How to locate facilities with uncertain agents?
Facility Location Problem with Aleatory Agents
This research paper introduces the Facility Location Problem with Aleatory Agents (FLPAA), where a facility needs to be optimally placed to serve both "deterministic agents" (whose locations are known) and "aleatory agents" (whose locations are unknown but follow a probability distribution).
The key point relevant to LLM-based multi-agent systems is the concept of optimizing for agents whose behavior is characterized by a probability distribution. This aligns with using LLMs to model agent behavior, as LLMs generate responses based on probabilistic distributions learned from training data. The paper explores mechanisms to elicit truthful information from deterministic agents and design algorithms that work well across various potential distributions of aleatory agents. This translates to designing robust multi-agent systems where LLM-based agents might not always behave predictably but follow probabilistic patterns.