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Traveling salesman problem (TSP) has been widely applied to various fields of production and life. In order to solve the TSP, this work optimizes the architecture of the particle swarm optimization (PSO) by introducing a preprocessing multi-subdomain grouping approach to divide the entire search space into several sub-regions, based on the geographical center of planned cities. To solve subdomain problems, the global search ability of PSO is further improved using genetic mutation and particle competition mechanism to maintain the population diversity during late iterations. An effective simplified 4-opt is finally employed to eliminate path-crossing after connecting all subdomain paths in a time saving way. Comparison with three of our previous algorithms and seven algorithms from other reports reveals that the proposed algorithm shows good performance in both the computing efficiency and route quality. Particularly, it is suitable for small (or medium)-sized TSP problems with relatively percentage error values below 4.8%.

Coordination control of large-scale urban traffic networks provides a more easy and feasible way to improve mobility in heterogeneous city centers. Urban traffic network partitioning is the foundation and prerequisite for achieving regional control. In order to describe the correlation strength between two adjacent intersections, a quantitative indicator considering the dynamic traffic flows is proposed to depict the congested degree in each link. Based on the simulation data collected from microscopic traffic model, the topology of urban traffic network could be converted into an adjacent matrix. Inspired by the concept of community detection in complex networks theory, spectral bisection method is utilized to find the spatial compactness areas in traffic networks. In addition, the modularity is adopted to evaluate the partitioning results and to point out the next partitioning direction at each step. The simulation is carried out for a peak hour in SUMO. Compared with other classical community detection methods, the proposed approach can obtain the adequate number of subnetworks with less computational complexity.

Siamese network based trackers formulate the visual tracking task as a similarity matching problem. Almost all popular Siamese trackers realize the similarity learning via convolutional feature cross-correlation between a target branch and a search branch. However, since the size of target feature region needs to be pre-fixed, these cross-correlation base methods suffer from either reserving much adverse background information or missing a great deal of foreground information. Moreover, the global matching between the target and search region also largely neglects the target structure and part-level information. In this paper, to solve the above issues, we propose a simple target-aware Siamese graph attention network for general object tracking. We propose to establish part-to-part correspondence between the target and the search region with a complete bipartite graph, and apply the graph attention mechanism to propagate target information from the template feature to the search feature. Further, instead of using the pre-fixed region cropping for template-feature-area selection, we investigate a target-aware area selection mechanism to fit the size and aspect ratio variations of different objects. Experiments on challenging benchmarks including GOT-10k, UAV123, OTB-100 and LaSOT demonstrate that the proposed SiamGAT outperforms many state-of-the-art trackers and achieves leading performance. Code is available at: https://git.io/SiamGAT

Hyperspectral images (HSIs) have evident advantages in image understanding because of enormous spectral bands, and rich spatial information. However, applying the limited labeled samples to obtain satisfactory classification results is a challenging task. Secondary screening algorithm and semisupervised learning are two promising methods to address this problem. Secondary screening algorithm exploits different query functions, which are on the basis of the evaluation of two criteria: uncertainty and diversity. The advantage of semisupervised learning is that with a small number of samples, classifiers could learn the structure of whole data sets without significant costs and efforts. Hence, combining secondary screening algorithm and semisupervised learning is a natural consideration. We firstly investigate nine secondary screening algorithms and compare their performance. Next, two novel frameworks are proposed in this paper. They are named the syncretic one-fold secondary screening algorithm and semisupervised learning framework (OFSS-SL) and syncretic multiple secondary screening algorithms and multiple-verification semisupervised learning framework (MSS-MVSL), respectively. We evaluate the performance of OFSS-SL and MSS-MVSL on three hyperspectral data sets and compare them with that of three state-of-the-art classification methods. In general, our results suggest that two proposed frameworks can apply limited labeled samples to achieve excellent classification results. And the computational costs of them are cheaper than previous methods.

In hyperspectral image classification, the foremost task is that: how can we apply limited labeled samples to achieve good classification results? Spatial–spectral classification methods, which assign a label to each pixel regarding both spatial and spectral information, are effective to improve classification performance. Moreover, semisupervised learning (SSL) focuses on the scenario that the number of labeled data is rather small while a large number of unlabeled data are available. To complement spatial–spectral classification methods and semisupervised learning for each other, we propose a novel learning landscape features semisupervised framework (LLFSF) based on M-training algorithm and weighted spatial-spectral double layer SVM classifiers module (WSS-DSVM). In this novel framework, we first propose a SLIC (simple linear iterative clustering) based non-local superpixel segmentation algorithm to initially learn landscape feature and spatial composition. Then, we apply WSS-DSVM module to obtain initial classification maps. To better characterize complex scenes of hyperspectral images, we quantizes both the landscape diversity and separability from the initial classification map, which increase availability of spatial details and structural information of objects. Finally, we put some patches with lower accuracy into Multiple-training algorithm for further classification. In order to achieve an unbiased evaluation, we have evaluated the performance of LLFSF on three different scene hyperspectral data sets and compare it with that of three state-of-the-art hyperspectral image classification methods. The experimental results confirm the efficacy of the proposed framework.

Equipped with mass market, social convenience and huge communications, Wechat has been the major channel of information in the new era. WeChat official subscriptions, due to the strong platform, are indispensable for health distribution. How to maximize platform advantages for better health dissemination effect has become debated. Comprehending the communication strategy holds key to the health enterprises, and even to improve the health awareness of the whole society. The official subscription of “Dingxiang Doctor”, an influential health knowledge medium, is selected for case study in the paper. Its 264 articles, published from July 1 to 31, 2019, are utilized as samples to analyze its communication effect and strategy. Communication effect mainly refers to the changes made by the audience in the four progressive stages of knowledge, emotion, attitude and behavior after receiving information. As the emerging media, WeChat official subscriptions know that the cognitive situation corresponds to the communication breadth, and the attitude and emotion transformation corresponds to the communication depth, with reads and likes as the specific evaluation indicator respectively. In terms of the communication breadth, the paper analyzes the strategy from the article position (headline and non-headline), title setting (expression and entertainment) and section setting (classification and subdivision), as well as the ranking of reads (total, highest and average reads). With regard to communication depth, it illustrates from multimedia usage (general picture and text, cartoons, audio and video), content science (the mark of scientific review) and topic selection and classification (health care, nutritious diet, disease prevention, etc.), as well as likes (total, highest and average likes). All of these are to bring forth suggestions to improve the health dissemination. Data analysis of the sample from “Dingxiang Doctor” conveys that, for communication breadth, the headline, and the enticing, emphatic and entertaining topic have higher reads. Additionally, compared to the interactive content, the promotion has higher reads, and the marketing highest. In terms of communication depth, the audio and video compared with the general picture and text have higher reads, and the cartoon has highest ones. Whether the articles are located in the front page or not, those marked with scientific review have higher likes. The topics closely related to readers' daily life also have a higher likes. The following strategies can be adopted to enhance health communication. Firstly, attention should be paid the headline role and the exquisite content, title and presentation. Secondly, the title should be eye-catching and engaging, and the plate classification should be concise and reasonable. Thirdly, the topic should be interconnected with life, content ought to be scientific and authoritative, and presentation is supposed to be rich and varied. These strategies allow the serious and boring science to be easily understood. In this way, they can help editors with scientific and entertaining articles for cultivating the proper health awareness of the audience.

In this paper, we consider a large-scale edge computing (EC)-enabled network. We consider multiple latency-sensitive services. We adopt a random service caching scheme and a computation resource allocation scheme at base stations (BSs). We first derive the successful service probability (SSP). Using tools from stochastic geometry and queuing theory, we formulate the SSP maximization problem with respect to (w.r.t.) the service caching distribution and computation resource allocation, which is a challenging non-convex problem due to the complicated form of the SSP. Using parallel successive convex approximation (SCA), we develop an efficient iterative algorithm to obtain a stationary point of the non-convex problem. Finally, by numerical simulations, we show that the proposed solution achieves a higher SSP than the baseline schemes. We also show the impacts of the cache size and service rate of EC servers.

We investigate stochastic snowdrift games in which the payoff of players are disturbed by stochastic noise and time delay in this paper. The stochastic replicator dynamic model is proposed so as to investigate stochastic stability of evolutionary games. Our most interesting results concern the impact of multiplicative noise and time delay on the cooperation behavior in large well-mixed populations. The theory of stochastic delay differential equation is used as the main research tool. A sufficient condition on time delay and noise is proposed that it is corrected to guarantee the stable equilibrium point is indeed the almost sure exponential stablility (ASES). Moreover, we get a generalization of the cooperation evolution in two-strategy games. Stochastic Lyapunov framework is used to prove the stochastic stability and finding the value of delay is the key and challenging in our case. Examples are illustrated our results.

In this paper, we investigate the stability analysis of stochastic opinion dynamics in which the agents are interfered by multiplicative noise. We propose a stochastic Altafini model of opinion evolution in signed social networks with multiplicative noise and give the analysis of almost sure exponential stability (ASES). Compared with the deterministic opinion dynamic and stochastic opinion dynamics in additive noise environments, our results concern the effects of the agents’ free will, i.e., multiplicative noise, in signed social networks. We establish a sufficient condition with stochastic multiplicative noise which can guarantee the stochastic system is almost sure exponential stability (ASES) when the parameters of the strength of noise is limited by the conditions. Numerical simulations are given to illustrate the above theoretical results.

As RFID system has fewer calculation and storage resources for RF tag, it is difficult to adopt the traditional encryption algorithm technology with higher security, which leads to the system being vulnerable to counterfeiting, tampering, leakage and other problems. To this end, a lightweight bidirectional security authentication method based on the combined public key is proposed. The method deals with the key management problem of the power Internet of things (IoT) in the terminal layer device by studying the combined public key (CPK) technology. The elliptic curve cryptosystem in the CPK has the advantages of short key length, fast calculation speed and small occupied bandwidth, which is very suitable for the hardware environment of RFID system with limited performance. It also ensures the security of the keys used in the access of the IoT terminal equipment to the authentication, and achieves overall optimization of speed, energy consumption, processing capacity and security.

In this paper, we study an intelligent reflecting surface (IRS)-assisted system where a multi-antenna base station (BS) serves a single-antenna user with the help of a multi-element IRS in the presence of interference generated by a multi-antenna BS serving its own single-antenna user. The signal and interference links via the IRS are modeled with Rician fading. To reduce phase adjustment cost, we adopt quasi-static phase shift design where the phase shifts do not change with the instantaneous channel state information (CSI). We investigate two cases of CSI at the BSs, namely, the instantaneous CSI case and the statistical CSI case, and apply Maximum Ratio Transmission (MRT) based on the complete CSI and the CSI of the Line-of-sight (LoS) components, respectively. Different costs on channel estimation and beamforming adjustment are incurred in the two CSI cases. First, we obtain a tractable expression of the average rate in the instantaneous CSI case and a tractable expression of the ergodic rate in the statistical CSI case. We also provide sufficient conditions for the average rate in the instantaneous CSI case to surpass the ergodic rate in the statistical CSI case, at any phase shifts. Then, we maximize the average rate and ergodic rate, both with respect to the phase shifts, leading to two non-convex optimization problems. For each problem, we obtain a globally optimal solution under certain system parameters, and propose an iterative algorithm based on parallel coordinate descent (PCD) to obtain a stationary point under arbitrary system parameters. Next, in each CSI case, we provide sufficient conditions under which the optimal quasi-static phase shift design is beneficial, compared to the system without IRS. Finally, we numerically verify the analytical results and demonstrate notable gains of the proposal solutions over existing ones., Comment: 14 pages, 9 figures, to appear in IEEE Trans. Wireless Commun

In this paper, we develop the energy-efficient resource allocation scheme for an edge computing-enabled vehicular network. We first introduce the novel prescheduled task splitting and offloading scheme, which splits the vehicle's task into several subtasks and offloads to multiple road side units (RSUs), located ahead along the route. We then formulate the energy minimization problem subject to the communication performance and computation capabilities of the RSUs, and the deadline constraints to optimally split the task and allocate resources at the RSUs. We show that the optimization problem is a convex optimization problem and derive the closed form optimal solutions for the task splitting, the transmission power allocation, the CPU frequency allocation, and the transmission time allocation. Finally, through numerical results, by analyzing the impact of network parameters on the total energy consumption, we verify that our proposed scheme consumes lower energy than baseline schemes.

By decomposing the visual tracking task into two subproblems as classification for pixel category and regression for object bounding box at this pixel, we propose a novel fully convolutional Siamese network to solve visual tracking end-to-end in a per-pixel manner. The proposed framework SiamCAR consists of two simple subnetworks: one Siamese subnetwork for feature extraction and one classification-regression subnetwork for bounding box prediction. Different from state-of-the-art trackers like Siamese-RPN, SiamRPN++ and SPM, which are based on region proposal, the proposed framework is both proposal and anchor free. Consequently, we are able to avoid the tricky hyper-parameter tuning of anchors and reduce human intervention. The proposed framework is simple, neat and effective. Extensive experiments and comparisons with state-of-the-art trackers are conducted on challenging benchmarks including GOT-10K, LaSOT, UAV123 and OTB-50. Without bells and whistles, our SiamCAR achieves the leading performance with a considerable real-time speed. The code is available at https://github.com/ohhhyeahhh/SiamCAR.

Device activity detection is one main challenge in grant-free random access, which is recently proposed to support massive access for massive machine-type communications (mMTC). Existing solutions fail to consider interference generated by massive Internet of Things (IoT) devices, or important prior information on device activities and interference. In this paper, we consider device activity detection at an access point (AP) in the presence of interference generated by massive devices from other cells. We consider the joint maximum likelihood (ML) estimation and the joint maximum a posterior probability (MAP) estimation of both the device activities and interference powers, jointly utilizing tools from probability, stochastic geometry and optimization. Each estimation problem is a difference of convex (DC) programming problem, and a coordinate descent algorithm is proposed to obtain a stationary point. The proposed ML estimation extends the existing ML estimation by considering the estimation of interference powers together with the estimation of device activities. The proposed MAP estimation further enhances the proposed ML estimation by exploiting prior distributions of device activities and interference powers. Numerical results show the substantial gains of the proposed joint estimation designs, and reveal the importance of explicit consideration of interference and the value of prior information in device activity detection., 6 pages, 5 figures, to be publised in IEEE WCNC 2020

Device activity detection and joint device activity and data detection (or equivalently, detection of pilots being transmitted) are main challenges in grant-free random access, which is recently proposed to support massive machine-type communications (mMTC). In this paper, we adopt a general and tractable model for distributions of pilot states (being transmitted or not), namely the multivariate Bernoulli (MVB) model, which can explicitly specify general correlation among device activities and relation among the states of pilots assigned to one device. Then, based on the MVB model, we formulate the estimation of pilot states as a maximum a posterior probability (MAP) estimation problem, which is a challenging non-convex problem. We propose a low-complexity coordinate descent algorithm to obtain a stationary point. The proposed MAP estimation enhances the existing maximum likelihood (ML) estimation and MAP estimation, by effectively exploiting the general prior distribution of pilot states and tackling the estimation problem in a rigorous way. Numerical results show the substantial gains of the proposed MAP-based design over well-known existing designs, and reveal the value of the proposed solution framework in pilot state detection.

The tradeoff between bandwidth efficiency and quality of experience (QoE) is a key issue in 360 video transmission. In this paper, we propose a QoE-oriented saliency-aware 360 video transmission framework to balance this tradeoff. The target is to reduce the bandwidth demand without declining the QoE. Specifically, the proposed model is based on the decision-making process. We use Lyapunov optimization to solve the decisionmaking problem. Furthermore, we integrate saliency information into the model to influence the decision policy, so that the model has the advantage of bandwidth efficiency. The simulation results show that the tradeoff parameter of Lyapunov optimization can balance the tradeoff between QoE and bandwidth efficiency, and 360 video saliency entropy limits the upper and lower bounds of QoE and bandwidth efficiency.

New energy value is defined by combining three traditional energy values. The comprehensive energy efficiency evaluation model is established by studying the generation, transformation and transportation of secondary energy. The effect of demand conditions on energy efficiency is analyzed based on data. The application scope of the model is briefly described.

With the widespread use of the Internet of Things (IoT), it is possible to continuously and accurately monitor different phenomena in the environment. For example, indoor environment detection of smart buildings, pollution source monitoring of smart cities, etc. This paper focuses on indoor environmental monitoring, using intelligent decives to collect indoor environmental data, analyzing the spatial correlation of data, using Gaussian Process (GP) to achieve spatial field reconstruction, and data prediction at any position in space. Most importantly, this method has practical significance in energy conservation and emission reduction and safety monitoring methods. The proposed approach was implemented in Intel Berkeley Lab, where the obtained results are highly promising.

A key approach for reducing motor impairment and regaining independence after spinal cord injuries or strokes is frequent and repetitive functional training. A compatible exoskeleton (Co-Exos II) is proposed for the upper-limb rehabilitation. A compatible configuration was selected according to optimum configuration principles. Four passive translational joints were introduced into the connecting interfaces to adapt the glenohumeral joint (GH) movements and improve the compatibility of the exoskeleton. This configuration of the passive joints could reduce the influence of gravity of the exoskeleton device and the upper extremities. A Co-Exos II prototype was developed and still owned a compact volume. A new approach was presented to compensate the vertical GH movements. The shoulder closed-loop was simplified as a guide-bar mechanism. The compatible models of this loop were established based on the kinematic model of GH. The compatible experiments were completed to verify the kinematic models and analyze the human-machine compatibility of Co-Exos II. The theoretical displacements of the translational joints were calculated by the kinematic model of the shoulder loop. The passive joints exhibited good compensations for the GH movements through comparing the theoretical and measured results, especially vertical GH movements. Co-Exos II showed good human-machine compatibility for upper limbs.

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found to provide improved clustering performance over the K-means. The ONMF model is a challenging optimization problem due to the orthogonality constraint, and most of the existing methods directly deal with the constraint in its original form via various optimization techniques. In this paper, we propose an equivalent problem reformulation that transforms the orthogonality constraint into a set of norm-based non-convex equality constraints. We then apply a penalty approach to handle these non-convex constraints. The penalized formulation is smooth and has convex constraints, which is amenable to efficient computation. We analytically show that the penalized formulation will provide a feasible stationary point of the reformulated ONMF problem when the penalty is large. Numerical results show that the proposed method greatly outperforms the existing methods.

Power Line Communication (PLC) is an effective technology to counteract problem of wiring harness increasing in intelligent vehicle. Besides the physical layer, the Medium Access Control (MAC) layer must meet the low latency requirements for automotive control information. Therefore, a hybrid MAC protocol is introduced based on the HomePlug AV protocol, which uses different media access control methods for periodic and aperiodic signals. In particular, for periodic signals, an LBBF heuristic algorithm is proposed in this paper for scheduling problems of TDMA time slots to improve the utilization of time slots and reduce TDMA time slot waste. Finally, compared with the traditional static scheduling scheme in FlexRay, the Left-Bottom Best Fit (LBBF) algorithm can improve the utilization of time slots and greatly reduce the number of time slots occupied, thus improving the performance of automobile communication.

In this paper, we investigate the optimization of task operation sequences for designing practical multi-user mobile edge computing (MEC) systems. First, we consider a computation task model with non-negligible sizes of computation results and arbitrary task arrival times and deadlines. Based on it, we further establish a computation offloading model considering non-negligible executing durations, allowing parallel transmissions and executions for different tasks, and reflecting the impact of task operation sequences. Then, we formulate the weighted sum energy consumption minimization problem to optimize the task operation sequences and starting times for uploading, executing and downloading as well as uploading and downloading time durations. The problem is a challenging mixed discrete-continuous optimization problem. By analyzing structural properties of task operation sequences, we develop an algorithm to obtain an optimal solution. In addition, using several optimization techniques, we transform the problem to an equivalent Difference of Convex (DC) problem, and develop a low-complexity algorithm to obtain a suboptimal solution using Penalty Convex Concave Procedure (CCP). Finally, numerical results demonstrate the advantages of the suboptimal solution over some optimized schemes with typical choices for task operation sequences.

Uniform opposition-based particle swarm optimization (NOPSO) is proposed to overcome the drawbacks, such as, slow convergence speed, falling into local optimization, of opposition-based particle swarm optimization. Two mechanisms are introduced to balance the contradiction between exploration and exploitation during searching process. 1) Firstly, a new particle's position update rule in which uniform term replaces the inertia term is designed to accelerate its convergence; 2) Secondly, an adaptive elite mutation strategy (AEM) is included to avoid trapping into local optimum. Experimental results show that the proposed method has a significant improvement in performance compared with some state-of-art PSOs.

This paper intends to solve problems such as the lack of motivation of personalized learning and the poor self-learning ability under the networked environment. To this end, we construct a mathematical model of personalized online learning incentive mechanism by analyzing personalized learning key elements and online learning behaviors. However, the effectiveness of the model remains to be verified in practical online learning environments.

In this paper, the downlink file transmission in one cell with the assistance of cache nodes is studied. Specifically, the base station (BS) reactively delivers files to cache nodes and a requesting user in a multicast manner. Therefore, one file transmission may lead to the cache status update, which further affects the future file transmissions. We consider the joint optimization of file placement and delivery. In particular, we first formulate the optimization of transmission power and time in one finite file lifetime as a Markov Decision Process (MDP) with a random number of stages, where the objective is to minimize the transmission resource at the BS. It is shown that the optimal solution can be obtained via a revised Bellman's equation. Due to the curse of dimensionality, a novel approximation approach is proposed, where the value functions of the Bellman's equation can be calculated from analytical expressions. Hence, iterative algorithms, which appear in the general approximate MDP solutions, can be avoided. Moreover, an bound on the approximation error is also provided.

Energy is an important supporting factor for social progress and economic development. The scientific development of energy systems has received worldwide attention, and theoretical research on energy supply and demand development is also deepening. This paper starts with China's energy data from 1997 to 2007 and discusses the relationship between energy structure, energy price, energy efficiency and economic development. Then the entropy weight method was used to establish an evaluation method for the relationship between energy saving and emission reduction and economic development. Finally, a prediction model of energy demand was established by using SPSS and verified by the real statistics.

Contract energy management is a new form of energy saving at present. This article introduces the meaning and application mode of contract energy management, and analyzes the energy consumption and distributed functional system of industrial park. Then the methods and suggestions on the application of contract energy management to industrial park are given.

As Internet expanding into offline, the traditional retail industry began to use the personalized recommendation algorithm to increase user stickiness, conversion and business income. Without considering the data segmentation problem, traditional recommendation algorithm did not perform well in the traditional business data. Accordingly, we considered the interest spread characteristic of retail industry behavior, adopted the method of complex network to construct a personalized recommendation algorithm using the segmentation data set. By using a real sales dataset of a large supermarket, we provided an evaluation of our algorithm. The results show that our algorithm have much better performance in accuracy and recall than the traditional ones, but with the disadvantage of being less coverage.

To improve signal-to-interference ratio (SIR) and make better use of file diversity provided by random caching, we consider the maximal ratio combining (MRC) receiver at each user in a large-scale cache- enabled single-input multi-output (SIMO) network. First, by utilizing tools from stochastic geometry, we derive a tractable expression and closed-form upper and lower bounds for the successful transmission probability in the general SIR threshold regime. We also derive a closed-form expression for the asymptotic outage probability in the low SIR threshold regime. The analytical results reveal that the successful transmission probability increases with the number of receive antennas M at each user in the general SIR threshold regime, the coefficient of the asymptotic outage probability decreases with M and the order gain of the asymptotic outage probability does not depend on M. Then, we consider the successful transmission probability maximization. In the general SIR threshold regime, we consider the maximization of the tight upper bound on the successful transmission probability by optimizing the caching distribution, which is a non-convex problem. We obtain a stationary point, by solving an equivalent difference of convex (DC) programming problem using concave-convex procedure (CCCP). We also obtain a closed-form asymptotically optimal solution in the low SIR threshold regime. The optimization results indicate that files of higher popularity get more storage resources, and the caching distribution becomes more flat when M is larger.

We consider the classical coded caching problem as defined by Maddah-Ali and Niesen, where a server with a library of $N$ files of equal size is connected to $K$ users via a shared error-free link. Each user is equipped with a cache with capacity of $M$ files. The goal is to design a static content placement and delivery scheme such that the average load over the shared link is minimized. We first present a class of centralized coded caching schemes consisting of a general content placement strategy specified by a file partition parameter, enabling efficient and flexible content placement, and a specific content delivery strategy, enabling load reduction by exploiting common requests of different users. For the proposed class of schemes, we consider two cases for the optimization of the file partition parameter, depending on whether a large subpacketization level is allowed or not. In the case of an unrestricted subpacketization level, we formulate the coded caching optimization in order to minimize the average load under an arbitrary file popularity. A direct formulation of the problem involves $N2^K$ variables. By imposing some additional conditions, the problem is reduced to a linear program with $N(K+1)$ variables under an arbitrary file popularity and with $K+1$ variables under the uniform file popularity. We can recover Yu {\em et al.}'s optimal scheme for the uniform file popularity as an optimal solution of our problem. When a low subpacketization level is desired, we introduce a subpacketization level constraint involving the $\ell_0$ norm for each file. Again, by imposing the same additional conditions, we can simplify the problem to a difference of two convex functions (DC) problem with $N(K+1)$ variables that can be efficiently solved., Comment: 30 pages, 8 figures, presented in part at IEEE WiOpt 2018