Energy-Efficient Joint Content Caching and Small Base Station Activation Mechanism Design in Heterogeneous Cellular Networks

Renchao Xie, Zishu Li＊, Tao Huang, Yunjie Liu

State Key Lab. of Networking and Switching Technology, Beijing University of Posts and Telecom., Beijing,. China

* The corresponding author, email: lizishu0321@sina.com

I. INTRODUCTION

With the forthcoming of 5G era, various services, such as mobile broadband, machine type communication, vehicle communications and so on, have been emerged, which require the network have the capability with high bandwidth and low latency [1]. In order to satisfy the requirements of the increasing services, by deploying highly heterogeneous cellular networks (HCNs) and enabling the caching capability at the base stations have been proposed as promising techniques.

Since the caching in HCNs has been proposed, many issues, such as resource allocation, contents placement, mobile access, power/energy control and so on, have been studied[3]-[18]. In [3], a dynamic game algorithm among the utility function, the cost of video placement and delay cost was proposed from the view of game theory. The authors in [4]explored the benefits of collaborative caching in wireless streaming services and proposed a collaborative mechanism that maximizes the social welfare in the context of Vickrey-Clarke-Groves (VCG) auctions. In [5], a commercialized small-cell caching system consisting of a video retailer (VR), multiple network service providers (NSP) and mobile users (MU) was considered and a Stackelberg game to jointly maximize the average profit of the VR and the NSPs is designed. Authors in [6] proposed a cost game between mobile network operators and SBS owners. In [7] and[8], constrained convex optimization problems with the goal of maximizing the average QoE were formulated. There also exists many literature studying content caching problems from an energy perspective. The authors in[9] studied an optimization framework that formalizes the inherent trade-off between the user perceived quality of wireless video and the energy consumption cost of network for optimizing user association and the average power they are allocated. A multi-objective optimization framework which contains QoE,power consumption and network resource consumption was proposed in [10] to address the joint mobile association and resource allocation problem in a video transmitted wireless heterogeneous network. In [11], a coded caching scheme for non-uniform content popularity that dynamically allocates user access to APs based on requested content was designed. The authors of [12] investigated the minimum energy consumption that CCN can achieve with optimal cache locations by considering different caching hardware technologies, number of downloads per hour, and content popularity.In [13], a collaborative framework in which the SBSs can access files from the caches of other SBSs within the same network domain was proposed and a cost model for the content retrieval of contents across SBSs and from the EPC was designed. In [14], the authors proposed an information-centric optimization framework for the energy efficient dynamic in-network caching problem which takes the mutual cooperation among SBS nodes into consideration. Authors in [15] formulated a preference profiles of SBSs and UEs on maximum Energy Efficiency under practical constrains of QoS, transmission power, backhaul capacity, and storage capacity. In [16], an energy efficient caching scheme was proposed that keeps the balance between the power consumption and the acceptable playout delay caused by caching that has direct influence on the perceived quality. Content caching paradigm is also applied in the fog radio access networks(F-RANs) to alleviate capacity constraints on the front haul and decrease the transmit latency [17]. Authors in [18] designed an in-network caching scheduling scheme for ICN, distinguishing different kinds of contents and dynamically allocating the cache size on-demand.

Although there are many works in content caching and an energy perspective, there obviously still exists another breakthrough point to achieve higher energy efficiency, for which they are simply focusing on the part of energy saving by intelligent content placement, ignoring another possibility of decreasing energy consumption in HCNs. Many studies have shown that mobile data traffic in heterogeneous cellular network has regularity in both time and space. For example, in the consumer area, the traffic tends to increase from afternoon to evening while in the business district the traffic presents a downward trend at the same time period. Therefore, not all the time are the base stations being fully utilized and what is more interesting is that [19] has directly demonstrated that in the most of the time the majority of the base stations are under-utilized, which provides an opportunity for us to apply the base station activation (deactivation)mechanism. The authors of [19] formulated the energy-minimizing problem by combining the activation policy and caching policy jointly. In[20], a novel dual-threshold-based sleep mode control strategy was proposed for the hope of controlling the sleep mode to minimize the network energy consumption while avoiding the frequent mode transitions of SBSs at the same time. The authors in [21] proposed a strategy to minimize the total power consumption of the network by switching BSs on/off adaptively while maintaining the network coverage. In [22], a two-stage base station (BS)sleeping scheme to save energy consumption in cellular networks was proposed. Authors of[23] formulated the problem as a non-cooperative game among the base stations that seek to minimize a cost function which captures the trade off between energy expenditure and load.In [24], the authors presented a novel activation and sleep mechanism for small cells to decrease the energy consumption in heterogeneous networks (HetNets) and used enhanced inter-cell interference coordination (eICIC)techniques to support range expanded small cells to avoid QoS degradation. An approach to quantify the benefits obtained by MNOs with the deployment of flexible BSs was proposed in [25], which in terms of maximum energy efficiency achievable with a given fraction of flexible BSs in their network.

Even some works have been done to consider the caching strategy design in HCNs for energy efficiency, there still exists much space to develop a more energy-efficient system by combining both the caching mechanism and the base station activation mechanism. Based on this inspiration, we introduce a novel joint caching and activation mechanism by taking the activation mechanism for the base stations and the caching into account. The main contributions of this work can be summarized as follows:

· We take both the caching mechanism and the small base station activation mechanism into consideration, hoping to achieve the maximization of the system energy savings,and then we formulate the problem as a Combination of Caching and Small Base Station Activation Strategy (CCAS), subjecting to knapsack constrains. To prove the superiority of our CCAS, we also compare it with the strategy of only considering content caching and the strategy of all content requests being served by MBS.

· Due to finding the optimal solution is NP-hard, we introduce an approximation algorithm, Quantum-inspired Evolutionary Algorithm (QEA), to iteratively reach the best solutions of our CCAS, which takes advantages in accuracy, global optimality and adaptability[26] compared to common algorithms solving NP-hard problem such as the greedy algorithm. To prove the performance advantages of QEA, we also draw a comparison among QEA, random sleeping algorithm and greedy algorithm.

· To decrease the simulation complexity,we no longer consider the user association problem, instead, we focus on the number and the type of the requests received in each SBS.Thus, we simplify our formation with only two sets of variables to be optimized. On the other hand, a set of mean values are used to replace parameters relevant to user level such as bandwidth and the signal to interference-plus-noise ratio (SINR) between base stations and users.Modifications in the two aspects degrade our problem dimension and thus greatly decrease simulation computation complexity.

The rest of the paper is organized as follows. The system model and problem formulation are described in Section II. In Section III,we propose a quantum-inspired evolutionary algorithm to achieve the best solutions of our proposed CCAS and a classical greedy algorithm as performance comparison, whereas Section IV provides simulation results and numerical analysis. Finally, conclusions are drawn in Section V.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In this section, we first describe the system model and then we formulate the problem as a Combination of Caching and Small Base Station Activation Strategy, which is apparently a NP-hard problem belonging to the category of mixed integer nonlinear programming (MINLP).

2.1 System model

We consider a heterogeneous cellular network consisting of a set of S={1,2,…,s,…,S} of small-cell base stations(SBSs) overlaid by a macro-cell base station (MBS). Those SBSs are cache-capable and can be deactivated when necessary, which can either be pico-cell base stations (PBSs) or femto-cell base stations (FBSs) [19]. In this formulation, S is the total number of SBS, and s is the index of SBS. The transmit power of the MBS is Pm(watt) and the transmit power of SBS s∈S is Ps(watt) where Pm≫Ps. We use a collection of F={1,2,…,f,…,F} to describe F content files which are potential candidates for user requesting, and for every file f∈F, there is a size denoted by Sf≥0(byte) correspondingly. Each SBS sS∈ is endowed with a cache of size Cs≥0(byte), that will be determined which file would be cached in at the beginning of every time slot T≥0 using our CCAS.The caching energy efficiency of SBS s∈S is ωcs≥0(J/byte). Particularly, we denote µsf≥0 the average requesting times in SBS sS∈ for content fF∈ during one time slot.

In our formulation, we assume that the MBS is always active, that is to say our activation-deactivation strategy will be applied to SBSs only. Now we describe the requesting and responding process. Every time when new requests for content f∈F arrive at SBS s∈S,there would be three possible occasions:

● The first is that the SBS is active but doesn’t hold the requested content in its’cache, in this case the SBS s will route the content from the MBS through wired link and then transmit it to the user through the wireless link.

● The second one is that the requested content is in the SBS’s cache and at the same time the SBS is active, those requests will be served by the SBS directly.

● The third occasion occurs when the SBS s is in the sleeping state, then the requests will be served by the nearest available MBS. Please notice that we don’t consider cooperations between SBSs, and it can not be promised three exists another active SBS caching the requested content if the current SBS is inactive, therefore, we regulate that the requests will be served by MBS if the current SBS is inactive.

Fig. 1 Three possible requesting-responding occasions

The three possible requesting-responding occasions are described in figure 1. Considering the fact that the introduction of caching is used for reducing back haul transport energy[19][27] and the caching cost will be significantly reduced with the development of caching technology, we don’t consider the scenario that content is routed from the Internet through back haul links to MBSs and transmitted to users, which means that all the contents are available at MBS thus the MBS can satisfies all file requests in its’ coverage range.

2.2 Problem formulation

Taking both the caching mechanism and SBS activation mechanism into consideration,the main problem can be abstracted into two aspects: content placement and SBS deactivation. Thus we use the following binary variables to indicate the status of content placement and SBS activation respectively.

From an energy efficiency perspective,our objective of devising the Combination of Caching and Base Station Activation Strategy to minimize the total energy consumption is equivalent to the one of maximizing the energy savings. Thus we study the energy savings of our system architecture in the following three occasions:

· Transport Energy, Etr: Notice that there exists two link transmission models. When contents are routed from MBS to SBS, we use wired link transmission model, where the energy consumption is proportional to the amount of data transmitted by the link [28].Here we let ems≥0 (joules/byte) be the link transmission energy efficiency between the MBS and SBS s. Another link transmission model is compliant with the case of routing files from the MBS or SBSs to users directly,which uses wireless links.

The average SINR between the MBS(SBS s) and users are denoted withThe total link bandwidth a MBS(SBS)can provide is WM(WS), which is fixed.The average link bandwidth between the MBS(SBS s) and users iswhich is equally shared by the current accessing users.And then we use the Shannon formula to fig-ure out the data transmission rate and thus the transport energy consumption [9].

Table I Main parameters used in the formulation

· Caching Energy, Ech: We use an energy proportional model. Assume that the file fF∈is cached at SBS sS∈, the energy consumed by caching content f is given by:[11][28].

· Static Energy, Est: This part of energy is consumed by SBS for cooling from active state to sleeping state [6], which we assume as a constant value.

Please notice that the energy models of above three energy types are different. Transport energy is modeled using the Shannon formula while caching energy follows an energy proportional model and static energy usually is a constant value, so it seems more reasonable to discuss them separately, rather than unifying the transport energy consumption and the caching energy consumption to a load-dependent BS energy cost [19].

The variables and constants used in the optimization problem formulation are summarized in table 1.

Comparing with [19] which uses the state when all the SBSs are deactivated and all the content requests are served by MBS as the reference state, we take the first requesting-responding circumstance when there exists neither caching nor activation strategy for SBSs as the reference state to describe the energy savings of our system. No activation strategy means that all SBSs are active under the reference state and can be deactivated if necessary,which not only indicates our HCN background but also the possibility of the implementation of activation strategy. No caching strategy complies with the original state that all SBSs are not cache-endowed at first, which indicates the possibility of the implementation of caching strategy. Thus, it is not hard to find that the reference state setting is more reasonable in our proposed model than in [19]. Clearly, the energy saving E1is equal to zero.

The second occasion omits the need of retrieving content from MBS to SBS, thus saves a portion of transport energy, meanwhile,SBSs that store files will consume correspond-ing caching energy. The amount of energy saving, E2, can be given:

The first term of the summation accounts for the transport energy saving while the second specifies the caching energy consumption.

For the third circumstance, we need to take the SBS sleeping into consideration. The total energy saving E3can be given:

The first and the second term account for the transport energy consumption that retrieve contents from MBS to SBS and then transmit to users, and the third term accounts for the transport energy consumption routing files from MBS to users. The last part of the summation denotes the static energy saving due to SBS deactivation.

Thus, the total energy saving in our system Etotcan be given:

The maximizing problem can be modeled as the following Integer Linear Programming problem(ILP):

Subject to:

In this formulation, the objective function consists of three parts of energy for the above mentioned three occasions, respectively. Thefirst constraint specifies that the total content size located in each SBS s should not exceed the maximize cache size,while the second constraint xsf≤ysspecifies that a caching policy can be applied to SBS s only when SBS s is active. (9) and (10)expose binary constraint to the indications of the status of content placement and SBS activation respectively.

III. PROPOSED ALGORITHM FOR CCAS

In this section, we propose a quantum-inspired evolutionary algorithm(QEA) to provide best solutions of our problem, and present a structure and pseudo code description of QEA.

Apparently, the above optimization problem is a NP-hard problem belonging to the category of mixed integer nonlinear programming(MINLP), which is hard to find a precise best solution in polynomial time [9].

To provide the best solutions of the problem, here we propose an approximate method, quantum-inspired evolutionary algorithm(QEA). QEA, as an efficient algorithm applied to knapsack problem, is firstly proposed by Kuk-Hyun Han and Jong-Hwan Kim in [26] in 2002, which takes advantages in population size, convergence speed and the ability of global optimizing than traditional algorithm such as greedy algorithm and thus has been widely applied to knapsack problems.

3.1 Description of QEA

Based on the concept and principles of quantum computing such as quantum bits and superposition of states, QEA uses a Q-bit as a probabilistic representation. A Q-bit may be in the “1” state or in the “0” state, which can be represented as

To facilitate algorithm description, the definition of a Q-bit is simplified to a pair of numbers (,)αβ as

where α and β specify the probabilities amplitudes of variables taking the corresponding states. For example, αsfand βsfpresent probabilities amplitudes of the binary variable xsftaking 0 and 1, respectively. Meanwhile, to meet the constrain of probability normalization, α and β must subject to the following constraint.

A Q-bit individual is a string of m Q-bits,which determines a binary solution in our formulation and can be denoted as

During the iterative process, the algorithm uses a quantum gate to change the state of Q-bits. A quantum gate is a reversible gate and can be represented as a unitary operator. Thereare serval quantum gates such as Not gate, Rotation gate and Hadamard gate can be implied.Here we use a rotation gate as a variation operator, to drive the individuals toward better solutions and eventually toward a single state,which can be presented as follows.

Table II Lookup Table for ∆θi

Algorithm 1 Quantum-inspired Evolutionary Algorithm(QEA)

where ∆θidenotes a rotation angle of each Q-bit toward the next state. ∆θiis determined by three factors: bi, the ith bit of the best solution b and xi, the ith bit of the binary solution x , as well as the relative size of the profit corresponding to b and x. ∆θiis defined as rules in table 2.

3.2 The Structure of QEA

Combining with our proposed formulation, the structure of QEA is described as Algorithm 1

In the above algorithm, QEA maintains two population of Q-bit individuals, Q(t)xand Q(t), whileand

yat generation t, which can be interpreted into probability amplitude matrix for xsfand ystaking 0 and 1. Pt()xand Pt()ystore m binary solutions of x and y at generation t, respectively, while Bt()xand Bt()ystore m best solutions of x and y among the previous t−1 generations, among which the value of m can be artificially set on demand. bxand byare the best solutions among Bt()xand Bt()yafter generation time reaches its’ limit, which are what we finally need to implement caching and activation to corresponding files and SBSs.

To reach convergence state more quickly,QEA introduces a migration, which is defined as the process of copyingin B(t)xor bxto B(t)xand copyingin B(t)yor byto B(t)y.A global migration means replacing all the solutions in B(t)xor B(t)yby bxor by, while a local migration replaces some of the solutions in B(t)xor B(t)yby the best one of them,respectively [26].

The ith item can be selected for the knapsack according to a probability of |βi|2or(1−|αi|2). To obtain the binary string x and y, the step of “make P(t)xby observing the states of Q(t−1)x” and “make P(t)yby observing the states of Q(t−1)y” can be implemented for each individual as procedure of QEA make.

When the binary solutions violate the SBS caching capacity constrain (7) and relative size constrain (8), the procedure of repair is employed.

In the procedure of QEA update, U(∆θi),as a rotation gate like of variation operator,is employed to update a Q-bit individual q.(αi,βi) in the ith Q-bit is updated as the following formula

where the value of ∆θifollows table 2.

IV. PERFORMANCE EVALUATION

This section, on the one hand, provides the performance comparison among our CCAS and the other two different content serving strategies, on the other hand, reveals the key system parameters that affect the performance of our proposed content strategy. Furthermore,we provide illustrations of the performance advantages of our introduced QEA by comparing to the traditional classical algorithms such as the random sleeping algorithm and the greedy algorithm [29] [30].

To meet the fore mentioned goals, we simulate the HCN architecture as a single MBS overlaid with multiple cache-endowed and deactivated-capable SBSs. The MBS, as mentioned in section II, is always active and playsa role of the content server, thus can deal with as many as content requests within its cover-age area.

Algorithm 2 Procedure of QEA make

Algorithm 3 Procedure of QEA repair

Algorithm 4 Procedure of QEA update

Table III Main parameter values used in the simulation

The three different serving strategies we investigate in the simulation are as follows:

· our proposed CCAS, which takes both the SBS caching and deactivation into consideration. SBSs are initially active and empty in cache. To obtain the maximum value of the energy saving, QEA algorithm iteratively places content into corresponding SBSs’cache and deactivates some SBSs.

· All the SBSs are active, in other words, we only care about SBS caching without considering deactivation under this strategy.We call this strategy “only-caching” mode.Similar to CCAS, with the iteration of QEA algorithm, initially empty SBSs will be filled in content copies to achieve higher energy saving, under the caching capacity constrain.

· All SBSs are deactivated, which indicates content requests will be served by the MBS through long-range, high-cost back haul,which we will denote as “all-MBS” mode in this section.

In our simulation, we consider that the SBSs are deployed uniformly at random within the MBS’s coverage area, and the arrival of file requests is uniformly distributed during our whole simulation period. Unless otherwise specified, the total number of requests is fixed and equals 600.

The parameters used for the simulation are summarized in table 3.

We study the system during a time period T, and every time there comes a best solution for xsfand ys, the system will update the cache and activate(deactivate) corresponding SBSs at the beginning of the time period according to the best solution.

In essence, QEA algorithm is a process of iterative approximation. Before we actually achieve the optimum solution using QEA, we must solve the convergence problem, which is the basis of our whole simulation. Figure 2 shows the relationship between the mean of the best profits and QEA iteration times.To study the impact of iterative times on QEA, we set the iterative time from 0 to 1000 and compute the energy saving at every 100 points. From figure 2, the tendency of convergence rate is shown clearly in the results of the mean of average energy saving. In the beginning, QEA convergence rate is fast, with the iteration times increasing to 300, it displays a premature convergence and then maintains at a nearly constant value. Our following simulations are carried out at the basis of the solution.

Figure 3 shows the impact of the number of SBS on the energy savings under the three different strategies. The blue curve presents the energy saving under our CCAS, with the increasing of SBS number, SBSs will become more and more under-utilized due to the fixed total number of requests, thus, CCAS will selectively deactivate some SBS while determine how to place file copies to achieve more energy saving. Thus, the value of energy saving performs a significant increasing. The black curve is plotted when only take SBS caching into account, the profit varies among a very small range no matter how SBS number increases, which can be derived from formula(3). The red curve displays the relationship between the energy saving when all requests are served by MBS and the number of SBS. As the curve depicts, the energy saving is positively related to the number of SBS, which can also be derived from formula (4). It is worth noting that energy saving in “all-MBS” mode is negative when SBS number is small, due to MBS’s high transmission power and high path loss in the backhaul between MBS and UEs.

We use Ecd+, Ec, EMto denote the energy savings under the three strategies respectively.Meanwhile, we use S1, S2, S3to denote the abscissa of the intersection of the blue curve and the black curve, the red curve and the line of energy saving equals 0, the black curve and the red curve, respectively. From figure 3, we draw a performance comparison as follows:

According to above analysis, when the amount of SBS is reasonable, our CCAS shows the best performance while the “all-MBS” mode usually wastes energy and the“only-caching” mode gains much less than our CCAS. When the amount of SBS is very small, the performance of our CCAS is very near to that in the “only-caching” mode, while both are outperforming than “all-MBS” mode.

Fig. 2 Iteration times impact on QEA convergence rate

Fig. 3 The number of SBS impact on energy savings under three different serving strategies

Fig. 4 The static energy of SBS impact on energy savings under three different serving strategies

Figure 4 shows the tradeoff between energy savings under the three strategies and the static energy of SBS, Est. With the increasing of Est, to maintain the SBSs being active will cause increasing energy consumption, thus deactivating some idle or near-idle SBSs will be a wise approach to save energy, that’s why the blue curve and the red curve present a rising trend with Estincreasing. The energy saving under the “only-caching” mode has no relationship with Est, which can be seen from formula (3), so the black curve maintains as a parallel line. According to above analysis, the static energy cost of SBSs has direct influence on the determination of whether to deactivate a SBS or not, so it is necessary to study the relationship between them, [19] seemingly does an inadequate work in this aspect.

Fig. 5 The number of requests impact on energy savings under three different serving strategies

Fig. 6 The number of SBS impact on energy savings under three different algorithms

Similarly to figure 3, we use Ec+d, Ec, EMto denote the energy savings under the three strategies respectively. Meanwhile, we useto denote the abscissa of the intersection of the blue curve and the black curve, the red curve and the line of energy saving equals 0, the black curve and the red curve, respectively. From figure 4, we draw a performance comparison as follows:

Although the number of SBSs is a factor that aspects the result of our algorithm, the total size of the data requested by users in one specific SBS is the decisive factor behind that aspects the very SBS’s active(inactive) state.Thus, we study the relationship between the energy saving and the total size of data requested by users in a specific SBS, which is a meaningful extension compared with the work in [19]. Figure 5 presents the variation of the energy saving with respect to the number of requests and describes under which circumstances a SBS should be deactivated. In this subsection, we assume that there is only one SBS. Apparently, energy saving under the “only-caching” mode increases and energy saving under the “all-MBS” mode decreases with the increasing of the requests number.

When the number of requests arriving at the SBS is rare, the SBS tends to be deactivated, leading to the coincidence of the blue curve and the red curve. With the increasing of the number of requests, the SBS tends to be in active state to cache those requested files,making the blue curve and the black curve well coincident in each other.

Figure 6 draws a performance comparison among the three algorithms: QEA, random sleeping and greedy algorithm, with the num-ber of SBS varies, which [19] also use the greedy algorithm to simulate its’ model. In this subsection we set the capacity of SBS to 2GB. Simulation results show that our proposed QEA performs best among the three algorithms and achieves the best profit, while the greedy algorithm comes second. And both QEA and the greedy algorithm far outperform the random sleeping algorithm. This outcome can be deduced from the fact that the greedy algorithm always solves problems from a limited local starting point, which only takes the local best solutions at present, without considering the global optimizing. When capacity of SBS is limited, QEA choose to cache the files which produce best profit in all files and all SBSs, while the greedy algorithm trend to cache file which produce best profit at present file and the present SBS. It’s not strange that the random sleeping algorithm gains the lowest profit due to its’ uncertainty for randomly regulates which SBS ought to be deactivated.With the increasing of the number of SBS,curves under the three algorithms uniformly present a raising trend.

Figure 7 depicts the relationship between the three algorithms with the capacity of SBS.In this subsection, the number of SBS we use equals to 5, and the capacity of SBS varies from 0.5GB to 4GB. With the increasing of SBS capacity, energy savings under QEA and the greedy algorithm increase, while the curve under the random sleeping algorithm presents an irregular trend. The relative size of energy savings under the three algorithm is similar with figure 6, QEA performs best due to its’ advantage in global optimizing and the random sleeping algorithm produces the worst outcomes. Furthermore, it can be predicted that when the SBS capacity achieves big enough, profits under QEA and the greedy algorithm will be very close to each other.

V. CONCLUSIONS

Fig. 7 The caching capacity of SBS impact on energy savings under three different algorithms

In this paper, we have proposed a combination of caching and small base station activation strategy(CCAS) to dynamically determine the placement of requested files and the switch time of SBSs between active and sleeping modes. We have formulated the problem as an Integer Linear Programming problem(ILP)to maximize the system energy saving, thus enhance the energy efficiency in HCN. To solve the problem, we introduced a quantum-inspired evolutionary algorithm(QEA) to simulate the proposed strategy and iteratively figured out the best solution. Simulation results showed that our CCAS yields more significant gains in term of reducing energy consumption and achieving high SBSs utilization ratio in the system, compared to the other two responding strategies in the actual, normal situation. Experiential outcomes also proved that QEA takes advantage in the ability of global optimizing than traditional algorithms such as the greedy algorithm and the random sleeping algorithm.

ACKNOWLEDGMENT

This work is jointly supported by the National Natural Science Foundation of China(No.61501042), the National High Technology Research and Development Program(863) of China (2015AA016101), Beijing Nova Program(Z151100000315078), and Information Network Open Source Platform and Technology Development Strategy(No.2016-XY-09).

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