# Evaluating LLMs for Combinatorial Optimization: One-Phase and Two-Phase Heuristics for 2D Bin-Packing

arXiv: https://arxiv.org/abs/2509.22255 · HTML: https://mlsanity.com/paper/2509.22255/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 2 of 2)

- [Machine Learning for the Multi-Dimensional Bin Packing Problem: Literature Review and Empirical Evaluation](https://mlsanity.com/paper/2312.08103/) (2023)
- [A Hierarchical Bin Packing Framework with Dual Manipulators via Heuristic Search and Deep Reinforcement Learning](https://mlsanity.com/paper/2506.01628/) (2025)

## Abstract (arXiv)

This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs with evolutionary algorithms to generate and refine heuristic solutions iteratively. Through comprehensive experiments comparing LLM generated heuristics against traditional approaches (Finite First-Fit and Hybrid First-Fit), we demonstrate that LLMs can produce more efficient solutions while requiring fewer computational resources. Our evaluation reveals that GPT-4o achieves optimal solutions within two iterations, reducing average bin usage from 16 to 15 bins while improving space utilization from 0.76-0.78 to 0.83. This work contributes to understanding LLM evaluation in specialized domains and establishes benchmarks for assessing LLM performance in combinatorial optimization tasks.