As distributed artificial intelligence (AI) and multi-agent architectures grow increasingly complex, the need for adaptive, context-aware routing becomes paramount. This paper introduces an enhanced, adaptive routing algorithm tailored for AI multi-agent networks, integrating priority-based cost functions and dynamic learning mechanisms. Building on an extended Dijkstra-based framework, we incorporate multi-faceted parameters such as task complexity, user request priority, agent capabilities, bandwidth, latency, load, model sophistication, and reliability. We further propose dynamically adaptive weighting factors, tuned via reinforcement learning (RL), to continuously evolve routing policies based on observed network performance. Additionally, heuristic filtering and hierarchical routing structures improve scalability and responsiveness. Our approach yields context-sensitive, load-aware, and priority-focused routing decisions that not only reduce latency for critical tasks but also optimize overall resource utilization, ultimately enhancing the robustness, flexibility, and efficiency of multi-agent systems.