The problem of multi-constraint routing is related to Multi-Objective Shortest Path Problem (MOSPP) and is known to be NP-hard. Despite decades of research, there is no state-of-the-art solution for this problem as Dijkstra algorithm for the single constraint case. This paper develops a systematic strategy to construct a model of an IP Network with multiple weight links and proposes a scalable and generalized AI-Native routing system and method (MORAI) to synthesize a composite cost to achieve optimal routing plane computation for multiple QoS-demands. The proposed method consists of an AI model and the training procedure and considers composite cost synthesis as an optimization process maximizing the number of feasible routes (satisfying multiple QoS-demands) in the Shortest Path Tree constructed with the composite cost as an edge weight. Using a composite cost for route identification with a Shortest Path First Algorithm guarantees that the routing is loop-free and fully distributed. The proposed system architecture is a combination of distributed and centralized modes. When the AI model is trained in a dedicated device, the following route computation is fully distributed, so the solution can be easily deployed in the current router architecture. Three system architectures are proposed, showing different combinations of AI-model training, execution, and composite cost computation in the network. Finally, the general paradigm of AI-Native Composite Cost synthesis is described, as well as the general AI model training scheme design is given.