Distributed Optimization Algorithms Over Large-Scale Networks with Applications to Microgrids

• Main Author: Ghaderyan, Diyako
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2023
• Subjects: Artificial intelligence; Communication; Connectivity; Graphs; Machine learning; Optimization algorithms
• ISBN: 9798382512969

In the last years, rapid advances in artificial intelligence, embedded systems, and communication technologies have led to computational network systems that require algorithms to solve optimization problems with enormous physically distributed and/or private data sets to achieve system level objectives such that every agent, represented by a node in the network, has to agree on a common decision. To reach a consensus decision, optimization techniques can be used to solve a consensus problem in a distributed manner by employing only local computations and communication among neighboring nodes that can directly communicate with each other.In the first part of this thesis, we propose a distributed optimization approach, which enjoys the advantages of both the primal and the dual domain methods, to solve the economic dispatch problem in a distributed way over undirected networks. A key requirement point is that the convergence rate of the optimization method must be fast when compared with recent state of the art distributed approaches. We show through simulations that for the IEEE 14-bus and the IEEE 39-bus distribution test systems, the proposed algorithm achieves indeed a significantly higher convergence rate effectively attaining this goal.In the second part of the thesis, we develop a fast row stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights, leading to certain practical advantages in broadcast communication settings over those requiring column-stochastic weights. In contrast to the existing methods for directed networks, we show that FRSD enjoys linear convergence without employing a gradient tracking (GT) technique explicitly. The key idea is that it implements a GT implicitly through a novel momentum term, which leads to a significant reduction in communication and storage overhead for each node. This is particularly remarkable when FRSD is implemented for solving high-dimensional problems over small-to-medium scale networks. In the numerical tests, we compare FRSD with other state-of-the-art methods, which use row-stochastic and/or column-stochastic weights showing that FRSD is indeed competitive with or outperforms other recent approaches.