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Accelerated quadratic penalty dynamic approaches with applications to distributed optimization

NEURAL NETWORKS 2025年 184卷 107032页

作者： He, Xin Guo, Luyao He, Dong Xihua Univ Sch Sci Chengdu 610039 Sichuan Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Sichuan Univ Pittsburgh Inst Chengdu 610207 Sichuan Peoples R China

In this paper, we explore accelerated continuous-time dynamic approaches with a vanishing damping a / t , driven by a quadratic penalty function designed for linearly constrained convex optimization problems. We replace these linear constraints with penalty terms incorporated into the objective function, where the penalty coefficient grows to +infinity as t tends to infinity. With appropriate penalty coefficients, we establish convergence rates of O (1/ (t min{2 a / 3 , 2)} ) for the objective residual and the feasibility violation when a > 0 , and demonstrate the robustness of these convergence rates against external perturbation. Furthermore, we apply the proposed dynamic approach to three distributed optimization problems: a distributed constrained consensus problem, a distributed extended monotropic optimization, and a distributed optimization with separated equations, resulting in three variant distributed dynamic approaches. Numerical examples are provided to show the effectiveness of the proposed quadratic penalty dynamic approaches.

关键词： Nesterov acceleration Quadratic penalty dynamic distributed optimization Convergence properties

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Economic Load Dispatch of A Multi-Area Power System Using Multi-Agent distributed optimization Based on Genetic Algorithm

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ENERGY SCIENCE & ENGINEERING 2025年第4期13卷 1679-1690页

作者： Fakhrmousavi, Seyed Yaser Mazafari, Seyed Babak Javadi, Shahram Aliabadi, Mahmood Hosseini Islamic Azad Univ Dept Elect Engn Cent Tehran Branch Tehran Iran Islamic Azad Univ Dept Elect Engn Sci & Res Branch Tehran Iran

This study presents a new methodology for distributed multi-agent optimization utilizing a genetic algorithm to address Multi-Area Economic Dispatch Problem (MAEDP) in a power system. While numerous studies have been conducted on various optimization methods for distributed multi-agent systems, this paper proposes a model for solving the optimal economic dispatch equations in different areas of the power system in a distributed and coordinated manner. In this model, each area is represented by an agent responsible for coordinating data exchange with other areas and solving the generation dispatch equations within its own area. The coordination model between agents and areas is described in the form of an algorithm, whereby the exchanged data values converge after several iterations, and the final solution to the problem is obtained from the perspective of each agent. The objective of each agent in each area is to minimize generation costs and meet its own area's load demand while maintaining voltage profiles. Each agent sets the power generation values of resources in each area using the genetic algorithm rules and then solves the distributed power flow equations using the proposed method. Upon achieving convergence, each agent evaluates all operational constraints within its designated region, calculates the associated generation cost, and shares the cost value to other agents, thereby facilitating the computation of the total cost for each agent. This process continues until the best possible solution is found. The results of implementing the proposed model and algorithm on several different test networks of power systems demonstrate the capability and effectiveness of the method in decomposing the optimal economic dispatch problem into smaller sub-problems and then finding the final optimal solution through simultaneous solving with agent consensus in coordinated steps.

关键词： distributed optimization economic load dispatch genetic algorithm multi-agent planning multi-area power system

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Radial partitioning with spectral penalty parameter selection in distributed optimization for power systems

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2025年 41卷

作者： Karimi, Mehdi Illinois State Univ Dept Math Normal IL 61761 USA

This paper introduces a novel concept of intelligent partitioning for group-based distributed optimization (DO) algorithms applied to optimal power flow (OPF) problems. Radial partitioning of the graph of a network is introduced as a systematic way to split a large-scale problem into more tractable sub-problems, which can potentially be solved efficiently with methods such as convex relaxations. Spectral parameter selection is introduced for group-based DO as a crucial hyper-parameter selection step in DO. A software package DiCARP is created, which is implemented in Python using the Pyomo optimization package. Through several numerical examples, we compare the proposed group-based algorithm to component-based approaches, evaluate our radial partitioning method against other partitioning strategies, and assess adaptive parameter selection in comparison to non-adaptive methods. The results highlight the critical role of effective partitioning and parameter selection in solving large-scale network optimization problems.

关键词： Optimal power flow distributed optimization Consensus optimization Alternating direction method of multipliers Graph partitioning

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Online distributed optimization algorithm with dynamic regret analysis under unbalanced graphs

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AUTOMATICA 2025年 174卷

作者： Yao, Songquan Xie, Siyu Li, Tao East China Normal Univ Sch Math Sci Shanghai 200241 Peoples R China Univ Elect Sci & Technol China Sch Aeronaut & Astronaut Chengdu 611731 Peoples R China

We consider online distributed convex optimization problems with a sum of locally dynamic loss functions under unbalanced graphs. When optimizing the dynamic local loss function, every node tracks the time-varying global optimal solution by communicating with neighboring nodes via communication networks in a cooperative way. We propose a novel online distributed Push-Pull algorithm and present that the proposed online optimization algorithm can track the dynamic optimal solution with proper step sizes. We analyze the dynamic regret of the proposed algorithm in two cases where the global loss function is strongly convex and smooth, or is convex, smooth and Lipschitz. Our results illustrate that the dynamic regret of the proposed online optimization algorithm can be sublinear, if the path length and the gradient variance are sublinear. At last, we demonstrate the property of the online distributed optimization algorithm by two simulation examples. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Dynamic regret distributed optimization Convex optimization Online learning Online push-pull algorithm

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Comments on "distributed optimization of multi-integrator agent systems with mixed neighbor interactions"[Automatica 157 (2023) 111245 ]

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AUTOMATICA 2025年 172卷

作者： Liu, Jiaxu Chen, Song Zhejiang Univ Sch Math Sci Hangzhou Zhejiang Peoples R China

This note aims to identify and rectify the flaws found in the proof of Chen et al. (2023), specifically in Lemma 2, Lemma 3, Theorem 1, and Theorem 2. While the conclusions of Lemma 2, Lemma 3, and Theorem 1 remain valid, certain aspects of their proofs are found to be flawed. This note provides modifications to address these flaws. Additionally, the statement and proof of Theorem 2 are shown to be incorrect. A corrected Theorem 2 with proof is given. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： distributed optimization Multi-integral agent systems Mixed neighbor interactions Cooperation-competition network

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distributed optimization for IoT attack detection using federated learning and Siberian Tiger optimizer

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ICT Express 2025年

作者： Gupta, Brij B. Gaurav, Akshat Alhalabi, Wadee Arya, Varsha Alharbi, Eman Chui, Kwok Tai Department of Computer Science and Information Engineering Asia University Taichung 413 Taiwan Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Symbiosis Centre for Information Technology (SCIT) Symbiosis International University Pune India School of Cybersecurity Korea University Seoul South Korea Kyung Hee University 26 Kyungheedae-ro Dongdaemun-gu Seoul South Korea Ronin Institute Montclair NJ United States International Center for AI and Cyber Security Research and Innovations (CCRI) Asia University Taichung 413 Taiwan Department of Computer Science Immersive Virtual Reality Research Group King Abdulaziz University Jeddah Saudi Arabia Hong Kong Metropolitan University Hong Kong SAR China Center for Interdisciplinary Research University of Petroleum and Energy Studies (UPES) Dehradun India Department of Computer Science Faculty of Computing and Information Technology King Abdulaziz University Jeddah Saudi Arabia

The rapid growth of IoT devices has heightened the risk of botnet attacks, calling for scalable and distributed detection solutions. In this context, this study proposes a distributed optimization system for IoT attack detection using CNN model utilizing federated learning. After optimizing the hyperparameters of the model at the server, the Siberian Tiger optimization (STO) method distributes these values to clients for dispersed training. Our model achieves accuracy, recall, and precision of 0.89978, 0.94355, and 0.94455, respectively, using the N-BaIoT dataset. These findings show, in spite of latency issues, the efficiency of federated learning in distributed IoT security systems. © 2025

关键词： CNN model distributed optimization Federated learning IoT attack detection Siberian Tiger optimization (STO)

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Penalty Removal Search Algorithm for distributed optimization of Nonconvex Functions in Economic Dispatch

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2025年

作者： Ge, Yiyang Wang, Zhanshan Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China State Key Lab Synthet Automation Proc Ind Shenyang 110819 Peoples R China

Nonconvexity is a usually overlooked factor in economic dispatch (ED). Enhancing the nonconvexity of the objective function leads traditional convex optimization algorithms easily to fall into the local optimum. To address the above problem, a penalty removal search algorithm (PRSA) is proposed for ED nonconvex optimization. It is composed of two distributed optimization algorithms embedded in a reinforcement learning framework. In Phase I of PRSA, a distributed optimization algorithm with projection operators is designed. It uses fewer variables to locate the region where the optimal solution belongs by the cooperative Q-learning. In Phase II of PRSA, the sigmoid function serves as a penalty function to form the second distributed optimization algorithm. This is used to skip the searched solutions and allow the algorithm to continue searching for more feasible solutions. The PRSA solves the problem that the algorithm misses feasible solutions when the nonconvex coefficients increase. Finally, the effectiveness of the PRSA is verified by numerical examples.

关键词： Linear programming Economics distributed algorithms Cost function Q-learning Germanium Costs Valves Fuels Convex functions Collaborative Q-learning (CQL) algorithm distributed optimization economic dispatch (ED) nonconvex optimization penalty removal search algorithm (PRSA)

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distributed Nonconvex optimization for Control of Water Networks with Time-coupling Constraints

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WATER RESOURCES MANAGEMENT 2025年第1期39卷 523-546页

作者： Jenks, Bradley Ulusoy, Aly-Joy Pecci, Filippo Stoianov, Ivan Imperial Coll London Dept Civil & Environm Engn London SW7 2BU England Princeton Univ Andlinger Ctr Energy & Environm Princeton NJ 08544 USA

In this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are exacerbated by the transition between pressure and water quality controls. The resulting optimization problem is a nonconvex, nonlinear program with nonseparable structure across time steps. This problem proves challenging for state-of-the-art nonlinear solvers, often precluding their direct use for near real-time control in large-scale networks. To overcome this computational burden, we investigate a distributed optimization approach based on the alternating direction method of multipliers (ADMM). In particular, we implement and evaluate two algorithms: a standard ADMM scheme and a two-level variant that provides theoretical convergence guarantees for our nonconvex problem. We use a benchmarking water network and a large-scale operational network in the UK for our numerical experiments. The results demonstrate good convergence behavior across all problem instances for the two-level algorithm, whereas the standard ADMM approach struggles to converge in some instances. With an appropriately tuned penalty parameter, however, both distributed algorithms yield good quality solutions and computational times compatible with near real-time (e.g. hourly) control requirements for large-scale water networks.

关键词： distributed optimization Nonconvex optimization Alternating direction method of multipliers Water distribution networks

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distributed Multiobjective optimization Scheme for Load Aggregators in Incentive-Based Demand Response Programs

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第4期55卷 2870-2883页

作者： Li, Xin Ding, Li Chen, Yi-Ru Yu, Zhen-Wei Lin, Qiao Wuhan Univ Sch Elect Engn & Automat Dept Artificial Intelligence & Automat Wuhan 430072 Peoples R China

Demand response (DR) programs are an effective means of mitigating power shortages. This article proposes a novel incentive-based DR program for peak shaving situations. The system operator (SO) determines the response power amount and provides tiered subsidy policies. The load aggregators (LAs) are rational decision-makers and formulate multiobjective optimization problems (MOPs) to make compromises for incentive income, user comfort, and environmental contribution. The innovation lies in the proposed distributed event-triggered solution methodology, including a distance-minimization algorithm to find the decision closest to the ideal point from the Pareto front, and a weighting coefficients optimization algorithm to allocate the importance of each objective at a predefined time. The distributed solution framework maintains the autonomy of each LA, and the event-triggered communication mechanism saves communication resources. Numerical simulations validate the effectiveness of the proposed solution methodology, including the realization of the response power target given by the SO, the optimal compromise of the MOP, and the saving of communication resources in the solution process.

关键词： optimization Event detection Electricity Programming Demand response Privacy Linear programming Indexes Convergence Voltage control distributed optimization event-triggered communication multiobjective optimization

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distributed constrained optimization over unbalanced graphs and delayed gradient

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JOURNAL OF THE FRANKLIN INSTITUTE 2025年第2期362卷

作者： Huang, Qing Fan, Yuan Cheng, Songsong Anhui Univ Sch Elect Engn & Automat Hefei 230601 Peoples R China

In this paper, we investigate a distributed constrained optimization problem subject to convex, closed, and nonidentical set constraints over unbalanced graphs, where each agent has local access to its strongly convex objective function and collaborates, minimizing the sum of these functions. To address this problem, we design a distributed projected delayed gradient algorithm by using the available delayed gradient information, which removes dependence on the current gradient information and increases iteration efficiency. Moreover, to improve communication robustness, the algorithm is only based on a row stochastic weight matrix and achieves an O (1/ T ) convergence rate for a non-negative and diminishing step size. Finally, we present a numerical example to verify the effectiveness of the algorithm.

关键词： distributed optimization Nonidentical constraints Unbalanced graphs Gradient delay Convergence

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