later stages, the crossover ability of the particles gradually becomes weaker and ostensibly the particles gradually tend to converge.However, since ln(1/u)is a random value,there is also a lower probability of obtaining a stronger crossover ability, which to some extent increases the diversity of the population.

    In Eq.(10),Ptiis given by

    where?is a random value drawn from [0,1],k?is rounded upward to determine the number of nodes to be randomly selected in Gbest or Pbest, and then the selected nodes are merged to obtain the local attractorPi.When selecting nodes at random, it is important to ensure that the selected nodes cannot be duplicated.The specific operation is shown in Fig.2, assuming that Pbesti={1,5,10,17,20}, Gbest={3,5,11,14,19},k=5,?=0.36,thenk?=2;therefore,two nodes in Pbset and three nodes in Gbest need to be taken for combination.

    Fig.2.Illustration of how to obtain local attractor Pi.The blue boxes represent the nodes to be randomly selected.

    In the original QPSO algorithm, mbest is the average of the best positions of all of the particles.When mbest takes this case, it does not guide the particles very well, and therefore mbest is redefined as the average of the optimal positions of the top three particles.First,the top three particles are divided into two portions,the first portion includes the common nodes belonging to the three particles,and the second portion maintains the remaining nodes in the particles.All of the nodes in the first portion are then selected into Mbest.Finally, the nodes are randomly selected from the second component until there areknodes in the Mbest.A detailed illustration of this operator is shown in Fig.3.It is assumed that the top three historical optimal positions are Pbest1={1,3,4,7,11},Pbest2={1,4,6,8,10},Pbest3={1,5,4,8,11},the identical nodes are then{1,4},and the remaining nodes are{3,10,11,6,8,7,5},finally Mbest={1,4,8,5,10}is obtained by the restructuring mechanism.

    Fig.3.Illustration of the calculation of Mbest.The blue boxes represent common nodes belonging to all three particles and the green boxes represent randomly selected nodes.

    The operator∩in Eq.(10)is a logical operator that is defined as a similar intersection operation to determine whether there are different elements in Mbest andXi.When a node inXiis a unique node to Mbest, the crossover probabilityβln(1/u)is calculated.Ifβln(1/u)is greater than a random value drawn from[0,1],then a node in Mbest that is not inXiis selected for the intersection exchange operation;otherwise,no operation is performed on that node.The⊕operation is the process of greedy search of the local attractorPsubject to the new particle position vectorXiobtained by the crossover operation.In this process, the nodes in the local attractorPithat are identical to those inXiare removed and then treated as a pool of candidate nodes.For each node inXi,an arbitrary node from the candidate node pool is selected to replace it.Meanwhile, the selected node is removed from the candidate node pool.When the position of the node after being replaced is better than the previous position, then any node from the candidate node pool continues to be selected for replacement;otherwise, the same operation is performed for the next node inXi.It should be noted that the operation is terminated when there is no node in the candidate pool.The framework of the DQPSO algorithm for IM is presented in Algorithm 4.

    Algorithm 4 DQPSO algorithm framework.Input Particle position vectors X,the size of particle swarm n,size of seed set k,particle local attractor position vectors P attr,iterator T,the mean of the best position of the top three particles Mbest,the number of iterations Tmax,and the contraction-expansion coefficient β1 and β2.for each i ≤n do if Xij /∈M best do Compute the probability of mutation pmu if pmu >rand do Xi ←replace(Xi j,Mbest)end if end if end for for each i ≤n do candidate pool= /0 if P attrij /∈Xi do cand pool ←cand pool∪P attrij end if X'i ←Xi for each j ≤k do if cand pool== /0 do break end if Flag ←False while Flag==False do if cand pool== /0 do break end if X'ij ←replace(X'i j,cand pool)if fitness(X'i)>fitness(Xi)do Xij ←X'ij else do Flag ←True end if end while X'ij ←Xij end for Xi ←X'i end for Output Output particle position vectors X.

    4.3.3.Algorithm transformation

    To avoid the DQPSO algorithm converging swiftly to a suboptimal global solution,a metric to assess the diversity of the population is conceived.The diversity metric can be formulated as follows:

    wherenis the size of the particle swarm,kis the size of the seed set, and the∩operation returns the number of identical nodes in the two position vectors.It can be seen from Eq.(13)that the diversity value becomes larger and the diversity of the population decreases with the evolution of the algorithm.When the diversity value of the population is less than its historical,it indicates that the population has converged to a stagnation.In this case,the algorithm will perform the second stage,i.e.,discrete L′evy flight,to identify a more optimal position.The framework of updating stage and identifying algorithm is given in Algorithm 5.

    Algorithm 5 Update Stage and identify Algorithm.Input.Particle position vectors X,particle best position vectors Pbest,evolution stage Stage,and historical diversity value HDV.switch Stage do case Stage==1 do Compute Mbest Compute P attr Compute the current diversity value CDV if CDV?HDV >0 do HDV=CDV Algorithm=“DQPSO”end if else do Stage=2 Algorithm=“DLF”end case case Stage==2 do Algorithm=“DLF”end case end switch Output Output the stage of the evolution Stage and identify the algorithm to be selected Algorithm.

    4.3.4.Discrete L′evy flight

    The original L′evy flight is not available to solve discrete IM problem directly.Therefore, a discrete L′evy flight mechanism based on the shortest path length of the network is proposed.

    Since the previous stage evolves through the DQPSO algorithm, the population tends to remain in an optimal state.Therefore,there is no need to perform discrete L′evy flight for all of the particles in the population but only for the Gbest.The shortest path length matrixMof graphGis first obtained in the initialization phase,and then L′evy flight step lengthlis derived from Eq.(7)and rounded upward.During the searching process, each node in Gbest will be replaced with a randomly selected node from the candidate pool, which is composed of nodes in Gbest with the same shortest path length in the network and the same flight step lengthlbut not the same as in Gbest.When the step flight lengthlis greater than the maximum shortest path length of that node in the network,the flight lengthltakes the maximum shortest path length of that node in the network.The detailed replacement process is the same as the⊕operation mentioned earlier.The framework of the DLF algorithm for IM is described in Algorithm 6.

    Algorithm 6 DLF framework of algorithm.Input The best position Gbest and the shortest path length matrix M.Gbest'←Gbest for each i ≤k do compute the step size of the L′evy flight l cand pool ←M(Gbest(i),l)if cand pool== /0 do break end if Flag ←False while Flag==False do if cand pool== /0 do break end if Gbest'i ←replace(Gbest'i,cand pool)if fitness(Gbest')>fitness(Gbest)do Gbest ←Gbest'else do Flag ←True end if end while Gbest'←Gbest end for Output Output the best position Gbest'.

    5.Experiment and analysis

    5.1.Network data sets and baselines

    To verify the performance of the proposed DTMO on the IM problem,we conducted extensive experiments on six realworld networks that were collected from NR with the topological characteristics shown in Table 1,where〈k〉represents the average node degree,Cis the average clustering coefficient,andACrepresents the assortativity coefficient.Figure 4 shows the node degree distribution of the networks.The results of influence spread are compared with several state-of-the-art methods, including the degree centrality (DC) based on the network topology, discrete moth-flame optimization (DMFO),[28]DDSE,[26]DPSO,[24]learning automatabased discrete particle swarm optimization(LAPSO),[27]costeffective lazy forward (CELF)[14]algorithm based on greedy strategy,and layered gravity bridge algorithm(LGB).[22]

    Table 1.Topological characteristics of the six social networks.

    5.2.Parameter configuration

    To test the scalability of the algorithm, the size of the seed setkwas set to 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50, respectively, the maximum iterationsTmaxwere 100 and the population size was chosen as 100.In DMFO,the amplification factor was set toc=4, the mutation probability was 0.1,and the coefficientωwas 0.8.In DPSO and LAPSO,the learning factors were set toc1=c2=2,the inertia weight was 0.8,and additionally the values of the reward and punishment parameters were set toar=bp=0.6 in LAPSO.In DDSE,the probabilities of mutation, crossover, and diversity operations were set to 0.1, 0.4, and 0.6, respectively.The number of Monte Carlo simulations for CELF was set to 10000.In addition, 1000 Monte Carlo simulations were performed on the optimal set of seeds obtained by all of the other algorithms to obtain the average spreading coverage under the IC model with propagation probabilityp=0.01.

    5.3.Comparison of the LIE evaluation

    To validate that DQPSO and DLF play a desirable effect on their respective phases, we compared the fitness values of the obtained optimal seed sets of DTMO,DQPSO,and DPSO.Figure 5 shows the average LIE of different seed sizekon the six networks.

    In the Delaunay network,as shown in Fig.5(a),all three algorithms perform competitive results over the entire interval, and a detail view atk=50 shows that DTMO gains a better marginal gain.In Blog and CaGrQc, the algorithms gradually show visible gaps as the seed numberkincreases and the gap gradually becomes more evident as the network’s scale increases.In Figs.5(d) and 5(e), it can be seen that DPSO is highly prone to suboptimal solutions, while DTMO and DQPSO have no evident instability, which indicates that the proposed algorithm has strong robustness.It is worth mentioning that, except for the Ca-GrQc network, the fitness values of DTMO and DQPSO are not significantly different throughout the interval ofk.In contrast, in Fig.5(c), there is a significant gap between the algorithm DTMO and DQPSO atk=50.This indicates that the random wandering strategy in the second stage of the algorithm compensates for the deficiency of the DQPSO algorithm falling into premature convergence.Overall,both the two-stage DTMO and the separate DQPSO achieved satisfactory results in all six networks.

    Fig.5.Comparison of LIE optimization of the three algorithms in the six social networks at different seed size k under p=0.01.

    5.4.Performance comparison of the typical algorithms

    To further validate the ability of the proposed DTMO algorithm to solve the IM problem,six state-of-the-art methods were selected to compare with DTMO in terms of the number of nodes activated in the network under the IC model.As shown in Fig.6, the spread size achieved by DTMO shows that it can return satisfactory propagation in the six networks.Moreover,it can be seen that DTMO has the most stable performance in different scenarios.

    More specially, in the Delaunay network, it can be observed that the algorithms achieve similar influence spread throughout the range of 5≤k ≤50,and the proposed DTMO algorithm achieves the best result.In the Blog network shown in Fig.6(b), comparable results are obtained for all six algorithms except DMFO on the interval of 15≤k ≤25.There is a significant decline in the effectiveness of DPSO whenk ≥30.Atk=50,DDSE outperforms the others by a significant margin,while DTMO comes in a close second.

    Figure 6(c)shows that CELF,DMFO,LGB,and DTMO can maintain good momentum whenk ≥15.LAPSO and LGB algorithms achieve similar performance over the entire interval,while the other algorithms show different levels of performance degradation.Atk=45 andk=50, both DTMO and DMFO outperformed the CELF and achieved the best influence spread.In addition,DTMO and DMFO achieved one optimal result each,indicating that both DTMO and DMFO have strong competitiveness in this network.Figure 6(d)shows that the ranking of all algorithms remains essentially constant over the entire range of seed size, with CELF and DTMO achieving comparable performance, and LAPSO coming in second.It should be noted that in Figs.6(c)and 6(d),both DDSE and DC showed lower efficiency.This is probably due to the fact that in both networks only the one-hop neighbors of the candidate nodes are evaluated,which leads to the problem of overlapped influence propagation in the propagation process.

    In Fig.6(e), similar experimental results were obtained by LAPSO,CELF,DC,LGB,and DTMO.More specifically,LAPSO performed the best in the interval of 15≤k ≤45,while CELF and DTMO were entangled with each other in the influence size.Atk=50,DTMO,LGB,and LAPSO obtained the same results.It is worth mentioning that the topology of the network is a star structure, so DC can achieve satisfactory results.Meanwhile,DC degenerated atk=50 because it suffers from the influence overlap problem as the number of selected nodes increases.In the AstroPh network of Fig.6(f),DMFO and DTMO have achieved relatively high performance but were slightly inferior to CELF.

    In summary, DTMO achieved comparable or even better results than CELF in most cases, indicating that DTMO can effectively solve the IM problem.DC and DDSE performed poorly in some networks because they only evaluated the one-hop neighbors of the nodes, resulting in inaccurate evaluation of influence.Although DPSO was more accurate in evaluating candidate nodes,the algorithm tended to be stagnant because its local search strategy easily returns the local optimum.LGB offers a dramatic improvement in influence dissemination when compared to traditional centrality-based approaches.LAPSO and DMFO achieved desirable results in some scenarios.This indicates that the improvement of PSO and the searching strategy in DMFO are very effective, and the respective evaluation functions can accurately evaluate the influence of the nodes.

    Fig.6.Comparison of the influence spread size of DTMO against six other algorithms under the IC model(p=0.01)on the six networks.

    5.5.Statistical tests

    To demonstrate the effectiveness of the proposed DTMO algorithm in identifying influence spreaders,a statistical analysis was employed to test the statistical significance of the performance differences of the six algorithms on the six networks,the results are reported in Table 2.In all six networks,the scenarios ofk=10,20,30,40, and 50 were chosen as independent problems,and hypotheses were tested for each scenario.Wilcoxon rank sum test at the confidence level of 0.05 was conducted to show the superior performance of DTMO over the other six algorithms.

    From the statistical results, it can be seen that the influence propagation obtained by the DTMO algorithm is better than DPSO algorithm on the whole selected interval.DDSE, DMFO, DC, and LGB have similar performance,while LAPSO has slightly better performance.At the same time, it can give a similar performance guarantee when compared with CELF.

    Table 2.Statistical results of the Wilcoxon test for the seven algorithms at α =0.05.

    6.Conclusion

    In this paper,a DTMO algorithm combining QPSO with L′evy is proposed to solve the IM problem.In the first stage of the algorithm,the evolutionary rules of the redefined DQPSO are used to update the particle positions to make the particles fly to a more optimal position.At the same time, population diversity is defined to determine whether the particles in the population converge to the optimal.When the particles in the population are in convergence, the second stage of the algorithm is performed to obtain the global optimal solution by updating the optimal positions of the particles in the population using the redesigned DLF mechanism.Finally, experiments with other well-known algorithms on six real networks show that the proposed algorithm obtains comparable or even slightly superior results to CELF but with less computational cost and obtains significantly better results when compared to the other algorithms.

    Acknowledgments

    Project supported by the Zhejiang Provincial Natural Science Foundation (Grant No.LQ20F020011), the Gansu Provincial Foundation for Distinguished Young Scholars(Grant No.23JRRA766),the National Natural Science Foundation of China (Grant No.62162040), and the National Key Research and Development Program of China (Grant No.2020YFB1713600).

    猜你喜歡
    張莉
    BLOW-UP SOLUTIONS OF TWo-COUPLEDNONLINEAR SCHRODINGER EQUATIONS IN THE RADIAL CASE*
    熟人好辦事
    故事會(2022年20期)2022-10-20 09:21:56
    追尋兩份立功喜報背后的故事
    黨史縱覽(2022年4期)2022-04-25 22:49:42
    是講述,也是辨認(外一篇)
    作品(2021年6期)2021-07-29 14:08:51
    Cluster mean-field study of spinor Bose–Hubbard ladder:Ground-state phase diagram and many-body population dynamics?
    教與學
    金秋(2021年18期)2021-02-14 08:25:40
    幼兒圖畫
    完美少婦欲出軌:你可知道放縱的代價多沉重
    冬天里的溫暖
    冬天里的溫暖
    東方劍(2017年4期)2017-06-19 16:25:32
    婷婷精品国产亚洲av在线| av天堂久久9| 午夜福利,免费看| 一级黄色大片毛片| www.精华液| 色精品久久人妻99蜜桃| 国产精品久久久久久精品电影 | 亚洲五月婷婷丁香| 两个人免费观看高清视频| 日韩欧美国产一区二区入口| 在线十欧美十亚洲十日本专区| 丰满人妻熟妇乱又伦精品不卡| 三级毛片av免费| 成人三级黄色视频| 人人澡人人妻人| www国产在线视频色| 久久九九热精品免费| 日本 欧美在线| 国产不卡一卡二| 国产视频一区二区在线看| 一本综合久久免费| 色综合婷婷激情| 真人做人爱边吃奶动态| 欧洲精品卡2卡3卡4卡5卡区| 美女高潮到喷水免费观看| 国产一级毛片七仙女欲春2 | 50天的宝宝边吃奶边哭怎么回事| 十分钟在线观看高清视频www| 嫩草影院精品99| 无遮挡黄片免费观看| 欧美不卡视频在线免费观看 | 久久精品国产清高在天天线| 曰老女人黄片| 欧美日韩一级在线毛片| aaaaa片日本免费| 国产精品国产高清国产av| 精品国产一区二区久久| 久久精品影院6| 亚洲国产高清在线一区二区三 | 正在播放国产对白刺激| 亚洲精品久久成人aⅴ小说| 国产极品粉嫩免费观看在线| 18禁国产床啪视频网站| 夜夜看夜夜爽夜夜摸| 久久草成人影院| 18美女黄网站色大片免费观看| 18禁国产床啪视频网站| 色哟哟哟哟哟哟| 女人爽到高潮嗷嗷叫在线视频| 国产精品亚洲av一区麻豆| av视频免费观看在线观看| 欧美另类亚洲清纯唯美| 精品国产美女av久久久久小说| 激情视频va一区二区三区| 亚洲第一电影网av| 国产黄a三级三级三级人| 国产亚洲精品久久久久久毛片| 国产成人av激情在线播放| 久久草成人影院| 91av网站免费观看| 亚洲精品中文字幕在线视频| 可以在线观看的亚洲视频| 午夜福利一区二区在线看| 国产精品99久久99久久久不卡| 自拍欧美九色日韩亚洲蝌蚪91| 久久久久久国产a免费观看| 人妻丰满熟妇av一区二区三区| 桃红色精品国产亚洲av| 国产av在哪里看| 国产亚洲精品综合一区在线观看 | 亚洲五月婷婷丁香| 日韩精品中文字幕看吧| 一级,二级,三级黄色视频| 久久中文字幕一级| 精品不卡国产一区二区三区| 精品久久久久久久久久免费视频| 99久久国产精品久久久| 亚洲国产中文字幕在线视频| 亚洲专区中文字幕在线| 亚洲一卡2卡3卡4卡5卡精品中文| 一个人免费在线观看的高清视频| 国产亚洲精品第一综合不卡| 校园春色视频在线观看| 天天添夜夜摸| 亚洲国产精品sss在线观看| 91精品国产国语对白视频| 一进一出抽搐动态| 亚洲人成77777在线视频| 亚洲精品在线观看二区| 久久青草综合色| 十分钟在线观看高清视频www| 欧美日本中文国产一区发布| 久久人人爽av亚洲精品天堂| 女人精品久久久久毛片| 国产欧美日韩精品亚洲av| 级片在线观看| 人人妻人人爽人人添夜夜欢视频| 亚洲专区中文字幕在线| 黄色毛片三级朝国网站| 欧美丝袜亚洲另类 | 精品一区二区三区四区五区乱码| 国产精品 国内视频| 男女下面进入的视频免费午夜 | 免费在线观看视频国产中文字幕亚洲| 一级片免费观看大全| 午夜a级毛片| 黑人巨大精品欧美一区二区蜜桃| 欧美精品亚洲一区二区| 亚洲国产欧美一区二区综合| 日韩欧美一区视频在线观看| 久热爱精品视频在线9| 免费久久久久久久精品成人欧美视频| 久久精品人人爽人人爽视色| 中文字幕av电影在线播放| 99在线视频只有这里精品首页| 啦啦啦 在线观看视频| 757午夜福利合集在线观看| 91大片在线观看| 欧美黄色淫秽网站| 亚洲九九香蕉| 两个人免费观看高清视频| 久久婷婷成人综合色麻豆| 久久青草综合色| 91国产中文字幕| 狠狠狠狠99中文字幕| 免费在线观看完整版高清| 一级黄色大片毛片| x7x7x7水蜜桃| 久久国产精品男人的天堂亚洲| 999久久久国产精品视频| 亚洲五月色婷婷综合| 国产精品亚洲av一区麻豆| 日韩视频一区二区在线观看| 波多野结衣av一区二区av| 亚洲一区二区三区不卡视频| 亚洲欧洲精品一区二区精品久久久| 欧美日韩一级在线毛片| 99在线人妻在线中文字幕| 中文字幕人成人乱码亚洲影| 日日摸夜夜添夜夜添小说| 给我免费播放毛片高清在线观看| 美女高潮喷水抽搐中文字幕| 999久久久国产精品视频| 国产精品亚洲美女久久久| 成人三级做爰电影| 久久性视频一级片| 亚洲av日韩精品久久久久久密| 日本五十路高清| 欧美 亚洲 国产 日韩一| 国产精品亚洲av一区麻豆| 一边摸一边做爽爽视频免费| av天堂久久9| 黄色片一级片一级黄色片| 亚洲九九香蕉| 国产xxxxx性猛交| 欧美国产精品va在线观看不卡| 一卡2卡三卡四卡精品乱码亚洲| 国产熟女午夜一区二区三区| 99国产综合亚洲精品| 精品一品国产午夜福利视频| 国产av在哪里看| 曰老女人黄片| 女人被狂操c到高潮| 制服丝袜大香蕉在线| 1024香蕉在线观看| 国产精品久久久av美女十八| 天天躁狠狠躁夜夜躁狠狠躁| 天天躁狠狠躁夜夜躁狠狠躁| 免费在线观看视频国产中文字幕亚洲| 老司机福利观看| 少妇裸体淫交视频免费看高清 | 国产精品,欧美在线| www.熟女人妻精品国产| 老鸭窝网址在线观看| 久久人妻福利社区极品人妻图片| 国产精品二区激情视频| 成人国产一区最新在线观看| 欧美 亚洲 国产 日韩一| 午夜精品在线福利| 俄罗斯特黄特色一大片| 成人av一区二区三区在线看| 韩国av一区二区三区四区| 日日爽夜夜爽网站| 国产成人av激情在线播放| 中文字幕最新亚洲高清| 国产成人影院久久av| 制服丝袜大香蕉在线| 久久久水蜜桃国产精品网| www.自偷自拍.com| 久久久久久久久中文| 久久青草综合色| 久久热在线av| 欧美日韩一级在线毛片| 免费在线观看完整版高清| 国产成人系列免费观看| 免费少妇av软件| 亚洲精品在线美女| 身体一侧抽搐| 极品人妻少妇av视频| 久久久久久久精品吃奶| 亚洲无线在线观看| 亚洲国产毛片av蜜桃av| 欧美日韩黄片免| 老司机深夜福利视频在线观看| 老司机午夜福利在线观看视频| 99riav亚洲国产免费| 一边摸一边抽搐一进一小说| 少妇被粗大的猛进出69影院| 成人国产一区最新在线观看| 亚洲 国产 在线| 国产免费男女视频| 欧美一级a爱片免费观看看 | 久久精品成人免费网站| 亚洲狠狠婷婷综合久久图片| 亚洲专区国产一区二区| 欧美一级毛片孕妇| 久久久国产成人精品二区| 最近最新中文字幕大全免费视频| 久久人妻av系列| 巨乳人妻的诱惑在线观看| 不卡av一区二区三区| 国产亚洲精品av在线| 怎么达到女性高潮| a在线观看视频网站| 男女下面进入的视频免费午夜 | 久久久久国内视频| 中文字幕av电影在线播放| 亚洲国产精品合色在线| 亚洲国产精品久久男人天堂| 欧美成人免费av一区二区三区| 一卡2卡三卡四卡精品乱码亚洲| 人妻久久中文字幕网| 99精品欧美一区二区三区四区| 国产男靠女视频免费网站| 精品一区二区三区视频在线观看免费| 精品久久久精品久久久| 亚洲色图综合在线观看| 50天的宝宝边吃奶边哭怎么回事| 熟女少妇亚洲综合色aaa.| 日本vs欧美在线观看视频| 免费搜索国产男女视频| 一个人免费在线观看的高清视频| 51午夜福利影视在线观看| 1024香蕉在线观看| 美女午夜性视频免费| 啦啦啦免费观看视频1| 亚洲中文字幕一区二区三区有码在线看 | 黄片播放在线免费| 亚洲成a人片在线一区二区| 成熟少妇高潮喷水视频| 久久久国产成人免费| 亚洲av日韩精品久久久久久密| 1024香蕉在线观看| 精品国产美女av久久久久小说| 国产又爽黄色视频| 99久久久亚洲精品蜜臀av| 中文字幕av电影在线播放| 一卡2卡三卡四卡精品乱码亚洲| 久久天堂一区二区三区四区| 巨乳人妻的诱惑在线观看| www.自偷自拍.com| 亚洲国产高清在线一区二区三 | 亚洲三区欧美一区| 国产精品 欧美亚洲| 欧美日韩一级在线毛片| 亚洲五月婷婷丁香| 亚洲精品久久国产高清桃花| 日本 欧美在线| 天天添夜夜摸| 国产午夜精品久久久久久| 99国产精品免费福利视频| 中文字幕人妻丝袜一区二区| 亚洲自拍偷在线| 女人高潮潮喷娇喘18禁视频| 大型黄色视频在线免费观看| 欧美日韩黄片免| 国产精品免费视频内射| 曰老女人黄片| 久久久久久亚洲精品国产蜜桃av| 男女之事视频高清在线观看| 大香蕉久久成人网| 俄罗斯特黄特色一大片| 中亚洲国语对白在线视频| 91精品三级在线观看| av欧美777| 久久国产乱子伦精品免费另类| 精品人妻在线不人妻| 精品久久久久久久毛片微露脸| 久久性视频一级片| 国产单亲对白刺激| 国产精品秋霞免费鲁丝片| 亚洲国产欧美一区二区综合| 丝袜人妻中文字幕| 无人区码免费观看不卡| svipshipincom国产片| 日日爽夜夜爽网站| 男男h啪啪无遮挡| 午夜久久久久精精品| 亚洲一区高清亚洲精品| 男人操女人黄网站| 美女 人体艺术 gogo| 欧美中文综合在线视频| 夜夜躁狠狠躁天天躁| 欧美精品啪啪一区二区三区| 亚洲精品在线美女| 91精品国产国语对白视频| 精品一区二区三区四区五区乱码| 国产成人一区二区三区免费视频网站| 51午夜福利影视在线观看| 1024视频免费在线观看| 真人一进一出gif抽搐免费| 操美女的视频在线观看| 国产激情久久老熟女| 精品熟女少妇八av免费久了| 日韩有码中文字幕| 丝袜人妻中文字幕| 亚洲av美国av| 久热这里只有精品99| 一二三四社区在线视频社区8| 一区福利在线观看| 黄色视频不卡| 高清黄色对白视频在线免费看| 99riav亚洲国产免费| 欧美成狂野欧美在线观看| 别揉我奶头~嗯~啊~动态视频| 99在线视频只有这里精品首页| 欧美成人免费av一区二区三区| 最近最新中文字幕大全电影3 | 亚洲专区字幕在线| 香蕉久久夜色| 免费在线观看视频国产中文字幕亚洲| 色老头精品视频在线观看| 夜夜看夜夜爽夜夜摸| 男人舔女人的私密视频| 欧美在线黄色| 99国产极品粉嫩在线观看| 亚洲专区中文字幕在线| 国产一区二区三区视频了| 国产激情久久老熟女| 天堂影院成人在线观看| 亚洲精品av麻豆狂野| 女性被躁到高潮视频| 少妇 在线观看| 国产欧美日韩一区二区精品| e午夜精品久久久久久久| av天堂久久9| 午夜日韩欧美国产| 欧美 亚洲 国产 日韩一| 女人爽到高潮嗷嗷叫在线视频| 精品卡一卡二卡四卡免费| 亚洲色图av天堂| 亚洲欧美精品综合久久99| 看免费av毛片| 最新美女视频免费是黄的| 最近最新中文字幕大全电影3 | 亚洲欧美精品综合久久99| 色av中文字幕| 高潮久久久久久久久久久不卡| 91老司机精品| 亚洲成国产人片在线观看| 如日韩欧美国产精品一区二区三区| 十八禁人妻一区二区| 国产麻豆69| 热99re8久久精品国产| 91大片在线观看| 欧美中文日本在线观看视频| 99久久精品国产亚洲精品| 国产精品永久免费网站| 亚洲精品av麻豆狂野| 一区二区三区国产精品乱码| 少妇熟女aⅴ在线视频| av中文乱码字幕在线| 黄色视频不卡| 久久精品成人免费网站| 久久精品国产99精品国产亚洲性色 | 精品一区二区三区视频在线观看免费| 亚洲精品国产区一区二| 国产亚洲精品第一综合不卡| 久久婷婷人人爽人人干人人爱 | 制服丝袜大香蕉在线| 如日韩欧美国产精品一区二区三区| 美女 人体艺术 gogo| 两人在一起打扑克的视频| 在线播放国产精品三级| 午夜日韩欧美国产| 亚洲精品一卡2卡三卡4卡5卡| 中文字幕人成人乱码亚洲影| 国产精品久久久av美女十八| 他把我摸到了高潮在线观看| 亚洲av美国av| or卡值多少钱| 亚洲aⅴ乱码一区二区在线播放 | 亚洲一区二区三区不卡视频| 岛国在线观看网站| 成人精品一区二区免费| 正在播放国产对白刺激| 欧美日韩福利视频一区二区| 免费在线观看亚洲国产| 亚洲成国产人片在线观看| 午夜久久久在线观看| 久久午夜综合久久蜜桃| 亚洲精品av麻豆狂野| 午夜精品在线福利| 久久久国产成人精品二区| 久久热在线av| 禁无遮挡网站| 久久人妻熟女aⅴ| 又大又爽又粗| 级片在线观看| 美女扒开内裤让男人捅视频| 欧美国产日韩亚洲一区| 色尼玛亚洲综合影院| 可以在线观看的亚洲视频| 国内精品久久久久久久电影| 一级毛片精品| 在线观看www视频免费| 国产精品香港三级国产av潘金莲| 国产私拍福利视频在线观看| 国产精品av久久久久免费| 亚洲人成电影观看| 法律面前人人平等表现在哪些方面| 在线国产一区二区在线| 成人国产一区最新在线观看| 丁香欧美五月| 精品人妻在线不人妻| 国产91精品成人一区二区三区| 亚洲人成77777在线视频| 国产精品久久视频播放| 成人亚洲精品av一区二区| 9191精品国产免费久久| 国产乱人伦免费视频| 黄色成人免费大全| 国产成人系列免费观看| 亚洲中文av在线| 黄片大片在线免费观看| 中出人妻视频一区二区| 最近最新中文字幕大全电影3 | 国产亚洲精品久久久久5区| 免费搜索国产男女视频| a在线观看视频网站| aaaaa片日本免费| 免费不卡黄色视频| 国产成人av激情在线播放| ponron亚洲| 欧美日本中文国产一区发布| 人人妻人人爽人人添夜夜欢视频| 亚洲一码二码三码区别大吗| 亚洲第一青青草原| a在线观看视频网站| 91老司机精品| 国产亚洲精品久久久久久毛片| 久久天堂一区二区三区四区| 久久久久久久精品吃奶| 亚洲一卡2卡3卡4卡5卡精品中文| 欧洲精品卡2卡3卡4卡5卡区| 女人爽到高潮嗷嗷叫在线视频| 国产三级在线视频| 久久中文字幕一级| 在线播放国产精品三级| 久久国产精品影院| 一进一出好大好爽视频| 国产熟女午夜一区二区三区| aaaaa片日本免费| 亚洲中文日韩欧美视频| 国产午夜福利久久久久久| 亚洲精品粉嫩美女一区| 亚洲精品国产精品久久久不卡| 51午夜福利影视在线观看| 欧美日韩亚洲国产一区二区在线观看| 欧美精品啪啪一区二区三区| 好看av亚洲va欧美ⅴa在| 亚洲国产欧美日韩在线播放| 国产91精品成人一区二区三区| 亚洲视频免费观看视频| 国产精品,欧美在线| 99国产精品免费福利视频| 国产亚洲av嫩草精品影院| 老司机福利观看| 国产亚洲精品一区二区www| 日韩欧美国产一区二区入口| 99在线人妻在线中文字幕| 欧美成狂野欧美在线观看| 一卡2卡三卡四卡精品乱码亚洲| 757午夜福利合集在线观看| 美女大奶头视频| 亚洲一码二码三码区别大吗| 日本在线视频免费播放| 九色亚洲精品在线播放| 婷婷六月久久综合丁香| 亚洲av熟女| 多毛熟女@视频| 日本黄色视频三级网站网址| 夜夜看夜夜爽夜夜摸| 女人被躁到高潮嗷嗷叫费观| 嫩草影视91久久| 免费av毛片视频| 一级片免费观看大全| 国产成人精品无人区| 婷婷丁香在线五月| 色婷婷久久久亚洲欧美| 亚洲欧美日韩无卡精品| 午夜免费观看网址| 色精品久久人妻99蜜桃| 精品国产一区二区久久| 欧洲精品卡2卡3卡4卡5卡区| 国产精品99久久99久久久不卡| 欧美黑人精品巨大| 高清毛片免费观看视频网站| 免费观看精品视频网站| 久热爱精品视频在线9| 色综合亚洲欧美另类图片| 久久九九热精品免费| 91老司机精品| 欧美一区二区精品小视频在线| 久久中文看片网| 男人操女人黄网站| 人人澡人人妻人| 天天躁夜夜躁狠狠躁躁| 少妇被粗大的猛进出69影院| 久久中文看片网| 久久婷婷人人爽人人干人人爱 | 国产精品乱码一区二三区的特点 | av超薄肉色丝袜交足视频| 黄色视频,在线免费观看| 亚洲欧美精品综合久久99| 90打野战视频偷拍视频| 精品欧美国产一区二区三| 午夜福利欧美成人| 别揉我奶头~嗯~啊~动态视频| 久久精品91蜜桃| 欧美午夜高清在线| 国产精品精品国产色婷婷| 波多野结衣一区麻豆| 999久久久国产精品视频| 精品欧美一区二区三区在线| 9热在线视频观看99| 色综合亚洲欧美另类图片| 99在线视频只有这里精品首页| 麻豆一二三区av精品| 欧美av亚洲av综合av国产av| 日韩大码丰满熟妇| 欧美色视频一区免费| 一级毛片高清免费大全| 黑人巨大精品欧美一区二区蜜桃| 国产精品精品国产色婷婷| 亚洲国产精品久久男人天堂| 亚洲精品中文字幕在线视频| 欧美黄色片欧美黄色片| 国内精品久久久久久久电影| 一本综合久久免费| 精品国产美女av久久久久小说| 69精品国产乱码久久久| 国产1区2区3区精品| 国产99白浆流出| av天堂在线播放| 国产三级黄色录像| 国产精品二区激情视频| 午夜福利在线观看吧| 一级毛片精品| 97人妻精品一区二区三区麻豆 | 国产在线精品亚洲第一网站| 国产精品久久久av美女十八| 操出白浆在线播放| 精品福利观看| 久久中文看片网| 日本在线视频免费播放| 两个人免费观看高清视频| 亚洲欧美激情综合另类| 亚洲伊人色综图| 两性夫妻黄色片| 在线观看66精品国产| 亚洲av日韩精品久久久久久密| 欧美中文日本在线观看视频| 亚洲国产日韩欧美精品在线观看 | 亚洲一区二区三区不卡视频| 亚洲成人精品中文字幕电影| 别揉我奶头~嗯~啊~动态视频| 亚洲 欧美 日韩 在线 免费| 麻豆av在线久日| 亚洲欧美精品综合一区二区三区| 亚洲国产欧美一区二区综合| 亚洲成人免费电影在线观看| 午夜精品在线福利| 午夜视频精品福利| 国产麻豆成人av免费视频| 久久精品亚洲精品国产色婷小说| 亚洲av美国av| netflix在线观看网站| 国产成人精品无人区| 亚洲中文字幕日韩| 国产欧美日韩综合在线一区二区| 免费看a级黄色片| 99久久综合精品五月天人人| 悠悠久久av| 亚洲一区高清亚洲精品| 欧美av亚洲av综合av国产av| e午夜精品久久久久久久| 亚洲国产精品sss在线观看| 桃色一区二区三区在线观看| 国产又爽黄色视频| 麻豆国产av国片精品| 黄色成人免费大全| 欧美日韩乱码在线| 久久国产精品影院| 午夜精品在线福利| 国产午夜福利久久久久久| 真人一进一出gif抽搐免费| 看免费av毛片| 欧美日本亚洲视频在线播放| 在线观看免费午夜福利视频| av天堂在线播放| 在线观看免费午夜福利视频| 欧美成人午夜精品| 大香蕉久久成人网| 国产精品1区2区在线观看.|