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In this paper, we investigate the finite-time distributed optimization problem for multiple Euler–Lagrange systems. A new distributed optimization control scheme is presented to achieve the state agreement in finite time while minimizing the sum of each agent's local cost function. The proposed algorithm has the advantage of being able to achieve distributed finite-time optimization consensus under general unbalanced connected directed communication graphs. By virtue of finite-time Lyapunov theory and convex optimization, the finite-time convergence for the algorithm is analyzed. A numerical example is also presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The colored traveling salesman problem (CTSP) generalizes the well-known multiple traveling salesman problem by utilizing colors to describe the accessibility of cities to individual salesmen. Many centralized algorithms have been developed to solve CTSP instances. This work presents a distributed solving framework and method for CTSP for the first time. The framework consists of multiple container-based computing nodes that rely on specific cloud infrastructures to perform distributed optimization in a pipeline style. In the framework, we develop a distributed Delaunay-triangulation-based variable neighborhood search (DDVNS) algorithm for solving a CTSP case decomposed into many traveling salesman problems. DDVNS exploits a two-stage initialization to generate an initial solution for all TSPs. After that, Delaunay-triangulation-based variable neighborhood search (DVNS) is employed to find local optima. Furthermore, the obtained solutions are improved by reallocating multicolor cities and iterating the search progress, ultimately leading to a group of CTSP solutions. Finally, extensive experiments show that DDVNS outperforms the state-of-the-art centralized VNS algorithms in terms of search efficiency and solution quality. Notably, we can achieve the best solution in a superscale case with 16 salesmen and 160,000 cities within 15 minutes, breaking the best record of CTSPs. [ABSTRACT FROM AUTHOR]

ABSTRACT Distributed optimization has emerged as a pivotal research area with widespread applications in machine learning and networked systems. While optimization algorithms efficiently collaborate to minimize a global objective function through information exchange among nodes, they are susceptible to privacy breaches, potentially leading to severe and unpredictable consequences. As differential privacy becomes the de facto standard for privacy preservation, recent studies have integrated differential privacy with distributed optimization. However, existing differential privacy distributed optimization algorithms typically require continuous communication and noise injection, which results in substantial communication overhead and degraded optimization performance. In this paper, we introduce a novel event‐triggered based differential privacy distributed optimization algorithm that leverages intermittent Laplace noise injection. Recognizing that event‐triggered timings may inadvertently reveal gradient information about the objective function, we introduce an enhanced ϵ$$ \epsilon $$‐Differential Privacy definition specifically tailored for event‐triggered communication, accounting for both the transmitted state information and the event‐triggered timings. By intermittently injecting Laplace noise, our mechanism significantly reduces the total amount of noise required, thereby minimizing its negative impact on the algorithm's performance. We rigorously prove that, even with reduced noise, our algorithm ensures rigorous privacy preservation. Furthermore, our algorithm achieves accurate convergence and improved optimization performance in constrained optimization problems, while reducing communication overhead. Numerical simulations confirm the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

In order to solve the mismatch between renewable energy and load in urban building microgrids, that is, the problem of renewable energy consumption in building microgrid clusters, while preserving the privacy of each user, this paper proposes a distributed low-carbon energy management method for urban building microgrid clusters. First, a low-carbon energy management method for the urban building microgrid is proposed in order to coordinate the power sharing of various subjects to minimize the total economic cost, unleash the consumption potential of low-carbon building clusters for renewable energy, and reduce carbon emissions on the spatial and time scale. Second, an ADMM-based distributed optimal energy management method is proposed to meet user energy needs while preserving local privacy; this includes energy storage systems, renewable energy generation, and the loads within each urban building microgrid. Finally, simulation experiments are conducted based on actual data from a certain area in Hangzhou, China, and the results verify the effectiveness of the model. [ABSTRACT FROM AUTHOR]

We propose a distributed optimization method based on a unified momentum method combined with the heavy ball method and optimized gradient method. We first prove that the stochastic version of the unified momentum method converges, and then prove the convergence of proposed distributed accelerated algorithm. Numerical experiments show that our algorithm has better performance than other methods. [ABSTRACT FROM AUTHOR]

This paper develops distributed algorithms for solving Sylvester equations. The authors transform solving Sylvester equations into a distributed optimization problem, unifying all eight standard distributed matrix structures. Then the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence rate. These results are obtained by carefully choosing the step-size of the algorithm, which requires particular information of data and Laplacian matrices. To avoid these centralized quantities, the authors further develop a distributed scaling technique by using local information only. As a result, the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable intervals. Finally, the authors provide three examples to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article proposes a framework for the swarm of unmanned aerial vehicles (UAVs) to swiftly construct a formation. The framework also enables the swarm to reconfigure the formation effectively in a distributed way when the number of UAVs changes. Different from the classic formation methods, we endow each UAV with an objective function and an assignment vector. Then, a novel distributed optimization protocol is designed for the formation construction, which enables the swarm to construct the desired formation within a prescribed time. The formation needs to be reconfigured when some UAVs leave or join the swarm. A distributed assignment protocol is raised for the reconfiguration problem, which aims at reassigning the relative positions for the UAVs and reconfiguring the swarm formation. This article integrates these two protocols into one framework, where the transition between the formation construction and its reconfiguration is smooth. The distributed design of the framework improves the individual UAV's decision-making ability. We further give the proofs of consensus and optimality of the two protocols. The simulation results confirm the effectiveness of the framework. [ABSTRACT FROM AUTHOR]

Mixed integer programming is inherently involved in solving a significant number of practical problems. This paper focuses on mixed integer programming, where the objective function is the summation of N functions, and the constraints include both scalar coupling and set constraints. Given the potentially large scale of these problems, the goal of this work is to propose a distributed method to solve large-scale problems more efficiently. The right-hand side allocation decomposition approach is employed to address the large-scale mixed integer programming problem. Algorithms are then proposed for solving these problems, based on the analysis of the continuity, differentiability, and local convexity properties of the decomposed subproblems. Simulation experiments with randomly generated coefficients demonstrate the superior performance of the proposed algorithms compared to the Gurobi solver, offering higher solution accuracy and faster processing time for large-scale mixed integer programming problems with nonlinear objective and constraint functions. [ABSTRACT FROM AUTHOR]

This article delves into the routing architecture and reliable transmission service framework of dual-network layered networks, with a focus on analyzing their core design ideas and implementation strategies. In the context of increasing network complexity today, traditional single-network architectures are unable to meet diverse application needs. Therefore, dual-network layered networks, as an innovative solution, are gradually receiving attention from both academia and industry. This article first analyzes the key technical elements in the dual-network layered network architecture, including the optimization of routing algorithms, distributed consensus, reliability assurance mechanisms for packet transmission, and dynamic allocation strategies for network resources. Through in-depth research on these technologies, this article elaborates on the important role of dual-network layered networks in building efficient and stable transmission environments, providing important theoretical foundations and technical support for the construction and optimization of future network systems. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper delves into the prescribed‐time distributed optimization problem for multi‐agent systems (MASs), considering set constraints. First, we transform the challenging optimization problem from the prescribed‐time t$$ t $$‐domain into the asymptotic time τ$$ \tau $$‐domain through a time‐domain transformation (TDT) technique. This strategic shift substantially mitigates the analytical complexities inherent in the original formulation. Second, we develop a novel class of TDT‐based optimization algorithms, utilizing gradient projection and Lagrange multipliers. This algorithm is tailored to efficiently tackle the distributed optimization problem while adhering to the set constraints. To further alleviate the computational and communication overheads, we introduce a corresponding TDT‐based event‐triggered optimization algorithm. Moreover, a rigorous analysis of both the optimal solution to the optimization problem and the system's stability is given by using optimization theory and Lyapunov stability theory. This comprehensive analysis provides valuable insights into the behavior and performance of our proposed approach. Finally, two numerical simulation results are presented to demonstrate the feasibility as well as effectiveness of the offered distributed control arrangement. [ABSTRACT FROM AUTHOR]

We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex-constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed to those derived for ergodic means for standard DDSG algorithms. Our work improves the recently published convergence rate of O (log T / T) with decaying step-sizes to O (1 / T) with constant step-size on a metric that combines sub-optimality and constraint violation. We then numerically evaluate the algorithm on three grid optimization problems. Namely, these are tie-line scheduling in multi-area power systems, coordination of distributed energy resources in radial distribution networks, and joint dispatch of transmission and distribution assets. The DDSG algorithm applies to each problem with various relaxations and linearizations of the power flow equations. The numerical experiments illustrate various properties of the DDSG algorithm–comparison with standard DDSG, impact of the number of agents, and why Nesterov-style acceleration can fail in DDSG settings. [ABSTRACT FROM AUTHOR]

The snow-shaped distribution network is developed and upgraded from the traditional single-loop network and double-loop network structure. It is composed of three or four groups of single-loop networks in pairs that form a feeder cluster in the form of a ring network. Based on this topology, the coordinated optimization operation problem is studied. First, the game elements are analyzed, and then a cooperative game-based, coordinated optimization operation model is established by taking the minimum network loss and voltage deviation of the system as the utility function. Then, the alternating direction multiplier method (ADMM) is employed in Cplex solver to solve the established optimization model. Finally, a numerical case is given to verify the effectiveness of the proposed model and method. The results show that, by using the complementary difference relationship of source–charge characteristics between different regions in the snow-shaped distribution networks, the cooperative game model can realize the energy interconnection among different regions to improve the operation level. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the increasing penetration rate of renewable energy sources over recent years, voltage fluctuations and violations due to the inherent intermittency of renewable energy sources pose a great challenge to the safe and steady operation of distribution networks. To tackle this problem, the voltage regulation problem in distribution networks is formulated as a state-based potential game and then solved in a distributed manner in this paper. Specifically, the power flow model of radial distribution networks is linearized at first. Then, based on the linearized power flow model, a voltage regulation problem in distribution networks is modeled, whose objective function is the sum of voltage profile deviations and reactive power generation costs. Next, the subproblems for each bus is designed based on the state-based potential game theory, in the solving of which only its local and neighbor information are required, facilitating the design of the distributed voltage regulation algorithm. Further, the proposed algorithm is improved by freezing the states of isolated buses during each iteration, increasing its resilience against random link failures. Simulation results show that the proposed distributed voltage regulation algorithm can achieve fast and effective voltage profile regulation in distribution networks while preserving the privacy of distributed generators, even in the presence of random communication link failures. In addition, compared to other distributed voltage regulation algorithms, the proposed algorithm exhibits a faster convergence rate and better voltage regulation performance.

A live time-dependent tasks execution based on a distributed multi-agent network relies strongly on the time synchronization ability of the system. Desynchronisation of the system may lead to incorrect results or even failure at performing a certain tasks. This paper presents a novel synchronization algorithm that addresses the challenge of time discrepancies. It employs a unique approach of dynamically accelerating and decelerating time. This method combines the strengths of consensus algorithm and a system based on Nesterov's accelerated gradient descent. The result is a real-time synchronization solution that avoids the common issue of dropped time points encountered in traditional algorithms.

In this article, we propose a distributed optimization approach to analyzing distributed-stored data based on linear regression with covariates missing at random. To solve distributed statistical learning problems, we construct a communication-efficient surrogate weighted loss function for the global weighted loss function based on inverse probability-weighted and communication-efficient surrogate loss method. Combining the advantages of the surrogate weighted loss function with alternating direction method of multipliers algorithm, a distributed algorithm is developed for the calculation of our proposed estimator. Under some mild assumptions, we establish the asymptotic properties of the proposed estimator. Simulation studies are performed to access the finite-sample performance of our method. We further illustrate the advantages of our method by a real-world dataset from Beijing Municipal Environmental Monitoring Center. [ABSTRACT FROM AUTHOR]

ObjectivesAs the proportion of renewable energy in power grids increases year by year, the volatility and uncertainty of the grid are significantly heightened, posing challenges to the safe operation of distribution networks. To address the issue of distributed network reconfiguration in high-proportion renewable energy grids, this paper proposed an online rolling optimization framework.MethodsThe framework utilized a distributed consensus protocol to obtain network topology and node operation information. It can enable automatic reconfiguration in the event of N-1 and N-2 line failures, allowing the distribution network to automatically restore normal operation without the need for additional external triggering signals, thus ensuring economic operation of the grid. Additionally, a rolling optimization method was employed to handle grid fluctuations caused by the high proportion of renewable energy, and generative adversarial network (GAN) technology was used to generate new data, which combined with historical data. It can help to achieve high-precision forecasting of grid operation data.ResultsThe proposed method can achieve automatic economic optimization and self-healing in normal, single-point failure, and two-point failure scenarios.ConclusionsThis method provides an effective solution for ensuring the safe operation of distributed networks in high-proportion renewable energy grids.

Abstract We study the main decomposition approaches (primal, dual and primal–dual) for a distributed optimization problem from a dynamical system perspective where the couplings among the variables of the optimization problem are described by an undirected, unweighted hypergraph. We conduct stability analysis for the respective dynamical systems of the decomposition cases by using non linear decentralized control theoretic techniques and spectral properties of the respective communication matrices, i.e., the incidence and the Laplacian matrices of the hypergraph. Finally, we provide numerical simulations under a specific coalitional setting that demonstrate the superiority of the hypergraph compared to its respective graph analogue, the clique expansion graph, for the given decomposition algorithms in terms of convergence rate and information transmission efficiency.

This paper introduces a novel fully distributed economic power dispatch (EPD) strategy for distribution networks, integrating dynamic tariffs. A two-layer model is proposed: the first layer comprises the physical power distribution network, including photovoltaic (PV) sources, wind turbine (WT) generators, energy storage systems (ESS), flexible loads (FLs), and other inflexible loads. The upper layer consists of agents dedicated to communication, calculation, and control tasks. Unlike previous EPD strategies, this approach incorporates dynamic tariffs derived from voltage constraints to ensure compliance with nodal voltage constraints. Additionally, a fast distributed optimization algorithm with an event-triggered communication protocol has been developed to address the EPD problem effectively. Through mathematical and simulation analyses, the proposed algorithm's efficiency and rapid convergence capability are demonstrated.

ABSTRACT The rapid advancements of intelligent technologies have brought about the potential vulnerability of confidential gradient information linked to cost functions when solving distributed optimization and its related problems. Within the context of distributed energy management, safeguarding such private information has risen to paramount importance. This article investigates a distributed energy management problem (DEMP) to minimize cost while simultaneously satisfying multiple local constraints and protecting the private gradient information of the cost function. To this end, a new privacy‐preserving distributed optimization algorithm under the framework of gradient tracking over time‐varying graphs is proposed for solving the DEMP. Specifically, the auxiliary variables are designed for each node in the algorithm to update the gradient while the original state variables are responsible for the interaction with original neighbors and auxiliary variables. Consequently, the devised algorithm can protect the confidentiality of private cost gradient information, even in the presence of eavesdroppers within the network. In contrast to the homomorphic encryption, signal masking method, and some other algorithms without utilizing the state decomposition, the designed algorithm does not require extra information or computing resources. Moreover, it is proven that the designed algorithm could theoretically converge to the exact optimum of the DEMP at a rate of O((lnk)/k)$$ O\left(\left(\ln k\right)/\sqrt{k}\right) $$ under some mild assumptions. [ABSTRACT FROM AUTHOR]

This paper focuses on a time-varying distributed convex optimization problem for multi-agent systems, with the objective of preserving their desired rigid formation. The core challenge is driving all agents to minimize the global objective function cooperatively with limited information each agent can share. To tackle the dual objective problem, here we propose a single-integrator and a double-integrator dynamic systems to solve the distributed optimization problem with desired shape achievement. It is proved that all agents can achieve the rigid formation while optimizing the global objective function asymptotically in two algorithms by using the Lyapunov theorem. Finally, the good performance of the control algorithms is demonstrated through numerical experiments and computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of distributed optimization for second-order multi-agent systems with fixed-time flocking. The objective is to concurrently steer the agents towards a common velocity while optimizing the global objective function. To solve the problem, we first design a fixed-time estimator to predict the global gradient of the objective functions, then based on which, each agent is endowed with fixed-time tracking controller to track the optimal solution. Motivated by the fact that the relative velocity information is difficult to obtain accurately, the proposed algorithm is designed without using neighbors’ velocity. The upper bounds of the settling time are provided without relying on the initial states of the agents, only requiring the adjustment of parameters. The effectiveness of the proposed control protocol is also demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on a distributed optimization problem under an undirectd and connected network affected by DoS attacks. First, new event‐triggered mechanisms are developed to schedule the communication between agents. Then, an event‐based resilient distributed optimization algorithm that removes the requirement of continuous communication in the existing results is designed to achieve consensus optimization. Assisted by the design of regulator equations and the algebraic graph theory, it proves that the proposed algorithm is exponentially convergent. Moreover, Zeno behavior can be excluded by reductio ad absurdum. The simulation results validate that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

Copyright of Power Generation Technology is the property of Power Generation Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Training large machine learning models requires a distributed computing approach, with communication of the model updates being the bottleneck. For this reason, several methods based on the compression of updates were recently proposed using sparsification or quantization. However, none of the prior methods are able to learn the gradients, which renders them incapable of converging to the true optimum in the batch mode. In this work we propose a new method – DIANA – which resolves this issue via compression of gradient differences. We provide theory in the strongly convex and nonconvex settings that shows improved convergence rates, and use it to obtain the first convergence rate for the previously proposed method TernGrad. Finally, we provide theory to support non-smooth regularizers. [ABSTRACT FROM AUTHOR]

The exponential proliferation of renewable energy has resulted in a significant mismatch between power supply and demand, especially during extreme events. This incongruity presents challenges in efficiently harnessing renewable energy and enhancing the resilience of the power grid. To address this issue, this paper proposes shared energy storage (SES) planning based on the adaptive alternating direction method of multipliers (AADMM). The objective is to fully leverage SES, enhance the local consumption level of renewable energy, ensure power grid resilience, and reduce operational costs. First, to ensure the effective utilization of SES while minimizing initial investment and construction costs, a planning model for SES is formulated. Secondly, to maximize the benefits for multiple prosumers within the renewable energy and SES station, a profit maximization model for multiple prosumers is established. Lastly, to guarantee the privacy security of SES and multi-prosumers while optimizing computational efficiency, a distributed computing model for SES based on AADMM is developed. The results of the example show that the proposed model can not only reduce the cost of 47.96 CNY, but also increase the power self-sufficiency rate by 21.86%. In addition, compared with the traditional distributed optimization, the number of iterations of AADMM is increased by 47.05%, and the computational efficiency is increased by 54.67%. In addition, market prices have a great impact on energy trading, and the impact of market pricing on the operation of the park is not considered in our current research. In this case, our future research aims to consider how to price reasonably between prosumers and between prosumers and SES, so as to realize the stable participation of each subject in the energy market. [ABSTRACT FROM AUTHOR]