Dual Decomposition Technique Research Articles

Sequential Clearing of Network-Aware Local Energy and Flexibility Markets in Community-Based Grids

In this paper, network-aware clearing algorithms for local energy markets (LEMs) and local flexibility markets (LFM) are proposed to be sequentially run and coordinate assets and flexible resources of energy communities (ECs) in distribution networks. In the proposed LEM clearing algorithm, EC managers run a two-stage stochastic programming while considering random events by scenario generation and network constraints using linearized DistFlow. As one of outcomes, maximum available up-and down-regulations provided by ECs are estimated in LEM and communicated to LFM. In the distributed LFM clearing algorithm, an iterative auction is designed using a dual-decomposition technique (Augmented Lagrangian) which is solved by consensus alternating direction method of multipliers. The LFM algorithm efficiently dispatches the flexibility provided by ECs in operating time while considering flexibility local marginal price as pricing method. Network constraints are included in the algorithm with an AC distribution optimal power flow for dynamic network topology in which branches and buses are decomposed to solve the problem in distributed fashion. The designed LFM algorithm can respond to exogenous and endogenous signals for flexibility requests. The simulation results in a test case display effectiveness of two proposed LEM and LFM algorithms for an efficient provision of flexibility.

Privacy-Preserving Operation Management of Battery Swapping and Charging System With Dual-Based Benders Decomposition

The battery swapping and charging system (BSCS) is an emerging and promising infrastructure to provide the energy refueling service for EVs. However, each operator (i.e., battery swapping module (BSM) operator and battery charging module (BCM) operator) in BSCS has privacy-preserving requirement and individual interest, which brings challenge to the operation management of BSCS. To this end, this paper investigates the privacy-preserving operation management problem (OMP) of BSCS from a social perspective, in which a comprehensive battery-swapping-charging process is modeled. Specifically, we first model the OMP as a constrained mixed-integer programming (MIP), where the evolutionary of the dynamic battery inventory and the SoC of charging batteries are considered simultaneously. Due to the privacy-preserving requirements of different operators and the strong coupling between continuous and binary decision variables, a novel dual-based Benders decomposition (DBD) algorithm is then developed, which has the following two merits: 1) Each BCM and BSM operator can independently solve its own charging and swapping scheduling problem, thus preserving the privacy of individual operator; 2) The combination of dual decomposition and Benders decomposition techniques facilitates a parallel implementation, thus improving the scheduling efficiency and saving the computational time. Finally, simulation results are provided to validate the effectiveness and scalability of the proposed algorithm.

UAV-Aided Vehicular Short-Packet Communication and Edge Computing System Under Time-Varying Channel

In this paper, a novel UAV-aided vehicular edge computing (VEC) network is proposed, where the vehicle and on-board UAV provide multi-access edge computing (MEC) service for the roadside Internet of Things (IoT) devices. In this system, considering the time-varying channel, we derive the lower bound of signal-to-noise ratio (SNR) based on the first-order Gauss-Markov process. Then, with the short-packet transmission, we maximize the total amount of computation by jointly optimizing the communication scheduling, the trajectories of the vehicle and on-board UAV, and the computing resource, subject to the mobility, connection and computation constraints. The formulated optimization problem is a mix-integer non-convex problem. To efficiently solve it, we propose an alternative algorithm based on the Lagrangian dual decomposition and successive convex approximation technique. Extensive simulation results are provided to show the performance gain of the proposed algorithm.

Identification of Alzheimer’s Disease Using Novel Dual Decomposition Technique and Machine Learning Algorithms from EEG Signals

Alzheimer’s disease (AD) is one of the neurodegenerative disorders. The rate of AD prevalence is rapidly increasing worldwide. The existing clinical invasive methods and neuro-imaging techniques to detect AD are time-consuming, subjective, and expensive. To overcome these issues, we proposed a new automatic framework for detecting AD at an early stage based on the dual decomposition method. Initially, EEG signals of mild cognitive impairment (MCI), AD, and normal control (NC) patients are divided into five subbands by employing discrete wavelet transform (DWT). Subsequently, a Variational mode decomposition (VMD) is applied to these five EEG subbands for further decomposition into various intrinsic mode functions (IMFs). Afterward, three different multiscale permutation entropy (PE) features, namely Shannon PE (SPE), Tsalli’s PE (TPE), and Renyi PE (RPE), have been measured from each IMF. Later, these features have been used to train and test ensemble bagged tree (EBT), k-nearest neighbor, support vector machine (SVM), decision tree (DT), and neural networks with a 10-fold cross-validation scheme. The proposed method has been verified using EEG signals of 59-AD, 7-MCI, and 102-NC subjects. The results obtained from the proposed DWT-VMD method provide 95.20% accuracy for three-class and 97.70% for two-class classification using an EBT classifier with 10-fold cross-validation. It shows a significant ability to distinguish AD from MCI. The proposed dual decomposition method can employ for other neurodegenerative disorders such as Parkinson’s disease, epilepsy, various sleep disorders, and major depressive disorders.

Energy-Efficient Multiprocessor-Based Computation and Communication Resource Allocation in Two-Tier Federated Learning Networks

In conventional federated learning (FL), multiple edge devices holding local data jointly train a machine learning model by communicating learning updates with a centralized aggregator without exchanging their data samples. Owing to the communication and computation bottleneck at the centralized aggregator and inaccurate learning model caused by the non-IID data, we here consider a two-tier FL network, in which IoT nodes are the core clients that hold data, the model aggregators at the middle tier are the low altitude aerial platforms (UAVs), and the model aggregator at the top-most layer is the high altitude aerial platform (UAV with relatively high altitude). Under the assumption that each IoT node has parallel computing ability, we study the energy-efficient computation and communication resource allocation in such a network within some time budget. Upon formulating the problem as an optimization problem, we solve the computation and communication resource allocation problems as the separate subproblems within a time frame, and then propose an iterative algorithm to solve the entire problem jointly. More specifically, We solve both the energyefficient computation and communication resource allocation subproblems using the dual decomposition technique, and then apply a bisection search-based recursive technique to solve the entire energy efficiency problem jointly. Moreover, we propose offline and online client scheduling schemes that not only select the optimal edge nodes for association but also assign workload to each client based on the data quality and workload constraint. With real data, extensive simulations are conducted to verify the effectiveness of the proposed resource allocation scheme. The results further reveal that the learning performance not only is dependent on the computation and communication energy consumption of the FL process but also the model divergence weight owing to the non-IID data at client IoT nodes.

Robust Longitudinal Distributed Model Predictive Control of Connected and Automated Vehicles With Coupled Safety Constraints

This paper deals with robust cooperative control of connected and automated vehicles (CAVs) with special consideration of the coupled safety inter-vehicle distance constraints. To address the hard constraints caused by the vehicle physical limitations and the coupled safety constraints among adjacent vehicles explicitly, the distributed model predictive control (DMPC) problem for CAVs is formulated. By virtue of the Lagrangian multiplier method and the dual decomposition technique, the DMPC problem subject to coupled constraints is recast into a distributed dual variable consensus optimization problem comprised of a series of subsystems with local copies of the dual variables, which is then cooperatively solved in parallel based on the alternating direction method of multiplier (ADMM) under the distributed information exchange mechanism. In addition, the disturbance is dynamically mitigated by the feedback control, and its influence on the vehicle status is quantified by the associated robust positively invariant set. Robust cooperative control protocols are proposed to regulate the cooperative operations of CAVs, and the recursive feasibility and the closed-loop stability are theoretically proved. Numerical experiments are carried out to illustrate the effectiveness of the proposed method.

Anti-Jamming Strategy for Federated Learning in Internet of Medical Things: A Game Approach.

Federated learning (FL) is a new dawn of artificial intelligence (AI), in which machine learning models are constructed in a distributed manner while communicating only model parameters between a centralized aggregator and client internet-of-medical-things (IoMT) nodes. The performance of such a learning technique can be seriously hampered by the activities of a malicious jammer robot. In this paper, we study client selection and channel allocation along with the power control problem of the uplink FL process in IoMT domain under the presence of a jammer from the perspective of long-term learning duration. We map the interaction between the FL network and the jammer in each learning iteration as a Stackelberg game, in which the jammer acts as the leader and the FL network serves as the follower. We consider the client and channel selection as well as the power control jointly as the strategy of this game. Upon formulating the game, we find the joint best response strategy for both types of players by leveraging the difference of convex (DC) programming approach and the dual decomposition technique. Beside the availability of the complete information to both the players, we also study the problem from the perspective that the FL network knows the partial information of the other player. Extensive simulations have been conducted to verify the effectiveness of the proposed algorithms in the jamming game.

Joint Optimization Framework for User Clustering, Downlink Beamforming, and Power Allocation in MIMO NOMA Systems

In this paper, we investigate the application of downlink beamforming along with non-orthogonal multiple access (NOMA) in a multi-user multiple-input multiple-output (MIMO) system. The joint optimization framework for user clustering, downlink beamforming and power allocation scheme is formulated as a novel mixed-integer non-linear program (MINLP), where the aim is to minimize the total transmission power while satisfying quality-of-service (QoS), user clustering and power constraints. Owing to the non-convexity and combinatorial nature of the problem, obtaining an optimal solution is challenging. To tackle this issue, we first develop an algorithm based on branch-and-bound (BB), whereby the feasible space is successively partitioned and searched by means of lower and upper bounds on the objective function. While this algorithm is shown to return an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -optimal solution within a finite number of iterations, it entails high computational complexity. Considering this limitation, we then reformulate the original problem into a more tractable form and conceive a low-complexity algorithm for its solution based on the penalty dual-decomposition technique. The proposed joint design algorithms for MIMO NOMA are evaluated by means of simulations over mmWave channels. Results show significant improvements in terms of total transmit power and spectral efficiency compared to benchmark approaches.

Task Allocation for Energy Optimization in Fog Computing Networks With Latency Constraints

Fog networks offer computing resources of varying capacities at different distances from end users. A Fog Node (FN) closer to the network edge may have less powerful computing resources compared to the cloud, but the processing of computational tasks in FN limits long-distance transmission. How should the tasks be distributed between fog and cloud nodes? We formulate a universal non-convex Mixed-Integer Nonlinear Programming (MINLP) problem minimizing task transmission- and processing-related energy with delay constraints to answer this question. It is transformed with Successive Convex Approximation (SCA) and decomposed using the primal and dual decomposition techniques. Two practical algorithms called Energy-EFFicient Resource Allocation (EEFFRA) and Low-Complexity (LC)-EEFFRA are proposed and their effectiveness is tested for various network and traffic scenarios. Using EEFFRA/LC-EEFFRA can significantly decrease the number of computational requests with unmet delay requirements when compared with baseline solutions (from 48% to 24% for 10 MB requests). Utilizing Dynamic Voltage and Frequency Scaling (DVFS) minimizes energy consumption (by one-third) while satisfying delay requirements.

Dock assignment and truck scheduling problem; consideration of multiple scenarios with resource allocation constraints

The notion of ‘resource’ plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert’ knowledge has been mobilized to enable modelling of the problem as an integer linear model. Two cases are taken into account: In the first one, the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while in the second one the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice and in a reasonable amount of time.

A Distributed Proximal Primal–Dual Algorithm for Energy Management With Transmission Losses in Smart Grid

This article aims to address the problem of distributed energy management for both the generation and demand sides in smart grid. Different from many existing works, we investigate the SWM problem with transmission losses. In addition, instead of transforming the local constraint into an approximate penalty function or the projection set, we consider it as a convex nonsmooth indicator function from a different viewpoint. For such a composite problem consisting of smooth and nonsmooth terms, we propose a distributed proximal primal–dual algorithm based on dual decomposition and operator splitting techniques. Each node performs the algorithm through only local computation and communication with limited information, especially not sharing the sensitive gradient directly. It is also proved that the proposed algorithm leads to the global optima at a convergence rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(\frac{1}{k})$</tex-math></inline-formula> with a fixed stepsize. Several simulations verify the theoretical analysis and demonstrate the effectiveness of the proposed algorithm.

Optimal Power Allocation for Achieving Secure Green Cognitive Radio Networks

In cognitive radio networks, wireless nodes adapt to the surrounding radio environment and utilize the spectrum of licensed users. The cognitive radio environment is dynamic, and wireless channels are accessible by both legitimate and illegitimate users. Therefore, maintaining the security of cognitive radio networks is a challenging task, which must be addressed thoroughly. Further, with the recent exponential surge in wireless nodes and associated high data rate requirements, energy consumption is also growing at an unprecedented rate. Hence, energy efficiency becomes an important metric that must be considered in the design of future wireless networks. Accordingly, by considering the great ecological and economic benefits of green wireless networks, this work focus on energy-efficient resource allocation in secure cognitive radio networks. Since physical-layer security is an emerging technique that improves the security of communication devices, in this paper, an ergodic secure energy efficiency problem for a cognitive radio network is formulated with a primary user, a secondary user, and an eavesdropper. As the formulated problem is non-convex, a concave lower bound is applied to transform the original non-convex problem into a convex one. Further, by adopting the fractional programming and dual decomposition techniques, optimal power allocation strategies are obtained with the aim of maximizing the ergodic secure energy efficiency of the secondary user with constraints on the average interference power and average transmit power. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.

A Generative Adversarial Network Based Learning Approach to the Autonomous Decision Making of High-Speed Trains

Nowadays, the autonomous driving transportation systems are at the heart of both academic and industry research for the distinguished advantages including increased network capacity, enhanced punctuality, greater flexibility and improved overall safety level. With the responsibility of transporting passengers in a safe, comfortable and efficient way, the decision making method plays a critical position in the autonomous driving of high-speed trains. Focusing on solving the autonomous decision making problem, this paper proposes a novel learning based framework by combining the deep learning technology with the distributed tracking control approach. To cope with the data insufficiency problem in training the deep learning network, a generative adversarial network (GAN) based data argumentation scheme is proposed to generate data samples that have the same distribution with actual data samples, and a hybrid learning network is constructed to predict the speed trajectory from the multi-attribute data with both temporal sequences and static features. Then, based on the model predictive control (MPC) scheme, a distributed tracking control model is formulated to minimize the tracking deviations and balance the performance of punctuality, energy-efficiency and riding comfort. Further, the dual decomposition technique is adopted to deal with the coupling constraints for the safe distance headway such that the separation for the autonomous driving of high-speed trains is achieved. Finally, simulation experiments based on actual scenarios of the Beijing-Shanghai high-speed railway are conducted to illustrate the effectiveness of our methods.

A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service

In this study, we propose a container slot allocation problem for a liner shipping service. A liner containership provides a regular shipping service with a fixed itinerary and schedule. In practice, the liner containership may not be fully loaded, which results in a loss of revenue. We therefore segment shippers into two classes: contract shippers and spot shippers. A contract shipper has a contract with the shipping company and negotiates a fixed minimum quantity, so that the shipping company can secure a steady revenue. The remaining containership slots are open to spot shippers, allowing the shipping company to obtain ad hoc revenue. The container slot allocation problem is investigated in this study using a two-stage stochastic mixed-integer nonlinear programming model. We use the sample average approximation based on Lagrangian relaxation and dual decomposition techniques to effectively solve the model. Finally, we conduct a case study to evaluate the applicability and effectiveness of the proposed model and the solution algorithm.

URLLC-Oriented Joint Power Control and Resource Allocation in UAV-Assisted Networks

Recently, ultrareliable and low-latency communication (URLLC) has attracted a significant interest for mission-critical applications in future wireless communication systems. Achieving strict requirements of latency and reliability for URLLC with a fixed infrastructure is challenging, and unmanned aerial vehicles (UAVs) have been deemed as promising enablers to handle this issue due to its salient attributes, such as high maneuverability, flexible deployment, and high probability of line-of-sight links. This article investigates a novel UAV-assisted URLLC service system, where the blocklength of channel codes is finite in Internet-of-Things (IoT) networks. Considering the limited energy of IoT devices, the average uplink transmit power of the IoT devices are minimized by jointly optimizing the device scheduling and association, power control and resource allocation, as well as UAV deployment. The formulated problem is a mixed-integer nonconvex optimization problem because of the finite blocklength regime. To tackle the problem, we derive the approximation of the achievable rate and propose an effective iteration algorithm by applying the block coordinate descent (BCD) and Lagrange dual decomposition techniques. Furthermore, the convergence of our proposed algorithm is analyzed and illustrated. The minimum average transmit power of IoT devices is calculated with a different resource allocation scheme. Simulation results demonstrate that our proposed iterative algorithm can obtain a performance gain of 15%–20% in terms of the average transmit power for URLLC. Moreover, compared with the average bandwidth allocation scheme, our proposed algorithm can get a stable minimum as the total bandwidth increases.

Height Optimization and Resource Allocation for NOMA Enhanced UAV-Aided Relay Networks

In this paper, we investigate the application of the non-orthogonal multiple access (NOMA) technique into the unmanned aerial vehicle (UAV) aided relay networks. Specifically, we first incorporate the NOMA protocol with the decode-and-forward (DF) relay protocol to enhance the performance of the cell edge users in a macrocell network. Theoretical analysis indicates that the NOMA-DF-relay protocol outperforms the conventional orthogonal multiple access (OMA) based DF-relay protocol in terms of data rate. To fully exploit the advantages of the proposed protocol, we formulate a joint UAV height optimization, channel allocation, and power allocation problem with the objective to maximize the total data rate of the cell edge users under the coverage of the UAV. For solving the formulated problem effectively, we first analyze its property and employ the golden section method to propose a general framework to obtain the optimal height of the UAV. Then, we design a low-complexity iterative algorithm to solve the joint channel-and-power allocation problem based on the matching theory and the Lagrangian dual decomposition technique. Finally, simulation results demonstrate that the NOMA-DF-relay protocol is superior to the OMA-DF-relay protocol even when the system parameters are not optimized, and the proposed algorithms can further significantly improve the network performance in comparison with the other schemes.

Coordinating Workload Scheduling of Geo-Distributed Data Centers and Electricity Generation of Smart Grid

With the rapidly increasing computing demand, data centers become more and more power-hungry, which incurs substantial electricity cost. Meanwhile, due to the time-dependent demand preference, power grid is suffering high load variations, which results in a large profit loss. In this paper, we consider a cost-efficient workload scheduling with a coordination between a cloud service provider operating multiple geo-distributed data centers and smart grids. The aim is to explore the flexibility of data center power demands to reduce the cost of the cloud service provider and smooth the load variations of smart grids simultaneously. We first present the penalty model of the computation workload scheduling at each data center, and introduce the cost model of smart grids, including power generation cost and the cost due to the power load variations. To jointly minimize the cost of smart grids and penalty of the cloud service provider resulted from workload scheduling, we formulate the objective function as a weighted sum of the cost and the penalty to study the tradeoffs, and obtain the optimal offline solution by the dual decomposition technique. In order to make the coordination implemented in an online fashion, we propose a Receding Horizon Control (RHC) based online algorithm to obtain the suboptimal workload management based on the predicted information, including the future amounts of interactive workload, batch workload, and power load, in the prediction horizon. The simulation results show that with the coordination between the cloud service provider and smart grids, the cost of smart grids can be significantly reduced, by up to 20 percent, and the load variations of smart grids can be well smoothed simultaneously.

Mobile Edge Computing Meets mmWave Communications: Joint Beamforming and Resource Allocation for System Delay Minimization

Mobile edge computing (MEC) has been identified as a key technique of next-generation wireless networks, which supports cloud computing along with other compelling service capabilities at the network’s edge with the objective of reducing the system delay. As one of the prospective candidates for new spectrum in next-generation networks, millimeter wave (mmWave) communications has been gaining significant attention as a benefit of its high rate. Hence we conceive a joint hybrid beamforming and resource allocation algorithm for mmWave MEC. Explicitly, we jointly optimize the analog beamforming vectors at the users, the analog and digital beamforming matrices at the base station (BS), the computation task offloading ratios and resource allocation at the MEC server for minimizing the maximum system delay subject to the affordable communication and computing budget. We conceive a powerful algorithm for solving this challenging nonconvex optimization problem with coupled constraints based on the penalty dual decomposition (PDD) technique. The proposed algorithm can be implemented in a parallel and distributed fashion. Our numerical results demonstrate the superiority of the proposed algorithm by quantifying the benefits of intrinsically amalgamating MEC with mmWave communications.

A Stabilizing Control Algorithm for Asynchronous Parallel Quadratic Programing via Dual Decomposition

Abstract This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programing (PQP) through a dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data at each iteration step due to the interdependency of data. The synchronization latency may incur a large amount of waiting time caused by an idle process during computation. We aim to mitigate this synchronization penalty in PQP problems by implementing asynchronous updates of the dual variable. The price to pay for adopting asynchronous computing algorithms is the unpredictability of the solution, resulting in a tradeoff between speedup and accuracy. In the worst case, the state of interest may become unstable owing to the stochastic behavior of asynchrony. The stability condition of asynchronous PQP problems is investigated by employing the switched system framework. A formal algorithm is provided to ensure the asymptotic stability of dual variables. Furthermore, it is shown that the implementation of the proposed algorithm guarantees the uniqueness of optimal solutions, irrespective of asynchronous behavior. To verify the validity of the proposed methods, simulation results are presented.

A Distributed Continuous-Time Algorithm for Nonsmooth Constrained Optimization

This article studies a distributed convex optimization problem with nonsmooth local objective functions subject to local inequality constraints and a coupled equality constraint. By combining the dual decomposition technique and subgradient flow method, a new distributed solution is developed in continuous time. Unlike the existing related continuous-time schemes either depending on specific initial conditions or on differentiability or strict (even strong) convexity of local cost functions, this study is free of initialization and takes into account general convex local objective functions which could be nonsmooth. Via nonsmooth analysis and set-valued LaSalle invariance principle, it is proved that a global optimal solution can be asymptotically obtained. Finally, the effectiveness of our algorithm is illustrated by numerical examples.