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

Abstract

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.