Distributed Optimization Techniques Research Articles

A distributed optimization approach via symmetric group actions under time-varying communication networks

The widespread adoption of edge computing has revolutionized data processing by decentralizing computational power, resulting in faster response times, decreased network latency, and enhanced privacy. This paradigm shift is crucial due to the increasing demand for real-time analytics and the growth of Internet of Things devices. Optimizing resource allocation and decision-making in on-board computing presents challenges, especially in dynamic and heterogeneous environments. Distributed optimization techniques address these challenges by allowing multiple agents to collaborate and make decisions based on local knowledge. This paper focuses on distributed optimization in multi-agent systems with time-varying communication networks and explores the advantages of considering symmetric group action to reach global optimization. In particular, we focus our study into a class of Integer Linear Programming (ILP) for modeling real-world optimization problems in decentralized environments. The paper introduces a novel approach that leverages group actions and probabilistic selection of initial states to enhance convergence to desirable solutions. The method guarantees feasibility while minimizing computational effort for the agents. Additionally, numerical simulations have been conducted to validate the proposed algorithm, demonstrating its efficacy in optimizing resource allocation for a class of scheduling problems.

Decentralized Stochastic Multi-Player Multi-Armed Walking Bandits

Multi-player multi-armed bandit is an increasingly relevant decision-making problem, motivated by applications to cognitive radio systems. Most research for this problem focuses exclusively on the settings that players have full access to all arms and receive no reward when pulling the same arm. Hence all players solve the same bandit problem with the goal of maximizing their cumulative reward. However, these settings neglect several important factors in many real-world applications, where players have limited access to a dynamic local subset of arms (i.e., an arm could sometimes be ``walking'' and not accessible to the player). To this end, this paper proposes a multi-player multi-armed walking bandits model, aiming to address aforementioned modeling issues. The goal now is to maximize the reward, however, players can only pull arms from the local subset and only collect a full reward if no other players pull the same arm. We adopt Upper Confidence Bound (UCB) to deal with the exploration-exploitation tradeoff and employ distributed optimization techniques to properly handle collisions. By carefully integrating these two techniques, we propose a decentralized algorithm with near-optimal guarantee on the regret, and can be easily implemented to obtain competitive empirical performance.

Learning Infused Quantum-Classical Distributed Optimization Technique for Power Generation Scheduling

Learning Infused Quantum-Classical Distributed Optimization Technique for Power Generation Scheduling

Distributed Optimization in Distribution Systems: Use Cases, Limitations, and Research Needs

Electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system.

Regenerative Topology Optimization of Fine Lattice Structures.

We present a generative approach for creating three-dimensional lattice structures optimized for mass and deflection composed of thousands of one-dimensional strut primitives. Our approach draws inspiration from topology optimization principles. The proposed method iteratively determines unnecessary lattice struts through stress analysis, erodes those struts, and then randomly generates new struts across the entire structure. The objects resulting from this distributed optimization technique demonstrate high strength-to-weight ratios that are at par with state-of-the-art topology optimization approaches, but are qualitatively very different. We use a dynamics simulator that allows optimization of structures subject to dynamic load cases, such as vibrating structures and robotic components. Because optimization is performed simultaneously with simulation, the process scales efficiently on massively parallel graphics processing units. The intricate nature of the output lattices contributes to a new class of objects intended specifically for additive manufacturing. Our work contributes a highly parallel simulation method and simultaneous algorithm for analyzing and optimizing lattices with thousands of struts. In this study, we validate multiple versions of our algorithm across sample load cases, to show its potential for creating high-resolution objects with implicit optimized microstructural patterns.

A Homomorphic Encryption-Based Private Collaborative Distributed Energy Management System

This article investigates the privacy issues in the distributed energy management system (EMS) of smart distribution systems and microgirds. A novel private collaborative distributed energy management system (P-CoDEMS) is proposed to solve the AC optimal power flow (ACOPF) problem in a distributed and private fashion. The proposed P-CoDEMS algorithm is based on an original primal dual subgradient distributed optimization technique and a state-of-the-art fully homomorphic encryption algorithm. The convergence and optimality of the proposed P-CoDEMS algorithm are evaluated on four representative systems. Simulation results indicate that the proposed P-CoDEMS algorithm can accurately solve the ACOPF problem in a fully distributed way while preserving individual agent privacy.

A Study on Distributed Optimization over Large-Scale Networked Systems

Distributed optimization is a very important concept with applications in control theory and many related fields, as it is high fault-tolerant and extremely scalable compared with centralized optimization. Centralized solution methods are not suitable for many application domains that consist of large number of networked systems. In general, these large-scale networked systems cooperatively find an optimal solution to a common global objective during the optimization process. Thus, it gives us an opportunity to analyze distributed optimization techniques that is demanded in most distributed optimization settings. This paper presents an analysis that provides an overview of decomposition methods as well as currently existing distributed methods and techniques that are employed in large-scale networked systems. A detailed analysis on gradient like methods, subgradient methods, and methods of multipliers including the alternating direction method of multipliers is presented. These methods are analyzed empirically by using numerical examples. Moreover, an example highlighting the fact that the gradient method fails to solve distributed problems in some circumstances is discussed under numerical results. A numerical implementation is used to demonstrate that the alternating direction method of multipliers can solve this particular problem, by revealing its robustness compared with the gradient method. Finally, we conclude the paper with possible future research directions.

Distributed optimization by Newton consensus over undirected graphs

This manuscript proposes a distributed optimization technique based on a Newton consensus approach. The approach implements a Newton step for both the primal and dual problems that can be implemented in a completely decentralized fashion. Unlike existing techniques, no exchange of derivative information between agents is required. In addition, no explicit inversion of the Hessian information is required to generate the required Newton step. The proposed Newton consensus is shown to reduce the dependency of the transient performance on the graph structure. A simulation study demonstrates the effectiveness of the technique to achieve uniform performance.

Distributed population dynamics for active and reactive power dispatch in islanded microgrids

This work proposes a distributed strategy to solve a joint active and reactive power dispatch in isolated microgrids. The information shared among neighboring local controllers allows the algorithm to achieve the optimal dispatch in a secondary layer, which is the reference for primary controllers in each generator. The method based on population dynamics facilitates the implementation in systems with high penetration of distributed generation and a basic communication network. The hierarchical strategy is evaluated in a co-simulation platform to emulate real conditions in a study case of a microgrid with a management control scheme programmed with the distributed optimization technique. Results show that the proposed technique provides an optimal dispatch in distinct scenarios with the expected reduction of losses, improvement in voltage profiles, and minimization of the generation costs.

A unitary distributed subgradient method for multi-agent optimization with different coupling sources

Distributed optimization techniques offer high quality solutions to various engineering problems, such as resource allocation and distributed estimation and control. In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed subgradient method with double averaging (abbreviated as DSA2) that only requires peer-to-peer communication and local computation to solve the global problem. The algorithmic framework builds on dual methods and dynamic average consensus; the sequence of test points is formed by iteratively minimizing a local dual model of the overall objective where the coefficients, i.e., approximated subgradients of the objective, are supplied by the dynamic average consensus scheme. We theoretically show that DSA2 enjoys non-ergodic convergence properties, i.e., the local minimizing sequence itself is convergent, a distinct feature that cannot be found in existing results. Specifically, we establish a convergence rate of O(1t) in terms of objective function error. Then, extensions are made to tackle distributed optimization problems with coupled functional constraints by combining DSA2 and dual decomposition. This is made possible by Lagrangian relaxation that transforms the coupling in constraints of the primal problem into that in cost functions of the dual, thus allowing us to solve the dual problem via DSA2. Both the dual objective error and the quadratic penalty for the coupled constraint are proved to converge at a rate of O(1t), and the primal objective error asymptotically vanishes. Numerical experiments and comparisons are conducted to illustrate the advantage of the proposed algorithms and validate our theoretical findings.

Distributed Wave-Domain Active Noise Control Based on the Diffusion Adaptation

Conducting the spatial active noise control (ANC) in wave-domain has been shown advantageous over conventional point-based methods. In the existing schemes, signals at all error microphones are collected and processed in a centralized manner to update the secondary source driving signals. The high computational complexity of this centralized strategy represents one of the major challenges for applying multi-channel ANC systems in large-scale applications. In order to address this issue, this work presents a distributed wave-domain ANC scheme by resorting to distributed optimization techniques. The global ANC problem is formulated as a sum of local costs, and the diffusion adaptation strategies are subsequently utilized to provide a distributed solution that only requires local information exchanges. Simulation results show that the proposed algorithms achieve sufficiently good performance compared to its centralized counterpart.

Decentralized PEV Power Allocation With Power Distribution and Transportation Constraints

Plug-in Electric Vehicles (PEVs) keep on penetrating the automobile market. However, uncoordinated PEV charging can impair the reliability of power grid. In this paper, an interesting problem of PEV charging power allocation is investigated, in which both power distribution and transportation constraints are considered. A novel approach for PEV charging management based on optimal power flow (OPF) analysis is proposed to optimize PEV charging energy in a power distribution system. Firstly, spatial and temporal PEV demand scheduling is introduced to maximize PEV charging service capacity while considering the maximum traveling distance of PEVs. Secondly, to ensure the scalability of the OPF analysis, a distributed optimization technique, i.e., proximal Jacobian alternating direction multiplier method, is applied to attain the optimal power allocation in a decentralized manner. The resulting PEV charging service capacity in the power distribution system is improved without violating power distribution and transportation constraints. Furthermore, kernel density estimation method is adopted to identify the PEV range anxiety constraint without the PEV battery information. Simulation results are presented to validate the effectiveness of our approach with high PEV penetration.

Symmetry Reduction for Performance Certification of Interconnected Systems

We exploit symmetries in the interconnection topology of a networked system to provide a dimensionality reduction in the certification of performance. The certification method exploits the dissipativity properties of the subsystems; thus the conservatism introduced by the reduction is minimal when the subsystems possess similar dissipativity characteristics. We combine this reduction with distributed optimization techniques to be able to analyze large interconnections efficiently.

On the Role of Communications Plane in Distributed Optimization of Power Systems

Distributed optimization methods have been widely studied in recent years as they could be instrumental in optimizing the operation of future power systems. Compared to the centralized approach, communications will have greater impact on distributed methods as their performance depends heavily on the information exchange among multiple control entities. However, it is not clear what communications infrastructures and technologies should be adopted for distributed methods in practice. To investigate this issue and bridge the gap between the power system communications research community and the distributed optimization research community, this paper models the communications infrastructures and schemes required by distributed methods using the OPNET modeler. The capabilities and limitations of centralized and distributed communications infrastructures are investigated in terms of communications delays incurred and their impact on the convergence of two distributed algorithms, namely, Alternating Direction Method of Multipliers (ADMM) and Optimality Condition Decomposition (OCD) for solving the AC Optimal Power Flow problem in the IEEE 118-bus system and in the large-scale Polish power system. Our simulation results show that the existing communications plane in power systems might not be able to support widely used distributed optimization techniques (such as ADMM and OCD), which is a major finding. In addition, our results indicate that the connectivity requirements of distributed optimization necessitate a mesh network architecture with additional communications links among substations.

A tool to prioritize code smells in distributed development

A code smell is a symptom in the source code that helps to identify a design problem. Several tools for detecting and ranking code smells according to their criticality to the system have been developed. However, existing works assume a centralized development approach, which does not consider systems being developed in a distributed fashion. The main problem in a distributed group of developers is that a tool cannot always ensure a global vision of (smells of) the system, and thus inconsistencies among the rankings provided by each developer are likely to happen. These inconsistencies often cause unnecessary refactorings and might not focus the whole team on the critical smells system-wide. Along this line, this work proposes a multi-agent tool, called D-JSpIRIT, which helps individual developers to reach a consensus on their smell rankings by means of distributed optimization techniques.

Deep Learning at Scale and at Ease

Recently, deep learning techniques have enjoyed success in various multimedia applications, such as image classification and multimodal data analysis. Large deep learning models are developed for learning rich representations of complex data. There are two challenges to overcome before deep learning can be widely adopted in multimedia and other applications. One is usability, namely the implementation of different models and training algorithms must be done by nonexperts without much effort, especially when the model is large and complex. The other is scalability, namely the deep learning system must be able to provision for a huge demand of computing resources for training large models with massive datasets. To address these two challenges, in this article we design a distributed deep learning platform called SINGA , which has an intuitive programming model based on the common layer abstraction of deep learning models. Good scalability is achieved through flexible distributed training architecture and specific optimization techniques. SINGA runs on both GPUs and CPUs, and we show that it outperforms many other state-of-the-art deep learning systems. Our experience with developing and training deep learning models for real-life multimedia applications in SINGA shows that the platform is both usable and scalable.

An Asynchronous Fixed-Point Algorithm for Resource Sharing With Coupled Objectives

Distributed resource allocation and sharing can often be formulated as a utility maximization problem, with the objective being the sum of user utilities minus a coupled cost. A traditional distributed solution to such problems, called “consistency pricing,” decouples the objective function via dual decomposition, which is then iteratively solved by the subgradient method. However, such gradient-based approaches may require many iterations of message passing to converge, which may not be sufficient in large-scale real-time applications. In this paper, we propose a new fixed-point-like distributed solution to resource sharing problems with coupled objective functions. While preserving the simple pricing interpretation, our approach speeds up convergence by exploiting the structural difference between user utilities and the coupled cost function. We theoretically analyze the asynchronous algorithm convergence conditions based on contraction mapping. Through a detailed case study of cloud bandwidth reservation based on real-world workload traces, we demonstrate the benefits of the proposed algorithm over state-of-the-art distributed optimization techniques including gradient descent, dual decomposition, and ADMM. In addition, we also extend the proposed algorithm to approach a more general class of consensus optimization problems with not only a coupled objective function, but also a certain class of coupled constraints.

Intelligent Partitioning in Distributed Optimization of Electric Power Systems

Distributed optimization techniques in electric power systems have drawn increased attention as they provide a scalable way to handle the increasingly complex and large-scale optimization problems associated with the optimal operation of the system. However, little effort has been reported on how to optimally partition the overall optimization problem into subproblems, which significantly affects the efficiency and convergence speed of distributed methods. To address this issue, this paper focuses on how to determine the optimal partition for a given system and optimization problem, and quantify the improvement obtained with the optimal partition in terms of number of iterations and convergence time for solving the ac optimal power flow problem. The proposed approach is based on spectral clustering using a combination of the Hessian matrix of the optimization problem and the admittance matrix as the affinity matrix. Simulation results for the IEEE test systems with 14, 30, 57, 118, and 300 buses confirm the effectiveness of the proposed partitioning method, and the robustness of the performance of a certain partition with respect to the operating point of the system.

Distributed Optimization for Shared State Systems: Applications to Decentralized Freeway Control via Subnetwork Splitting

Optimal control problems on dynamical systems are concerned with finding a control policy, which minimizes a desired objective, where the objective value depends on the future evolution of the system (the state of the system), which, in turn, depends on the control policy. For systems which contain subsystems that are disjoint across the state variables, distributed optimization techniques exist, which iteratively update subsystems concurrently and then exchange information between subsystems with shared control variables. This article presents a method, based on the asynchronous alternating directions method of multiplier algorithm, which extends these techniques to subsystems with shared control and state variables, while maintaining similar communication structure. The method is used as the basis for splitting network flow control problems into many subnetwork control problems with shared boundary conditions. The decentralized and parallel nature of the method permits high scalability with respect to the size of the network. For highly nonconvex applications, an efficient method, based on adjoint gradient computations, is presented for solving subproblems with shared state. The method is applied to decentralized, coordinated ramp metering and variable speed limit control on a realistic freeway network model using distributed model predictive control.

Distributed spatio-temporal association and tracking of multiple targets using multiple sensors

The problem of tracking multiple targets using nonlinear observations acquired at multiple sensors is addressed by combining particle filtering (PF) with sparse matrix decomposition techniques. Sensors are spatially scattered, while the unknown number of targets may be time varying. A framework is put forth where norm-one regularized factorization is employed to decompose the sensor data covariance matrix into sparse factors whose support facilitates recovery of sensors that acquire informative measurements about the targets. This novel sensors-to-targets association scheme is integrated with PF mechanisms to perform accurate tracking. Precisely, distributed optimization techniques are employed to associate targets with sensors, and PF is integrated to perform target tracking using only the sensors selected by the sparse decomposition scheme. Different from existing alternatives, the novel algorithm can efficiently track and associate targets with sensors even in noisy settings. Extensive numerical tests are provided to demonstrate the tracking superiority of the proposed algorithm over existing approaches.