Alternating Direction Method Of Multipliers Research Articles

Decentralized distributionally robust chance-constrained operation of integrated electricity and hydrogen transportation networks

Hydrogen energy offers a promising pathway to decarbonizing future energy systems. Renewable energy-based hydrogen production and road transportation-based hydrogen delivery have strengthened the coupling between the power distribution network (PDN) and the hydrogen transportation network (HTN). In this article, we propose a decentralized distributionally robust chance-constrained (DRCC) method for the integrated electricity and hydrogen transportation network (IEHTN) to foster synergies between PDN and HTN. First, an optimal scheduling framework is developed to coordinate hydrogen production and transportation in the IEHTN, where multiple operational states of water electrolyzers and the time-constrained tube trailer routing are modeled. Second, a data-driven DRCC approach is proposed to model the uncertain behaviors of renewable power generation and hydrogen demand. A conditional value-at-risk approximation is then employed to convert the DRCC problem to a tractable mixed-integer linear program that can be solved by the off-the-shelf solver. Third, an alternating direction method of multipliers (ADMM) based solving scheme is designed to solve the problem in a distributed manner with limited information exchange between PDN and HTN. To address the non-convexity brought by binary variables in the ADMM, a tractable alternating optimization procedure (AOP) strategy is utilized to guarantee the convergence of solution. Finally, case studies are conducted on an IEHTN composed of the modified IEEE 33-bus PDN and 52-node HTN to verify the validity of the proposed method.

Multi‐image encryption and authentication using computational ghost imaging and singular value decomposition

AbstractThe non‐local imaging characteristics of computational ghost imaging (CGI) make it widely used in the field of information security. However, the information processing method based on traditional CGI has some problems in the process of multi‐image encryption, such as low efficiency and unsatisfactory reconstruction quality. Therefore, this article proposes to use wavelet transform and singular value decomposition technology to help computational ghost imaging to efficiently complete the coding and encryption of multiple images, and use alternating direction multiplier method (ADMM) in the process of image restoration to carry out high‐quality reconstruction of the original encrypted image. The results show that the scheme has good reconstruction effect, strong security and robustness even at a low sampling rate. It provides some reference for digital watermarking technology and cryptography.

An adaptive low‐rank group sparse model based on edge‐preserving for eliminating mixed noise in SRTM

AbstractThe Shuttle Radar Topography Mission (SRTM) is a digital representation of the terrain surface morphology that contains rich terrain information and is widely used in environmental analyses. However, SRTM is adversely affected by mixed noise, which typically include random and stripe noise. Mixed noise results in the significant loss of topographic information, which reduce the validity of related research. To eliminate mixed noise in SRTM data, we propose an adaptive low‐rank group sparse model based on edge preservation (ALGS_EP) to remove mixed noise from datasets. The method relies on a low‐rank group sparse model that considers the gradient features of the terrain. It calculates a terrain factor to adapt the noise elimination model to terrain changes. Additionally, it integrates with the edge structure of elevation data and applies a double‐gradient constraint to preserve the structural details of the elevation data. The proposed model, built upon the alternating direction multiplier method framework, enhances the traditional weighted kernel paradigm minimization algorithm by introducing variable weights that adjust according to the gradient of elevation data during iterations. Additionally, it incorporates the correlation between strip noise and residual data blocks when computing the iteration count, ensuring an iterative solution approach that converges to the optimal solution. We used ALGS_EP to process global SRTM 1 data and published a higher‐quality and higher‐precision elevation dataset. The elevation data noise before and after noise elimination were statistically analyzed. Simulated and empirical results show that the model is highly robust and more effective than existing methods in both visual and quantitative evaluations. The noise elimination rate was 97.6%, compared to the original data. Therefore, this research was valuable for applications that use digital elevation model as an important data layer.

Decision Making Under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers

This paper proposes a novel numerical method for solving the problem of decision making under cumulative prospect theory (CPT), where the goal is to maximize utility subject to practical constraints, assuming only finite realizations of the associated distribution are available. Existing methods for CPT optimization rely on particular assumptions that may not hold in practice. To overcome this limitation, we present the first numerical method with a theoretical guarantee for solving CPT optimization using an alternating direction method of multipliers (ADMM). One of its subproblems involves optimization with the CPT utility subject to a chain constraint, which presents a significant challenge. To address this, we develop two methods for solving this subproblem. The first method uses dynamic programming, whereas the second method is a modified version of the pooling-adjacent-violators algorithm that incorporates the CPT utility function. Moreover, we prove the theoretical convergence of our proposed ADMM method and the two subproblem-solving methods. Finally, we conduct numerical experiments to validate our proposed approach and demonstrate how CPT’s parameters influence investor behavior, using real-world data. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms: Continuous. Funding: This research was supported by the National Natural Science Foundation of China [Grants 12171100, 71971083, and 72171138], the Natural Science Foundation of Shanghai [Grant 22ZR1405100], the Major Program of the National Natural Science Foundation of China [Grants 72394360, 72394364], the Program for Innovative Research Team of Shanghai University of Finance and Economics [Grant 2020110930], Fundamental Research Funds for the Central Universities, and the Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science, Ministry of Education, East China Normal University. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0243 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0243 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Techno-economic synergy analysis of integrated electric power and hydrogen system

This study introduces an integrated renewable-penetrated electric power and hydrogen energy system (IRPHS) framework to address the integration challenges of renewable energy sources (RESs) through the development of a hydrogen-based multi-carrier energy system. The IRPHS combines a renewable-penetrated electric power system (RP-EPS) with hydrogen energy system (HES), integrating urban transportation systems (UTSs), and incorporating short and long-term hydrogen storage. By employing scenario-based stochastic programming and the alternating direction method of multipliers (ADMM), the study tackles uncertainties of renewable power and complexities of IRPHS problem. The research evaluates benefits of integrated versus stand-alone operation, focusing on flexibility across hydrogen generation, transportation, and storage. Findings highlight cost-efficient hydrogen generation, enhanced efficiency, and economic benefits in RES deployment, particularly with long-term hydrogen storage.

Multiagent Trust Region Policy Optimization.

We extend trust region policy optimization (TRPO) to cooperative multiagent reinforcement learning (MARL) for partially observable Markov games (POMGs). We show that the policy update rule in TRPO can be equivalently transformed into a distributed consensus optimization for networked agents when the agents' observation is sufficient. By using a local convexification and trust-region method, we propose a fully decentralized MARL algorithm based on a distributed alternating direction method of multipliers (ADMM). During training, agents only share local policy ratios with neighbors via a peer-to-peer communication network. Compared with traditional centralized training methods in MARL, the proposed algorithm does not need a control center to collect global information, such as global state, collective reward, or shared policy and value network parameters. Experiments on two cooperative environments demonstrate the effectiveness of the proposed method.

SSGCNet: A Sparse Spectra Graph Convolutional Network for Epileptic EEG Signal Classification.

In this article, we propose a sparse spectra graph convolutional network (SSGCNet) for epileptic electroencephalogram (EEG) signal classification. The goal is to develop a lightweighted deep learning model while retaining a high level of classification accuracy. To do so, we propose a weighted neighborhood field graph (WNFG) to represent EEG signals. The WNFG reduces redundant edges between graph nodes and has lower graph generation time and memory usage than the baseline solution. The sequential graph convolutional network is further developed from a WNFG by combining sparse weight pruning and the alternating direction method of multipliers (ADMM). Compared with the state-of-the-art method, our method has the same classification accuracy on the Bonn public dataset and the spikes and slow waves (SSW) clinical real dataset when the connection rate is ten times smaller.

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27 % compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36 % and 1.57 %, respectively.

Asymmetric Nash bargaining model for operation optimization of multi-integrated energy systems considering peer-to-peer energy trading

Energy interactions across integrated energy systems constitute crucial means to enhance energy efficiency and match supply and demand. However, the cooperative operation and benefit distribution among multiple integrated energy systems still need in-depth exploration. To fill this gap, this paper presents an asymmetric Nash bargaining optimization model for multiple integrated energy systems considering peer-to-peer trading. First, a scheduling model for multi-integrated energy systems is formulated considering carbon trading. Then, the model is incorporated into Nash bargaining framework and transformed into the alliance cost minimization subproblem and peer-to-peer trading payment bargaining subproblem. The bargaining power factor is introduced to measure the contribution of participants in energy sharing. The alternating direction multiplier method is utilized to handle the proposed model. Finally, a case study is carried out to validate the validity of the proposed strategy. The results show that compared with the independent operation mode, the performances of three integrated energy systems in collaborative operation mode are enhanced by 11.7 %, 9.0 %, and 4.8 % respectively. The distributed algorithm can reduce the computation time by 30 % and obtain highly efficient solutions while protecting private information of each participant. This research provides support and practical tools for conducting peer-to-peer transactions of multiple integrated energy systems.

Distributed Cooperative Dispatch Method of Distribution Network with District Heat Network and Battery Energy Storage System Considering Flexible Regulation Capability

Flexible resources, including district heat networks (DHN) and battery energy storage systems (BESS), can provide flexible regulation capability for distribution networks (DN), thereby increasing the absorption capacity for renewable energy. In order to improve the operation economy of DN and ensure the information privacy of different operators, a distributed cooperative dispatch method of DN with DHN and BESS considering flexible regulation capability is proposed. First, a distributed cooperative dispatch framework of DN-DHN-BESS is constructed. Then, an optimal dispatch model of DHN under constant flow-variable temperature control strategy is established in order to utilize the heat storage capacity to provide flexible regulation capability for DN. Next, the optimal dispatch models of BESS and DN are established with the objective of minimizing the operation cost, respectively. Finally, a solution method based on the alternating direction multiplier method of distributed cooperative dispatch for DN-DHN-BESS is proposed. Case studies are performed on a system consisting of a 33-node DN and a 44-node DHN, and simulation results demonstrate that the proposed method differs from the centralized dispatch method by only 0.52% in the total system cost, and the proposed method reduces the total system cost by 34.5% compared to that of the independent dispatch method.

Fully distributed convex hull pricing based on alternating direction method of multipliers

In certain power markets, due to the non-convex operation characteristics, generators adhering to the decisions of Independent System Operators (ISO) may struggle to recover costs through local marginal energy sales. ISOs impose discriminatory additional payments as incentives for generator compliance. Convex hull pricing is a unified scheme that significantly reduces these supplementary payments. The Lagrangian dual problem of the Unit Commitment (UC) problem is solved within the dual space to determine convex hull prices. To navigate the computational challenges posed by the real large-scale power systems, we propose a methodology for a global convergence distributed solution, which addresses the Lagrangian dual problem. This methodology is based on the Alternating Direction Method of Multipliers (ADMM) algorithm and incorporates convex hull cut planes to enhance computational efficiency. Moreover, a tight and compact UC model is employed to reduce the number of iterations. Numerical results indicate that if the convex hull descriptions of units can be obtained, our algorithm is capable of providing precise convex hull prices and high-quality solutions within a feasible timeframe, while also maintaining the confidentiality of individual subset unit information.

A robust underwater polarization image recovery based on Angle of Polarization with low-rank and sparse decomposition

Underwater imaging method based on the Angle of Polarization (AoP) is extremely popular due to its ability to remove the backscattered light effectively. However, existing methods overlook a potentially important phenomenon: the AoP contains significant noise in the real world, which leads to inaccurate estimations of key parameters. In this study, we propose a novel robust underwater polarization image recovery method based on AoP with low-rank and sparse decomposition. Based on the analysis of polarization, the AoP of backscattering exhibits low-rank characteristics, whereas the AoP of noise and targets demonstrates sparsity. Considering different sparsity of AoP, we combine Robust Principal Component Analysis and Alternating Direction Multiplier Method (RPCA-ADMM) with an adaptive threshold shrinkage method for low-rank and sparse decomposition, the AoP of the backscattering is obtained. Moreover, according to the low-rank component of the AoP, the Degree of Linear Polarization (DoLP) of backscattering can be effectively and automatically estimated without considering whether the background region exists, relying on a frequency prior strategy. Finally, the degraded image is recovered utilizing underwater polarization imaging model. Extensive experimental results demonstrate that the recovered images from the proposed method have abundant detail, high contrast, and minimal color distortion, which is competitive with most state-of-the-art methods.

A low-rank support tensor machine for multi-classification

In recent decades, there has been an increasing demand for effectively handling high-dimensional multi-channel tensor data. Due to the inability to utilize internal structural information, Support Vector Machine (SVM) and its variations struggle to classify flattened tensor data, consequently resulting in the ‘curse of dimensionality’ issue. Furthermore, most of these methods can not directly apply to multiclass datasets. To overcome these challenges, we have developed a novel classification method called Multiclass Low-Rank Support Tensor Machine (MLRSTM). Our method is inspired by the well-established low-rank tensor hypothesis, which suggests a correlation between each channel of the feature tensor. Specifically, MLRSTM adopts the hinge loss function and introduces a convex approximation of tensor rank, the order-d Tensor Nuclear Norm (order-d TNN), in the regularization term. By leveraging the order-d TNN, MLRSTM effectively exploits the inherent structural information in tensor data to enhance generalization performance and avoid the curse of dimensionality. Moreover, we develop the Alternating Direction Method of Multipliers (ADMM) algorithm to optimize the convex problem inherent in training MLRSTM. Finally, comprehensive experiments validate the excellent performance of MLRSTM in tensor multi-classification tasks, showcasing its potential and efficacy in handling high-dimensional multi-channel tensor data.

Symmetric ADMM-Based Federated Learning with a Relaxed Step

Federated learning facilitates the training of global models in a distributed manner without requiring the sharing of raw data. This paper introduces two novel symmetric Alternating Direction Method of Multipliers (ADMM) algorithms for federated learning, Two algorithm utilize a convex combination of current local and global variables to generate relaxed steps to improve computational efficiency. They also integrate two dual-update steps with varying relaxation factors into the ADMM framework to boost the accuracy and the convergence rate. Another key feature is the use of weak parametric assumptions to enhance its computational feasibility. Furthermore, the global update in the second algorithm occurs only at certain steps (e.g., at steps being a multiple of a pre-defined integer) to improve the communication efficiency. Theoretical analysis demonstrates linear convergence under reasonable conditions, and experimental results confirm the superior convergence and heightened efficiency of the proposed algorithms compared to the existing methodologies.

A robust must‐run capacity identifying approach in power system dispatch considering interdependence with natural gas system

AbstractIdentifying the must‐run capacity (MRC) could help to accelerate the unit commitment and assess market power, thus critical for achieving an efficient power system dispatch. However, the existing approaches identify the MRC without considering the ever‐strengthening interdependence between power system and natural gas (NG) system, as well as neglecting either the uncertainties of renewables or the constraints on start‐up/shut‐down states for thermal units. To fill the gaps, this article proposes a novel model and methodology for identifying the MRC in power system considering the interdependence with NG system, with adopting a distributionally robust (DR) approach to consider the uncertainties of renewables. A constraint‐generation based algorithm is devised to solve the model, with a relax‐round‐polish based Alternating Direction Method of Multipliers (ADMM) algorithm to address the interaction between the two energy systems. Comparative studies show the effectiveness in MRC assessment over the existing approaches.

Joint vehicular power and RIS reflection coefficient optimization to maximize the minimum bit rate in VANETs

Reconfigurable intelligent surfaces (RISs) have recently gained significant attention for improving reliability in vehicular communications. However, ensuring reliable communication between far-distance vehicles remains a challenge. This work investigates an RIS-aided vehicular ad hoc network (VANET) in a road section where the distance between vehicles is too large for a single roadside unit (RSU) to provide reliable communication. We propose a novel RIS architecture where several RIS panels are connected by cables and each is equipped with a power amplifier. We then optimize vehicle power and RIS reflection coefficients to maximize the minimum bit rate of the VANET. Due to the non-convex nature of the formulated problem, we use fraction programming (FP) to reformulate it into a convex form, allowing solution using tools like CVX which is a MATLAB-based modeling system for convex optimization. The reformulated problem is then decoupled into subproblems. Block coordinate descent (BCD) is employed to optimize all variables alternately and obtain the joint optimal solution. Additionally, the alternating direction method of multipliers (ADMM) ensures that the phase shift of each reflecting element remains a unit vector. Finally, semidefinite relaxation (SDR) is used to solve the boolean quadratically constrained problem. Simulation results demonstrate the effectiveness of the proposed method and confirm that our architecture outperforms conventional approaches.

Capturing opportunity costs of peer-to-peer energy transactions in microgrids via virtual state-of-charge bids

Since the prosumers can absorb or generate power in the P2P energy market, we equivalently model the prosumers as virtual energy storages (VESs) and employ the latest state-of-charge (SOC)-dependent bids to depict the prosumers’ bidding strategies. We first model the P2P market participants’ trading behaviors considering their loads, batteries, and distributed energy resources (DERs). To derive the equivalent VESs, we develop an algorithm to estimate the prosumers’ virtual capacities. We analyze the market operator’s model to guarantee energy delivery in the distribution network. Then, we project the operator’s network constraints to the prosumers’ feasible regions for privacy preservation and iteration reduction. Based on the virtual capacities, we develop VSOCs to depict the prosumers’ different trading states during market operation. We finally convexify the market-clearing problem and modify the alternating direction method of multipliers (ADMM) to calculate the optimal trading results with VSOC-dependent bids. Two cases are employed to verify that the VSOC-dependent bids can accommodate the prosumers’ parameter changes and trading preferences. The opportunity costs are reduced by 41.2% when allowing prosumers to bid differently in various VSOCs.

An Alternating Direction Multiplier Method for the Inversion of FDEM Data

In this paper, we focus on the numerical solution of nonlinear inverse problems in applied geophysics. Our aim is to reconstruct the structure of the soil, i.e., either its electrical conductivity or the magnetic permeability distribution, by inverting frequency domain electromagnetic data. This is a very challenging task since the problem is nonlinear and severely ill-conditioned. To solve the nonlinear inverse problem, we propose an alternating direction multiplier method (ADMM), we prove its convergence, and propose an automated strategy to determine the parameters involved. Moreover, we present two heuristic variations of the ADMM that either improve the accuracy of the computed solutions or lower the computational cost. The effectiveness of the different proposed methods is illustrated through few numerical examples.

Elastic reweighted sparsity regularized sparse unmixing for hyperspectral image analysis

Sparse unmixing is a crucial component in the analysis of hyperspectral images because of its ability to sparsely estimate abundances with a spectral library of considerable scale. The existing sparse unmixing techniques tend to employ the sparsity from a single perspective, i.e., ℓ1 or ℓ2,1. In this paper, we accurately estimate abundances from element-wise and channel-wise sparsity perspectives, which forms a new elastic reweighted sparse regularized sparse unmixing method, termed ElSpaSU. The proposed ElSpaSU method leverages the abundance matrix simultaneously using ℓ1 and ℓ2,1 sparsity regularizations. To further promote sparsity in the abundances, the proposed ElSpaSU incorporates two types of iterative reweighting weights. We utilize the alternating direction method of multipliers (ADMM) framework to ensure guaranteed convergence in solving the optimization problem. Experimental outcomes from simulated and real hyperspectral images highlight the remarkable efficacy of the suggested ElSpaSU in contrast to competing approaches.

Nonconvex low-rank regularization method for video snapshot compressive imaging

The reconstruction of snapshot compressive imaging (SCI) presents a significant challenge in signal processing. The primary goal of SCI is to employ a low-dimensional sensor to capture high-dimensional data in a compressed form. As a result, compared to traditional compressive sensing, SCI emphasizes capturing structural information and enhancing the reconstruction quality of high-dimensional videos and hyperspectral images. This paper proposes a novel SCI reconstruction method by integrating non-convex regularization approximation in conjunction with rank minimization. Furthermore, we address the characterization of structural information by leveraging nonlocal self-similarity across video frames to improve the reconstruction quality. We also develop an optimization algorithm based on the alternating direction method of multipliers (ADMM) to solve the model and provide a convergence algorithm analysis. Extensive experiments demonstrate that the proposed approach can potentially reconstruct SCI effectively.