A Design Framework for Scalable and Adaptive Multi-Agent Coordination in Dynamic Environments: Addressing Concurrent Agent and Environment Interactions

In dynamic environments, such as box-pushing tasks, multi-agent systems (MAS) face significant challenges in coordinating agents within high-density settings while managing uncertainties arising from fluctuations in agent configurations and environmental dynamics. In this paper, we explore the integration of surrogate response surface modeling (SRSM) with optimization algorithms, comparing Stochastic Gradient Descent (SGD) with a fixed learning rate, and adaptive learning rate (ALR) optimizers - including Adaptive Moment Estimation (ADAM) and Adaptive Approximate Direction Method Algorithm (AADMA) - to enhance MAS performance metrics, such as Agent Collision Rate (ACR), Agent Movement Frequency (AMF), and Task Completion Time (TCT). Through systematic experimentation across five scenarios, SRSM is employed to uncover key trends in MAS performance and identify configurations that improve scalability and adaptability. From the analysis of simulation data, it has been observed that SGD struggles significantly in dynamic environments, while ADAM demonstrates moderate improvements. However, AADMA consistently outperforms both by reducing loss, lowering collision rates, increasing movement efficiency, and achieving shorter task completion times. Performance comparison charts and loss function graphs emphasize AADMA's superiority in addressing the complexities of real-time coordination and adaptability. Through this study, we highlight the critical role of combining SRSM with ARL to design MAS that is capable of thriving in complex, dynamic, and high-density environments. By addressing key scalability and adaptability challenges, the proposed framework significantly advances MAS design, paving the way for improved multi-agent coordination in real-world applications.