Zijie Lei

Tao Feng, Fangxu Yu, Haozhen Zhang et al.

No single large language model (LLM) is optimal across all queries and budget constraints, making model routing essential for cost-effective deployment. Existing routers adopt diverse formulations and implementations, making fair comparison and extension difficult. We present a unified formulation of LLM routing as a sequential decision process characterized by five components: context encoders, model encoders, scoring functions, decision rules, and learning signals, covering single-turn, multi-turn, and personalized routing. Based on this formulation, we develop an automated pipeline for constructing routing supervision and evaluating routers jointly on response quality and inference cost. The resulting benchmark, xRouteBench, spans generic LLM, memory-augmented, vision, time-series, and personalized routing tasks. We further introduce LLMRouter, an open-source modular infrastructure with more than 16 representative routers. Our empirical study shows that learned routers outperform the strongest fixed-model baseline by 14.6% relatively, lightweight routers become more competitive under tight cost constraints, and user-conditioned routing consistently improves personalization.

Tao Feng, Haozhen Zhang, Zijie Lei et al.

LLM routing has achieved promising results in integrating the strengths of diverse models while balancing efficiency and performance. However, to support more realistic and challenging applications, routing must extend into agentic LLM settings, where task planning, multi-round cooperation among heterogeneous agents, and memory utilization are indispensable. To address this gap, we propose GraphPlanner, a heterogeneous graph memory-augmented agentic router for multi-agent LLMs that generates routing workflows for each query and supports both inductive and transductive inference. GraphPlanner formulates workflow generation as a Markov Decision Process (MDP), where at each step it selects both the LLM backbone and the agent role, including Planner, Executor, and Summarizer. By leveraging a heterogeneous graph, denoted as GARNet, to capture interaction memories among queries, agents, and responses, GraphPlanner integrates historical memory and workflow memory into richer state representations. The entire pipeline is optimized with reinforcement learning, jointly improving task-specific performance and computational efficiency. We evaluate GraphPlanner across 14 diverse LLM tasks and demonstrate that: (1) GraphPlanner outperforms strong single-round and multi-round routers, improving accuracy by up to 9.3% while reducing GPU cost from 186.26 GiB to 1.04 GiB; (2) GraphPlanner generalizes robustly to unseen tasks and LLMs, exhibiting strong zero-shot capabilities; and (3) GraphPlanner effectively leverages historical memories, supporting both inductive and transductive inference for more adaptive routing. Our code for GraphPlanner is released at https://github.com/ulab-uiuc/GraphPlanner.