# Large Language Models for Multi-Facility Location Mechanism Design

arXiv: https://arxiv.org/abs/2503.09533 · HTML: https://mlsanity.com/paper/2503.09533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 8 of 8)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [Understanding the Importance of Evolutionary Search in Automated Heuristic Design with Large Language Models](https://mlsanity.com/paper/2407.10873/) (2024)
- [Mechanism Design for Facility Location Problems: A Survey](https://mlsanity.com/paper/2106.03457/) (2021)

## Abstract (arXiv)

Designing strategyproof mechanisms for multi-facility location that optimize social costs based on agent preferences had been challenging due to the extensive domain knowledge required and poor worst-case guarantees. Recently, deep learning models have been proposed as alternatives. However, these models require some domain knowledge and extensive hyperparameter tuning as well as lacking interpretability, which is crucial in practice when transparency of the learned mechanisms is mandatory. In this paper, we introduce a novel approach, named LLMMech, that addresses these limitations by incorporating large language models (LLMs) into an evolutionary framework for generating interpretable, hyperparameter-free, empirically strategyproof, and nearly optimal mechanisms. Our experimental results, evaluated on various problem settings where the social cost is arbitrarily weighted across agents and the agent preferences may not be uniformly distributed, demonstrate that the LLM-generated mechanisms generally outperform existing handcrafted baselines and deep learning models. Furthermore, the mechanisms exhibit impressive generalizability to out-of-distribution agent preferences and to larger instances with more agents.