What decisions must multi-agent routing systems optimize simultaneously?

Standard LLM routing (RouteLLM, Hybrid-LLM) optimizes a single decision: which model handles this query. MasRouter argues this is an incomplete optimization for multi-agent systems, where routing involves four simultaneous decisions:

1. Collaboration mode determination — choosing the optimal communication topology (Chain, Tree, Graph) for varying task complexities
2. Dynamic agent number — determining how many expert agents are required based on input difficulty
3. Agent role allocation — selecting suitable roles per agent according to the query domain
4. Agent LLM routing — assigning each agent the appropriate LLM backbone

The formal definition of Multi-Agent System Routing (MASR) integrates all four into a unified framework. MasRouter implements this through a cascaded controller network: a variational latent variable model routes the query to a collaboration module, a structured probabilistic cascade generates agent roles progressively, and a multinomial distribution model recommends LLM backbones per agent. The cascade is sequential by design — topology constrains which roles make sense, and roles constrain which LLMs are appropriate.

The results validate the multi-dimensional approach: MasRouter surpasses RouterDC (SOTA single-model routing) by 3.51% average accuracy while reducing HumanEval cost from $0.363 to $0.185 (49% reduction). The framework generalizes to unseen LLM backbones and collaboration modes, and integrates with mainstream MAS for 17-28% cost reduction.

Since Can AI systems design unique multi-agent workflows per individual query?, MasRouter provides a more structured alternative — FlowReasoner generates system designs via RL-trained code generation (maximum flexibility, less interpretability), while MasRouter's topology→role→LLM cascade provides interpretable intermediate decisions at the cost of fixed structure types. Since Can multi-agent teams automatically remove their weakest members?, DyLAN prunes within a running network while MasRouter constructs the optimal network from scratch — complementary approaches that could be composed (MasRouter for initial construction, DyLAN for runtime adaptation).

The formalization matters because it surfaces what single-model routing leaves on the table. Since When does adding more agents actually help systems?, routing to the right topology per query is MasRouter's direct response to topology-dependent error amplification — rather than accepting a fixed topology's scaling limitations, route around them.