# Large Language Model for Discrete Optimization Problems: Evaluation and Step-by-step Reasoning

arXiv: https://arxiv.org/abs/2603.07733 · HTML: https://mlsanity.com/paper/2603.07733/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 34 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [Enough Coin Flips Can Make LLMs Act Bayesian](https://mlsanity.com/paper/2503.04722/) (2025)
- [Verbalized Machine Learning: Revisiting Machine Learning with Language Models](https://mlsanity.com/paper/2406.04344/) (2024)

## Abstract (arXiv)

This work investigated the capabilities of different models, including the Llama-3 series of models and CHATGPT, with different forms of expression in solving discrete optimization problems by testing natural language datasets. In contrast to formal datasets with a limited scope of parameters, our dataset included a variety of problem types in discrete optimization problems and featured a wide range of parameter magnitudes, including instances with large parameter sets, integrated with augmented data. It aimed to (1) provide an overview of LLMs' ability in large-scale problems, (2) offer suggestions to those who want to solve discrete optimization problems automatically, and (3) regard the performance as a benchmark for future research. These datasets included original, expanded and augmented datasets. Among these three datasets, the original and augmented ones aimed for evaluation while the expanded one may help finetune a new model. In the experiment, comparisons were made between strong and week models, CoT methods and No-CoT methods on various datasets. The result showed that stronger model performed better reasonably. Contrary to general agreement, it also showed that CoT technique was not always effective regarding the capability of models and disordered datasets improved performance of models on easy to-understand problems, even though they were sometimes with high variance, a manifestation of instability. Therefore, for those who seek to enhance the automatic resolution of discrete optimization problems, it is recommended to consult the results, including the line charts presented in the Appendix, as well as the conclusions drawn in this study for relevant suggestions.