Evaluating LLMs for Combinatorial Optimization: One-Phase and Two-Phase Heuristics for 2D Bin-Packing
Abstract
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.
Cite
@article{arxiv.2509.22255,
title = {Evaluating LLMs for Combinatorial Optimization: One-Phase and Two-Phase Heuristics for 2D Bin-Packing},
author = {Syed Mahbubul Huq and Daniel Brito and Daniel Sikar and Chris Child and Tillman Weyde and Rajesh Mojumder},
journal= {arXiv preprint arXiv:2509.22255},
year = {2025}
}
Comments
1 table, 6 figures. 39th Conference on Neural Information Processing Systems (NeurIPS 2025) Accepted for the Workshop: Evaluating the Evolving LLM Lifecycle Benchmarks, Emergent Abilities, and Scaling