Non-deterministic Polynomial-time Hard Problem Research Articles

Self-Optimization of Wireless Systems With Knowledge Management: An Artificial Intelligence Approach

In this paper, we propose a new concept of a knowledge management framework to enable a self-optimizing and self-learning for wireless system operation in real time. The framework encapsulates both environment and intelligent agent to reach optimal operation through sensing, perception, reasoning, and learning in a truly autonomous fashion. The agent derives adequate knowledge from previous actions improving the quality of future decisions. Domain experience was provided to guide the agent while exploring and exploiting the set of possible actions in the environment. Thus, it guarantees low-cost learning and achieves a near-optimal network configuration addressing the non-deterministic polynomial-time hardness problem of joint channel and location optimization in a wireless system. Extensive simulations are run to validate its fast convergence, high throughput, and resilience to dynamic interference conditions. We deploy the framework on off-the-shelf wireless devices to propose autonomous self-optimization with knowledge management.

Pr x Ca 1 − x MnO 3 based stochastic neuron for Boltzmann machine to solve “maximum cut” problem

The neural network enables efficient solutions for Nondeterministic Polynomial-time (NP) hard problems, which are challenging for conventional von Neumann computing. The hardware implementation, i.e., neuromorphic computing, aspires to enhance this efficiency by custom hardware. Particularly, NP hard graphical constraint optimization problems are solved by a network of stochastic binary neurons to form a Boltzmann Machine (BM). The implementation of stochastic neurons in hardware is a major challenge. In this work, we demonstrate that the high to low resistance switching (set) process of a PrxCa1−xMnO3 (PCMO) based RRAM (Resistive Random Access Memory) is probabilistic. Additionally, the voltage-dependent probability distribution approximates a sigmoid function with 1.35%–3.5% error. Such a sigmoid function is required for a BM. Thus, the Analog Approximate Sigmoid (AAS) stochastic neuron is proposed to solve the maximum cut—an NP hard problem. It is compared with Digital Precision-controlled Sigmoid (DPS) implementation using (a) pure CMOS design and (b) hybrid (RRAM integrated with CMOS). The AAS design solves the problem with 98% accuracy, which is comparable with the DPS design but with 10× area and 4× energy advantage. Thus, ASIC neuro-processors based on novel analog neuromorphic devices based BM are promising for efficiently solving large scale NP hard optimization problems.

Folo: Latency and Quality Optimized Task Allocation in Vehicular Fog Computing

With the emerging vehicular applications, such as real-time situational awareness and cooperative lane change, there exist huge demands for sufficient computing resources at the edge to conduct time-critical and data-intensive tasks. This paper proposes Folo, a novel solution for latency and quality optimized task allocation in vehicular fog computing (VFC). Folo is designed to support the mobility of vehicles, including vehicles that generate tasks and the others that serve as fog nodes. Considering constraints on service latency, quality loss, and fog capacity, the process of task allocation across stationary and mobile fog nodes is formulated into a joint optimization problem. This task allocation in VFC is known as a nondeterministic polynomial-time hard problem. In this paper, we present the task allocation to fog nodes as a bi-objective minimization problem, where a tradeoff is maintained between the service latency and quality loss. Specifically, we propose an event-triggered dynamic task allocation framework using linear programming-based optimization and binary particle swarm optimization. To assess the effectiveness of Folo, we simulated the mobility of fog nodes at different times of a day based on real-world taxi traces and implemented two representative tasks, including video streaming and real-time object recognition. Simulation results show that the task allocation provided by Folo can be adjusted according to actual requirements of the service latency and quality, and achieves higher performance compared with naive and random fog node selection. To be more specific, Folo shortens the average service latency by up to 27% while reducing the quality loss by up to 56%.

Hybrid Particle Swarm Algorithm for Products’ Scheduling Problem in Cellular Manufacturing System

Industries have to produce high quality products with low cost because of the competitive environment and customer demand. To cope with the increasing demand of customized products at low cost, the concept of cellular manufacturing systems (CMS) has been introduced under the umbrella of lean manufacturing. Industries are facing three major problems in CMS; selection of product families, cell formation and products scheduling. This paper deals with the products scheduling problem in CMS. As it is a non-deterministic polynomial-time (NP) hard problem, a hybrid particle swarm optimization algorithm with Nawaz, Enscore, Ham-NEH (NEPSO) embedded with local search is proposed to find optimized sequence results for two conflicting performance measures (work in process and machine cell utilization). Here, particle swarm optimization (PSO) is integrated with an NEH algorithm to quickly achieve better optimal sequence. For this purpose, the solution obtained from the NEH algorithm is used as a seed for PSO optimization. A mathematical model is presented for conflicting performance measures; minimization of work in process (WIP) and maximization of average machine cell utilization. A case study of automotive manufacturing cells was conducted. Results of the NEPSO were compared with the existing method, standard PSO, genetic algorithm (GA), and NEH algorithm, showing that the NEPSO performed better in term of problem optimization of the cellular layouts.

Modeling of the time-dependent multi-skilled RCPSP considering learning effect

PurposeThe purpose of this paper is to propose a new mixed-integer formulation for the time-dependent multi-skilled resource-constrained project scheduling problem (MSRCPSP/t) considering learning effect. The proposed model extends the basic form of the MSRCPSP by three concepts: workforces have different efficiencies, it is possible for workforces to improve their efficiencies by learning from more efficient workers and the availability of workforces and resource requests of activities are time-dependent. To spread dexterity from more efficient workforces to others, this study has integrated the concept of diffusion maximization in social networks into the proposed model. In this respect, the diffusion of dexterity is formulated based on the linear threshold model for a network of workforces who share common skills. The proposed model is bi-objective, aiming to minimize make-span and total costs of project, simultaneously.Design/methodology/approachThe MSRCPSP is an non-deterministic polynomial-time hard (NP-hard) problem in the strong sense. Therefore, an improved version of the non-dominated sorting genetic algorithm II (IM-NSGA-II) is developed to optimize the make-span and total costs of project, concurrently. For the proposed algorithm, this paper has designed new genetic operators that help to spread dexterity among workforces. To validate the solutions obtained by the IM-NSGA-II, four other evolutionary algorithms – the classical NSGA-II, non-dominated ranked genetic algorithm, Pareto envelope-based selection algorithm II and strength Pareto evolutionary algorithm II – are used. All algorithms are calibrated via the Taguchi method.FindingsComprehensive numerical tests are conducted to evaluate the performance of the IM-NSGA-II in comparison with the other four methods in terms of convergence, diversity and computational time. The computational results reveal that the IM-NSGA-II outperforms the other methods in terms of most of the metrics. Besides, a sensitivity analysis is implemented to investigate the impact of learning on objective function values. The outputs show the significant impact of learning on objective function values.Practical implicationsThe proposed model and algorithm can be used for scheduling activities of small- and large-size real-world projects.Originality/valueBased on the previous studies reviewed in this paper, one of the research gaps is the MSRCPSP with time-dependent resource capacities and requests. Therefore, this paper proposes a multi-objective model for the MSRCPSP with time-dependent resource profiles. Besides, the evaluation of learning effect on efficiency of workforces has not been studied sufficiently in the literature. In this study, the effect of learning on efficiency of workforces has been considered. In the scarce number of proposed models with learning effect, the researchers have assumed that the efficiency of workforces increases as they spend more time on performing a skill. To the best of the authors’ knowledge, the effect of learning from more efficient co-workers has not been studied in the literature of the RCPSP. Therefore, in this research, the effect of learning from more efficient co-workers has been investigated. In addition, a modified version of the NSGA-II algorithm is developed to solve the model.

Effective Neighborhood Generation Method in Search Algorithm for Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSSP) is an extension of the classical job shop scheduling problem (JSSP) that allocates jobs to resources while minimizing the maximum completion time of all the jobs. Machine assignment and job sequence are determined in the FJSSP. To efficiently solve the FJSSP, which is a non-deterministic polynomial-time hard problem, a heuristic method must be used. In previous studies, the FJSSP has been solved using neighborhood algorithms that employ various metaheuristic methods. These approaches constrain the neighborhood operation to jobs on a critical path and simultaneously change the machine assignment and job sequence. Branches on the critical path are easily generated in the FJSSP search processes; this branch structure can improve the efficiency of the FJSSP. This study investigates two neighborhood search algorithms used for changing the machine assignment and job sequence via a critical path. The first method changes the machine assignment and job sequence simultaneously, whereas the second method changes them independently. In this study, we propose an efficient neighborhood generating method using a branch block of critical path.

Recent trend in mixed-model assembly line balancing optimization using soft computing approaches

Purpose This paper aims to review and discuss four aspects of mixed-model assembly line balancing (MMALB) problem mainly on the optimization angle. MMALB is a non-deterministic polynomial-time hard problem which requires an effective algorithm for solution. This problem has attracted a number of research fields: manufacturing, mathematics and computer science. Design/methodology/approach This paper review 59 published research works on MMALB from indexed journal. The review includes MMALB problem varieties, optimization algorithm, objective function and constraints in the problem. Findings Based on research trend, this topic is still growing with the highest publication number observed in 2016 and 2017. The review indicated that the future research direction should focus on human factors and sustainable issues in the problem modeling. As the assembly cost becomes crucial, resource utilization in the assembly line should also be considered. Apart from that, the growth of new optimization algorithms is predicted to influence the MMALB optimization, which currently relies on well-established algorithms. Originality/value The originality of this paper is on the research trend in MMALB. It provides the future direction for the researchers in this field.

A PSO and BFO-Based Learning Strategy Applied to Faster R-CNN for Object Detection in Autonomous Driving

Recently outstanding object detection results are achieved by the faster region-based convolutional network (faster R-CNN). Particularly, high-quality detection proposals are obtained by the region proposal network (RPN). Nevertheless, part of the parameters in RPN is assigned by prior knowledge. Therefore the underfitting problem is likely to appear on the training model of RPN. In other words, the generalization ability of RPN is not enough. Increasing parameters is an effective solution to this problem. Thereupon a strengthened RPN (SRPN) is designed to expand the exploring space of RPN. Acquiring the optimal parameter values of SRPN is a non-deterministic polynomial-time hard problem, which can be solved by swarm intelligence algorithms. Thereafter a particle swarm optimization (PSO) and bacterial foraging optimization (BFO)-based learning strategy (PBLS) is introduced to optimize the classifier and loss function of SRPN. In SRPN, a novel multi-level extracting network is created to improve the feature sampling ability. Moreover, the mathematical model of the smooth L1 loss function is improved to boost the fitting ability. Additionally, support vector machine (SVM) method is applied to enhance the classifier learning capability. PBLS is applied to SRPN (PBLS_SRPN). The parameters of SVM and the improved loss function are optimized by the BFO and PSO methods, respectively. Then, the performance of SRPN is further promoted. The excellent results are obtained by our proposed methods on PASCAL VOC 2007, 2012, MS COCO, and KITTI data sets. Consequently, PBLS_SRPN is effective for object detection in autonomous driving.

Solving a multi-objective model of job rotation minimizing the chemical exposure and cost by particle swarm optimization

Today in developing countries, perilous chemicals are widely used that have harmful effect on human resources. National and global organizations developed different approaches to control chemicals exposure and their consequences in that one of them is job rotation. Since job rotation is categorized as nondeterministic polynomial-time hardness problem, meta-heuristic methods are used to solve it such as particle swarm optimization (PSO) algorithm. In this article, because job rotation can have different and contradictory objectives, the multi-objective PSO (MOPSO) method with parallel vector evaluated PSO approach is implemented. At first, a new MOPSO algorithm is presented that solves job rotation problems to minimize chemical exposures and is finally compared with non-dominated sorting genetic algorithm. The achievement of this algorithm reduces chemicals exposure in manufacturing processes such as casting, welding, foam injection, plastic injection, which ensure workers’ health.

Energy-Efficient Scheduling for a Job Shop Using an Improved Whale Optimization Algorithm

Under the current environmental pressure, many manufacturing enterprises are urged or forced to adopt effective energy-saving measures. However, environmental metrics, such as energy consumption and CO2 emission, are seldom considered in the traditional production scheduling problems. Recently, the energy-related scheduling problem has been paid increasingly more attention by researchers. In this paper, an energy-efficient job shop scheduling problem (EJSP) is investigated with the objective of minimizing the sum of the energy consumption cost and the completion-time cost. As the classical JSP is well known as a non-deterministic polynomial-time hard (NP-hard) problem, an improved whale optimization algorithm (IWOA) is presented to solve the energy-efficient scheduling problem. The improvement is performed using dispatching rules (DR), a nonlinear convergence factor (NCF), and a mutation operation (MO). The DR is used to enhance the initial solution quality and overcome the drawbacks of the random population. The NCF is adopted to balance the abilities of exploration and exploitation of the algorithm. The MO is employed to reduce the possibility of falling into local optimum to avoid the premature convergence. To validate the effectiveness of the proposed algorithm, extensive simulations have been performed in the experiment section. The computational data demonstrate the promising advantages of the proposed IWOA for the energy-efficient job shop scheduling problem.

Interactive livestock feed ration optimization using evolutionary algorithms

The profitability of the livestock industry largely depends on cost-effective feed ration formulation as feed accounts for between 60 and 80% of production costs. Therefore, feed formulation is a recurring problem for breeders. In addition, the presence of linear and non-linear constraints, and multiple possible combinations that are subject to upsurge makes the formulation of feed a Non-deterministic Polynomial-time hard (NP-hard) problem. Generally, feed formulation is done by specifying the nutritional requirements as rigid constraints and an algorithm attempts to find a feasible cost-effective formulation. However, relaxing the constraints can sometimes provide a huge reduction in the cost of feed while not seriously affecting the economic performance of the livestock. This entails the development of a feed formulation software that has an inbuilt mechanism to enable relaxation to the constraints based on the users’ necessities. Accordingly, the problem formulation and the optimization algorithm should facilitate this. We modified the conventional problem formulation with a tolerance parameter (as a percentage of the actual value) to accommodate the relaxation of constraints. We solved this problem with differential evolution, a variant of evolutionary algorithms, which are good for handling NP-hard problems. In addition, the relaxation of the constraints was done in an interactive way using the proposed method without penalties. In other words, the proposed method is flexible and possesses the ability to search for a feasible and least-cost solution if available or otherwise, the best solution and finds the suitable feed components to be used in ration formulation at an optimal cost depending on the nutrient requirements and growth stage of the animal.

Sustainable Service Allocation Using a Metaheuristic Technique in a Fog Server for Industrial Applications

Reducing energy consumption in the fog computing environment is both a research and an operational challenge for the current research community and industry. There are several industries such as finance industry or healthcare industry that require a rich resource platform to process big data along with edge computing in fog architecture. As a result, sustainable computing in a fog server plays a key role in fog computing hierarchy. The energy consumption in fog servers depends on the allocation techniques of services (user requests) to a set of virtual machines (VMs). This service request allocation in a fog computing environment is a nondeterministic polynomial-time hard problem. In this paper, the scheduling of service requests to VMs is presented as a bi-objective minimization problem, where a tradeoff is maintained between the energy consumption and makespan. Specifically, this paper proposes a metaheuristic-based service allocation framework using three metaheuristic techniques, such as particle swarm optimization (PSO), binary PSO, and bat algorithm. These proposed techniques allow us to deal with the heterogeneity of resources in the fog computing environment. This paper has validated the performance of these metaheuristic-based service allocation algorithms by conducting a set of rigorous evaluations.

Assignment of Virtual Networks to Substrate Network for Software Defined Networks

Assigning multiple virtual network resources to physical network resources, called virtual network embedding (VNE), is known to be non-deterministic polynomial-time hard (NP-hard) problem. Currently software-defined networking (SDN) is gaining popularity in enterprise networks to improve the customizability and flexibility in network management service and reduced operational cost. A central controller in SDNs is an important factor that we need to take care of when we want to assign virtual networks to physical resources. In this work, we address virtual network embedding problems for SDNs. Indeed, our objective is to propose a method to assign virtual networks in the substrate network with minimum physical resources, and also minimizing delays between the virtual network controller and the switches in the virtual network. Our proposed algorithm considers the link and node constraints such as CPU and bandwidth constraints which is necessary to consider when we try to solve virtual network embedding problems.

A Dynamic Scheduling Method for Carrier Aircraft Support Operation under Uncertain Conditions Based on Rolling Horizon Strategy

The efficient scheduling of carrier aircraft support operations in the flight deck is important for battle performances. The supporting operations and maintenance processes involve multiple support resources, complex scheduling process, and multiple constraints; the efficient coordination of these processes can be considered a multi-resource constrained multi-project scheduling problem (MRCMPSP), which is a complex non-deterministic polynomial-time hard (NP-hard) problem. The renewable resources include the operational crews, resource stations, and operational spaces, and the non-renewable resources include oil, gas, weapons, and electric power. An integer programming mathematical model is established to solve this problem. A periodic and event-driven rolling horizon (RH) scheduling strategy inspired by the RH optimization method from predictive control technology is presented for the dynamic scheduling environment. The periodic horizon scheduling strategy can track the changes of the carrier aircraft supporting system, and the improved event-driven mechanism can avoid unnecessary scheduling with effective resource allocation under uncertain conditions. The dual population genetic algorithm (DPGA) is designed to solve the large-scale scheduling problem. The activity list encoding method is proposed, and a new adaptive crossover and mutation strategy is designed to improve the global exploration ability. The double schedule for leftward and rightward populations is integrated into the genetic process of alternating iterations to improve the convergence speed and decrease the computation amount. The computational results show that our approach is effective at solving the scheduling problem in the dynamic environment, as well as making better decisions regarding disruption on a real-time basis.

Identify Congested Links with Network Tomography Under Multipath Routing

Identifying congested links accurately to ensure the Service Level Agreements is an important but challenging task, since it is costly or even practically unfeasible to monitor massive interior links directly for large networks. Network tomography has been proposed to overcome this problem by using end-to-end (path) measurements. However, most of existing tomographic methods only focus on the loss performance degradation, while paying much less attention the fact that network congestion will also greatly worsen the delay performance. Nevertheless, most of them normally work under single-path routing, which may also get violated in today’s Internet as multipath routing is increasingly common. In this paper, we consider the problem of using end-to-end measurements to identify congested links when multipath routing is employed in a non-tree network. Firstly, we use both link delay variances and link loss rates to model the system constraints between end- to-end paths and the interior links, and transfer the issue of congested link identification as an optimization problem. By theoretically demonstrating that the link delay variances are identifiable from the end-to-end delay measurements with certain topology conditions, we further prove that the above optimization problem is a Non-deterministic Polynomial-time hard (NP-hard) problem. Then in order to solve such an NP-hard problem, two greedy algorithms based on bool and additive congestion statuses are proposed. Lastly, simulation studies show that with extra delay constraints, our proposed algorithms are able to achieve better identification performances than existing methods under multipath routing.

Predicting Model and Algorithm in RNA Folding Structure Including Pseudoknots

The prediction of RNA structure with pseudoknots is a nondeterministic polynomial-time hard (NP-hard) problem; according to minimum free energy models and computational methods, we investigate the RNA-pseudoknotted structure. Our paper presents an efficient algorithm for predicting RNA structure with pseudoknots, and the algorithm takes O([Formula: see text]) time and O([Formula: see text]) space, the experimental tests in Rfam10.1 and PseudoBase indicate that the algorithm is more effective and precise. The predicting accuracy, the time complexity and space complexity outperform existing algorithms, such as Maximum Weight Matching (MWM) algorithm, PKNOTS algorithm and Inner Limiting Layer (ILM) algorithm, and the algorithm can predict arbitrary pseudoknots. And there exists a [Formula: see text] ([Formula: see text]) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximation scheme in RNA-pseudoknotted structure. We have improved several types of pseudoknots considered in RNA folding structure, and analyze their possible transitions between types of pseudoknots.

A GENETIC ALGORITHM APPROACH FOR SOLVING INBOARD OUTER FIXED LEADING EDGE-DRIVE RIB 1 PRODUCTION SCHEDULING AT PT DIRGANTARA INDONESIA

The scheduling of production floor is a sophisticated problem which seeks the optimal task allocation to certain resources under a number of constraints. The use of optimization techniques facilitates the determination of acceptable solutions that considered optimized for a specific problem. This paper proposes production scheduling solution based on job priority in a Non-Deterministic Polynomial-time hard (NP-hard) problem. The case study was taken from the Spirit Aerosystem Project, particularly in the Inboard Outer Fixed Leading Egde - Drive Rib 1 component production process. The problem consists of finding the machine operations schedule, taking into account the precedence constraints. The main objective is to minimize total delays or tardiness. The genetic algorithm was employed to determine the optimized production scheduling solution. The parameter for genetic operators in this study consists of a roulette wheel selection, 1 elitist chromosome, partially-mapped crossover mutation and 1 point mutation. The termination condition was achieved when there has been no improvement in the population for 30 iterations.The results show that the algorithm is capable to generate optimum production schedule with minimum tardiness for the given problem.
 Keywords: Genetic algorithm, job shop problem, scheduling problem

ModuleDiscoverer: Identification of regulatory modules in protein-protein interaction networks

The identification of disease-associated modules based on protein-protein interaction networks (PPINs) and gene expression data has provided new insights into the mechanistic nature of diverse diseases. However, their identification is hampered by the detection of protein communities within large-scale, whole-genome PPINs. A presented successful strategy detects a PPIN’s community structure based on the maximal clique enumeration problem (MCE), which is a non-deterministic polynomial time-hard problem. This renders the approach computationally challenging for large PPINs implying the need for new strategies. We present ModuleDiscoverer, a novel approach for the identification of regulatory modules from PPINs and gene expression data. Following the MCE-based approach, ModuleDiscoverer uses a randomization heuristic-based approximation of the community structure. Given a PPIN of Rattus norvegicus and public gene expression data, we identify the regulatory module underlying a rodent model of non-alcoholic steatohepatitis (NASH), a severe form of non-alcoholic fatty liver disease (NAFLD). The module is validated using single-nucleotide polymorphism (SNP) data from independent genome-wide association studies and gene enrichment tests. Based on gene enrichment tests, we find that ModuleDiscoverer performs comparably to three existing module-detecting algorithms. However, only our NASH-module is significantly enriched with genes linked to NAFLD-associated SNPs. ModuleDiscoverer is available at http://www.hki-jena.de/index.php/0/2/490 (Others/ModuleDiscoverer).

Top K representative: a method to select representative samples based on K nearest neighbors

Short text categorization involves the use of a supervised learning process that requires a large amount of labeled data for training and therefore consumes considerable human labor. Active learning is a way to reduce the number of manually labeled samples in traditional supervised learning problems. In active learning, the number of samples is reduced by selecting the most representative samples to represent an entire training set. Uncertainty sampling is a means of active learning but is easily affected by outliers. In this paper, a new sampling method called Top K representative (TKR) is proposed to solve the problem caused by outliers. However, TKR optimization is a nondeterministic polynomial-time hardness (NP-hard) problem, making it challenging to obtain exact solutions. To tackle this problem, we propose a new approach based on the greedy algorithm, which can obtain approximate solutions, and thereby achieve high performance. Experiments show that our proposed sampling method outperforms the existing methods in terms of efficiency.

Efficient ℓ0 -norm feature selection based on augmented and penalized minimization.

Advances in high-throughput technologies in genomics and imaging yield unprecedentedly large numbers of prognostic biomarkers. To accommodate the scale of biomarkers and study their association with disease outcomes, penalized regression is often used to identify important biomarkers. The ideal variable selection procedure would search for the best subset of predictors, which is equivalent to imposing an ℓ0 -penalty on the regression coefficients. Since this optimization is a nondeterministic polynomial-time hard (NP-hard) problem that does not scale with number of biomarkers, alternative methods mostly place smooth penalties on the regression parameters, which lead to computationally feasible optimization problems. However, empirical studies and theoretical analyses show that convex approximation of ℓ0 -norm (eg, ℓ1 ) does not outperform their ℓ0 counterpart. The progress for ℓ0 -norm feature selection is relatively slower, where the main methods are greedy algorithms such as stepwise regression or orthogonal matching pursuit. Penalized regression based on regularizing ℓ0 -norm remains much less explored in the literature. In this work, inspired by the recently popular augmenting and data splitting algorithms including alternating direction method of multipliers, we propose a 2-stage procedure for ℓ0 -penalty variable selection, referred to as augmented penalized minimization-L0 (APM-L0 ). The APM-L0 targets ℓ0 -norm as closely as possible while keeping computation tractable, efficient, and simple, which is achieved by iterating between a convex regularized regression and a simple hard-thresholding estimation. The procedure can be viewed as arising from regularized optimization with truncated ℓ1 norm. Thus, we propose to treat regularization parameter and thresholding parameter as tuning parameters and select based on cross-validation. A 1-step coordinate descent algorithm is used in the first stage to significantly improve computational efficiency. Through extensive simulation studies and real data application, we demonstrate superior performance of the proposed method in terms of selection accuracy and computational speed as compared to existing methods. The proposed APM-L0 procedure is implemented in the R-package APML0.