Distributed Optimization Method Research Articles

Research on distributed optimal scheduling method based on consensus

Abstract With access to large-scale distributed power sources, the physical structure of the power grid system tends to be distributed. The application of traditional centralized optimal scheduling methods will lead to a surge in communication overhead and computational complexity, which will affect the performance and efficiency of the solution. In this paper, the minimum operating cost of the system is taken as the goal, and the distributed direct current optimal power flow (DC-OPF) optimization calculation of the photovoltaic-storage power generation system is considered to approximately solve the economic dispatch problem. The DC optimal power flow model with energy storage charging penalty is constructed. Then, the distributed optimization method based on the consensus alternating direction multiplier method (ADMM) is adopted. By decoupling the objective function and constraints of the whole system problem, the fully distributed DC-OPF calculation is realized by introducing the global consensus variable to deal with the boundary buses. Finally, the improved IEEE 30-bus example is used to test the method, and the simulation results verify the convergence and accuracy of the method.

Distributed Optimization Strategy for New Energy Stations and Energy Storage Stations Considering Multiple Time Scales

The “dual carbon” goal has made it a mainstream trend for new energy stations (NESs) and energy storage stations (ESSs) to jointly participate in market regulation. This paper proposes a multiple time scale distributed optimization method for NESs and ESSs based on the alternate direction multiplier method (ADMM). By first considering the uncertainty of new energy output and the volatility of electricity market prices, a multi time scale revenue model is constructed for day-ahead, intraday, and real-time markets. Then, the objective function is built by maximizing the comprehensive market revenues and is simplified using the synergistic effect of NESs and ESSs. Next, the simplified objective function is solved by the ADMM, and the revenues are maximized while each energy meets the relevant constraints. Lastly, the 33-node network topology is used to illustrate the feasibility of the proposed method. The simulation results show that after optimization, the output of NESs and ESSs can coordinate work in day-ahead, intraday, and real-time markets, while the abandonment power of wind and light is significantly improved.

Distributed Optimization Methods for Multi-Robot Systems: Part 1—A Tutorial [Tutorial

Distributed Optimization Methods for Multi-Robot Systems: Part 1—A Tutorial [Tutorial

Distributed predefined-time economic dispatch based on event-triggered strategy for microgrids under directed graphs

The proliferation of new energy solutions and the enhanced accessibility of distributed power sources have significantly increased the complexity and variability of microgrid structures. Due to inherent limitations in its operational mode, the traditional centralized optimization method falls short in effectively addressing the economic dispatch problem in contemporary microgrids. In this paper, a distributed optimization method is devised to address the economic dispatch problem of microgrids under directed graphs by leveraging the consensus algorithm of multi-agent systems. We define the incremental cost of each microgrid unit as the consensus variable, achieving convergence through a pioneering combination of event-triggered strategy and predefined-time control theory. This approach not only optimizes resource use but also ensures timely and efficient solution convergence, addressing critical gaps in existing methodologies. This approach enables control over the upper bound of convergence time for optimal solutions by directly adjusting time parameters in the controller under the directed graph. Consequently, it achieves coordinated control of the power output in microgrids within a predefined time while reducing the communication resources between nodes with event-triggered mechanism. The effectiveness of the proposed algorithm is verified through simulation and analysis.

Distributed Optimization of Multi-Microgrid Integrated Energy System with Coordinated Control of Energy Storage and Carbon Emissions

The mutual optimization of a multi-microgrid integrated energy system (MMIES) can effectively improve the overall economic and environmental benefits, contributing to sustainability. Targeting a scenario in which an MMIES is connected to the same node, an energy storage coordination control strategy and carbon emissions management strategy are proposed, and an adaptive step-size method is applied to improve the distributed optimization of MMIESs based on the alternating direction multiplier method (ADMM). Firstly, the basic framework of MMIESs is established, and a coordinated control strategy limiting the time of charge and the discharge of the battery storage system (BSS) is proposed. Then a multi-objective optimization model based on operating and environmental cost is formulated. Considering that different microgrids may be managed by different operators and a different convergence speed of multi-objective optimization iteration, an adaptive step-size distributed iterative optimization method based on ADMM is used, which can effectively reduce the cost and protect the privacy of each microgrid. Finally, a system composed of three microgrids is taken as an example for simulation analysis. The results of distributed optimization are accurate, and the proposed coordinated control strategy can effectively enhance the revenue of ESS, which verifies the effectiveness of the proposed method.

Differentially private distributed estimation and learning

We study distributed estimation and learning problems in a networked environment where agents exchange information to estimate unknown statistical properties of random variables from their privately observed samples. The agents can collectively estimate the unknown quantities by exchanging information about their private observations, but they also face privacy risks. Our novel algorithms extend the existing distributed estimation literature and enable the participating agents to estimate the expected value of a complete sufficient statistic from private signals acquired offline or online over time and to preserve the privacy of their signals and network neighborhoods. This is achieved through linear aggregation schemes with adjusted randomization schemes that add noise to the exchanged estimates subject to differential privacy constraints, both in an offline and online manner. We provide convergence rate analysis and tight finite-time convergence bounds. We show that the noise that minimizes the convergence time to the best estimates is the Laplace noise, with parameters corresponding to each agent’s sensitivity to their signal and network characteristics. Our algorithms are amenable to dynamic topologies and balancing privacy and accuracy trade-offs. Finally, to supplement and validate our theoretical results, we run experiments on real-world data from the US Power Grid Network and electric consumption data from German Households to estimate the average power consumption of power stations and households under all privacy regimes and show that our method outperforms existing first-order, privacy-aware, distributed optimization methods.

Energy-Efficiency Optimization With Model Convexification for Wireless Ad Hoc Networks With Multi-Packet Reception Capability

Energy efficiency is a significant requirement of resource management and design optimization in information networks. In this work, we propose an iterative fractional programming framework embedded with a distributed primal-dual extra-gradient projection algorithm, which addresses a wide class of the energy-efficiency optimization problems in wireless ad hoc networks with full-duplex radios and multi-packet reception capability. Specifically, we propose a model convexification mechanism by joining an affine transformation and an exponential transformation into the nonlinear fractional programming, which enables us to deal with the challenge arising from the complexity and non-convex structure of the original problem. With the model convexification, we can map the non-convex power control space into a convex space and equivalently derive a sequence of convex subproblems, which relaxes the convexity assumption widely adopted in the existing literature. We further propose a distributed primal-dual algorithm based on extra-gradient projection to solve the convex subproblem at each iteration of the fractional programming. The convergence of the proposed iterative fractional programming and the distributed optimization method is theoretically proven. Numerical results also verify the proposed method and demonstrate its superior performance over other representative distributed and centralized schemes in terms of achieving global energy efficiency.

Communication Efficient Distributed Newton Method over Unreliable Networks

Distributed optimization in resource constrained devices demands both communication efficiency and fast convergence rates. Newton-type methods are getting preferable due to their superior convergence rates compared to the first-order methods. In this paper, we study a new problem in regard to the second-order distributed optimization over unreliable networks. The working devices are power-limited or operate in unfavorable wireless channels, experiencing packet losses during their uplink transmission to the server. Our scenario is very common in real-world and leads to instability of classical distributed optimization methods especially the second-order methods because of their sensitivity to the imprecision of local Hessian matrices. To achieve robustness to high packet loss, communication efficiency and fast convergence rates, we propose a novel distributed second-order method, called RED-New (Packet loss Resilient Distributed Approximate Newton). Each iteration of RED-New comprises two rounds of light-weight and lossy transmissions, in which the server aggregates the local information with a new developed scaling strategy. We prove the linear-quadratic convergence rate of RED-New. Experimental results demonstrate its advantage over first-order and second-order baselines, and its tolerance to packet loss rate ranging from 5% to 40%.

Game‐based distributed energy‐sharing model for prosumers in microgrids considering carbon emissions and its fast equilibrium‐finding method

Game‐based distributed energy‐sharing model for prosumers in microgrids considering carbon emissions and its fast equilibrium‐finding method

A Machine Learning-Assisted Distributed Optimization Method for Inverter-Based Volt-VAR Control in Active Distribution Networks

The number of smart inverters in active distribution networks is growing rapidly, making it challenging to realize a fast, distributed Volt/Var control (VVC). This work proposes a machine learning-assisted distributed algorithm to accelerate the solution of the VVC strategy. We first observe the convergence process of the Alternating Direction Method of Multipliers (ADMM)-based VVC problem and explore the potential relationships between the convergence and time-series regression. Then, the long short-term memory (LSTM) technique is applied to learn the convergence process and regress the converged values of the dual and global variables with previous ADMM observations. After that, the LSTM-assisted ADMM algorithm is proposed, where the regressions are used for ADMM parameter updates. In this algorithm, the inputs of the LSTM model are carefully designed since the complementary conditions implied in the conventional ADMM should be considered. Unlike existing methods, the proposed method does not use the LSTM to determine the VVC strategy directly, indicating that it is non-intrusive and can satisfy all safety constraints during operations. The proof of its optimality and convergence is also given. The numerical simulations on the 33-bus distribution system demonstrate the effectiveness and efficiency of the proposed method.

Tailoring Gradient Methods for Differentially Private Distributed Optimization

Decentralized optimization is gaining increased traction due to its widespread applications in large-scale machine learning and multi-agent systems. The same mechanism that enables its success, i.e., information sharing among participating agents, however, also leads to the disclosure of individual agents' private information, which is unacceptable when sensitive data are involved. As differential privacy is becoming a de facto standard for privacy preservation, recently results have emerged integrating differential privacy with distributed optimization. However, directly incorporating differential privacy design in existing distributed optimization approaches significantly compromises optimization accuracy. In this paper, we propose to redesign and tailor gradient methods for differentially-private distributed optimization, and propose two differential-privacy oriented gradient methods that can ensure both rigorous <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> -differential privacy and optimality. The first algorithm is based on static-consensus based gradient methods, and the second algorithm is based on dynamic-consensus (gradient-tracking) based distributed optimization methods and, hence, is applicable to general directed interaction graph topologies. Both algorithms can simultaneously ensure almost sure convergence to an optimal solution and a finite privacy budget, even when the number of iterations goes to infinity. To our knowledge, this is the first time that both goals are achieved simultaneously. Numerical simulations using a distributed estimation problem and experimental results on a benchmark dataset confirm the effectiveness of the proposed approaches.

Optimizing brushless direct current motor design: An application of the multi-objective generalized normal distribution optimization

In this study, we tackle the challenge of optimizing the design of a Brushless Direct Current (BLDC) motor. Utilizing an established analytical model, we introduced the Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) method, a biomimetic approach based on Pareto optimality, dominance, and external archiving. We initially tested MOGNDO on standard multi-objective benchmark functions, where it showed strong performance. When applied to the BLDC motor design with the objectives of either maximizing operational efficiency or minimizing motor mass, the MOGNDO algorithm consistently outperformed other techniques like Ant Lion Optimizer (ALO), Ion Motion Optimization (IMO), and Sine Cosine Algorithm (SCA). Specifically, MOGNDO yielded the most optimal values across efficiency and mass metrics, providing practical solutions for real-world BLDC motor design. The MOGNDO source code is available at: https://github.com/kanak02/MOGNDO.

Cooperative Multiagent Reinforcement Learning With Partial Observations

In this paper, we propose a distributed zeroth-order policy optimization method for Multi-Agent Reinforcement Learning (MARL). Existing MARL algorithms often assume that every agent can observe the states and actions of all the other agents in the network. This can be impractical in large-scale problems, where sharing the state and action information with multi-hop neighbors may incur significant communication overhead. The advantage of the proposed zeroth-order policy optimization method is that it allows the agents to compute the local policy gradients needed to update their local policy functions using local estimates of the global accumulated rewards that depend on partial state and action information only and can be obtained using consensus. Specifically, to calculate the local policy gradients, we develop a new distributed zeroth-order policy gradient estimator that relies on one-point residual-feedback which, compared to existing zeroth-order estimators that also rely on one-point feedback, significantly reduces the variance of the policy gradient estimates improving, in this way, the learning performance. We show that the proposed distributed zeroth-order policy optimization method with constant stepsize converges to the neighborhood of a policy that is a stationary point of the global objective function. The size of this neighborhood depends on the agents' learning rates, the exploration parameters, and the number of consensus steps used to calculate the local estimates of the global accumulated rewards. Moreover, we provide numerical experiments that demonstrate that our new zeroth-order policy gradient estimator is more sample-efficient compared to other existing one-point estimators.

Distributed Coordinated Operation of Active Distribution Networks with Electric Heating Loads Based on Dynamic Step Correction ADMM

In order to change the centralized operation framework of the active distribution network with electric heating loads (EHLs), a distributed optimization method is proposed for the coordinated operation of the active distribution network with EHLs. Firstly, considering the thermal delay effect and heat loss of the thermal system, a centralized optimization operation model for active distribution networks with EHLs is established. Then, based on the centralized optimization operation model, it is rephrased as a standard sharing problem, and a distributed optimization operation model for the EHL active distribution network is established based on the alternating direction multiplier method (ADMM) solution. In the process of solving ADMM, dynamic step correction was further considered. By updating the steps during the iteration process, the number of iterations was reduced, and the convergence and computational efficiency of ADMM were improved. Finally, the effectiveness of the distributed coordinated operation method proposed in this paper was simulated and verified by constructing an IEEE33 distribution system. The results showed that the proposed distributed coordinated operation method has strong robustness to the randomness of the number of distributed units and parameters, and EHLs participating in coordinated operation can expand the consumption space of wind power and photovoltaic power, and improve the economic efficiency of system operation.

Microscopic parasite malaria classification using best feature selection based on generalized normal distribution optimization.

Malaria disease can indeed be fatal if not identified and treated promptly. Due to advancements in the malaria diagnostic process, microscopy techniques are employed for blood cell analysis. Unfortunately, the diagnostic process of malaria via microscopy depends on microscopic skills. To overcome such issues, machine/deep learning algorithms can be proposed for more accurate and efficient detection of malaria. Therefore, a method is proposed for classifying malaria parasites that consist of three phases. The bilateral filter is applied to enhance image quality. After that shape-based and deep features are extracted. In shape-based pyramid histograms of oriented gradients (PHOG) features are derived with the dimension of N × 300. Deep features are derived from the residual network (ResNet)-50, and ResNet-18 at fully connected layers having the dimension of N × 1,000 respectively. The features obtained are fused serially, resulting in a dimensionality of N × 2,300. From this set, N × 498 features are chosen using the generalized normal distribution optimization (GNDO) method. The proposed method is accessed on a microscopic malarial parasite imaging dataset providing 99% classification accuracy which is better than as compared to recently published work.

MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods.

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration makes it difficult to achieve a substantive acceleration of convergence. In this article, we propose an accelerated framework named multiupdates single-combination (MUSIC) allowing each agent to perform multiple local updates and a single combination in each iteration. More importantly, we equip inexact and exact distributed optimization methods into this framework, thereby developing two new algorithms that exhibit accelerated linear convergence and high communication efficiency. Our rigorous convergence analysis reveals the sources of steady-state errors arising from inexact policies and offers effective solutions. Numerical results based on synthetic and real datasets demonstrate both our theoretical motivations and analysis, as well as performance advantages.

A Cooperative Dynamic Game via Hypergraph Distributed Optimization

We propose a novel cooperative dynamic game with the use of distributed optimization methods. Each coalition has an objective function and the goal of all the coalitions is to optimize the summation of their objectives given the interactions of their agents. The internal interactions are described by a multigraph but we will use directly a stochastic matrix to describe them while the external interactions are described by a hypergraph. The objective functions are quadratic and they encompass information for both types of interactions to highlight their importance in the outcome for the coalitions. The problem is formulated by means of distributed optimization where the actions of the agents at each iteration are the optimum solutions of the sequential optimization problem and the game is evolving by using a tilted matrix mechanism. We show that the optimization problem at each iteration can be solved in one step via a dual decomposition algorithm by exploiting the hypergraph structure of the optimization problem. For the complete description of the dynamic game we propose a switched dynamical system and we demonstrate its convergence numerically.

Distributed economic optimisation of multi‐energy park operation based on cloud platform architecture considering network delivery capacity

AbstractTo address the issues of node interaction power overrun and high carbon emissions that may arise during distributed optimization in multi‐energy parks (MEPs), this paper proposes a distributed low‐carbon and economic operation method for multi‐energy parks based on a cloud platform that considers network transmission capacity.The proposed method achieves maximun profit by designing a two layer collaborative architecture for distributed optimization operations. At the top level, cloud platform services are utilized to build a model for checking network transport capacity and carbon emission quotas, optimizing network node over‐limit inspection . The bottom layer constructs a distributed optimization model for multi‐energy complementation in each park, taking into account the information privacy and individual interests of each multi‐energy park. An improved alternating direction multiplier method (ADMM) is proposed to effectively solve the two‐layer framework. The case studies show that the distributed optimization method under cloud platform services proposed in this paper can achieve maximum revenue for integrated energy service provider while ensuring the safe operation of multi‐energy parks, and reasonably allocate the benefits of collaborative operation among various parks while promoting carbon emission reduction.

A two-stage distributed optimization method for home energy management systems via multi-modal data-driven algorithm

The home energy management system (HEMS), which utilizes multi-modal data from multiple sensors to generate the knowledge about decision making, is essential to the optimization of home energy management efficiency. Load scheduling based on HEMS can improve the utilization efficiency of multi-modal data and derived knowledge, achieve power supply-demand balance, and reduce users’ electricity costs. This paper proposes a distributed load optimization scheduling method for the load scheduling problem in HEMS based on multi-modal data-driven algorithm. Additionally, a two-stage data-driven optimization method is proposed, including a first-stage optimization model based on minimizing electricity costs and a second-stage optimization model based on minimizing system load fluctuations. In the first stage, cost self-optimization is performed based on energy storage devices. In the second stage, a load optimization instruction is issued by the control center, and each user optimizes the load fluctuations based on the system load data. Compared to centralized control methods, this approach reduces the computational overhead of the control center. Finally, simulation experiments based on load scheduling in the HEMS are conducted. The results of the first optimization stage show that when the battery capacity integrated into the system increases from 3.68 kWh to 6.68 kWh, user costs can be reduced from 57.572 cents to 42.064 cents. It is not only evident that the proposed method can effectively save users on electricity costs, but the introduction of larger capacity batteries also lowers these costs. The second stage of load fluctuation optimization results show that the proposed method can effectively optimize the usage data of a group of users and decrease the absolute peak-valley difference by 8.8%.

Dynamic Weighted-Gradient Descent Method With Smoothing Momentum for Distributed Energy Management of Multi-Microgrids Systems

Distributed optimization methods are powerful tools to deal with complex systems. However, the slow convergence rates of some widely used distributed methods have restricted their applications. In this paper, a dynamic weighted-gradient descent method is proposed to improve the convergence rate significantly, where the construction of the dynamic weighted matrix is the key of our distributed method. To form the matrix, the maximal differences of gradients between neighbor agents are calculated to derive entries of the matrix, which is an effective way to accelerate convergence while the equality constraint is always satisfied. Furthermore, the momentum terms based on the last updates of decision variables are also introduced, which reduce frequent change of gradients and speed up convergence rates further. Next, two propositions and a theorem are proved in the analysis of convergence part, which show the values of objective functions are monotonically decreasing to optima. Finally, simulations are carried out, and the results show that for a given accuracy, the number of iterations of our method are only one fourth of three widely used methods or even less. Additionally, applying our method, the optimal dispatches in a multi-microgird (MMG) system are achieved fast in a distributed manner, and the MMG can still work well, even if agents fail on communication networks.