A Robust Population Dynamics Model With Carrying Capacity Constraints for Centrally Coordinated Distributed Optimization

Distributed optimization is crucial for managing complex, large-scale systems, yet faces challenges in achieving robustness and efficiency under practical constraints. This paper introduces the Capacity Constrained Replicator Dynamics (CCRD) model and its robust variant (RCCRD), novel population dynamics frameworks inspired by ecological principles. These frameworks are designed for constrained optimization in distributed settings that employ a centralized coordinator. CCRD extends classic replicator dynamics by incorporating carrying capacity constraints and is proven to converge to Nash equilibria in full-potential games. RCCRD further enhances robustness through a self-correcting mechanism, ensuring constraint satisfaction and reliable performance even with computational errors. Theoretical analysis demonstrates the convergence properties of (R)CCRD, and comparative simulations reveal that RCCRD outperforms some existing methods in terms of runtime, optimality gap, and constraint satisfaction, particularly in noisy environments. The (R)CCRD framework offers a practically relevant and efficient anytime optimization approach for centrally coordinated distributed constrained optimization, with significant potential for real-time applications in large-scale systems.