How to optimally assign tasks to agents using optimal transport?
Task allocation for multi-agent systems via unequal-dimensional optimal transport
This paper tackles the problem of efficiently assigning many delivery tasks to many transport agents (like drones) by minimizing the total travel distance. It frames this as an unequal-dimensional optimal transport problem, where the distribution of agents (e.g., drone locations) is matched with the joint distribution of task origins and destinations.
For LLM-based multi-agent systems, this research offers a mathematical framework for optimizing task allocation. It demonstrates how to consider the collective, probabilistic behavior of agents rather than individual assignments, which is crucial for scalability. The concepts of twist and nestedness conditions provide guarantees for solution uniqueness and smoothness, which can inform the design of robust LLM-based multi-agent coordination strategies. The cost function's index form simplification facilitates computation, a significant concern for practical LLM-based system implementation.