# Combinatorial Optimization for All: Using LLMs to Aid Non-Experts in Improving Optimization Algorithms

arXiv: https://arxiv.org/abs/2503.10968 · HTML: https://mlsanity.com/paper/2503.10968/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 54 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Better Zero-Shot Reasoning with Role-Play Prompting](https://mlsanity.com/paper/2308.07702/) (2023)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [The Prompt Report: A Systematic Survey of Prompt Engineering Techniques](https://mlsanity.com/paper/2406.06608/) (2024)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [At Which Training Stage Does Code Data Help LLMs Reasoning?](https://mlsanity.com/paper/2309.16298/) (2023)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [Large Language Model-Aware In-Context Learning for Code Generation](https://mlsanity.com/paper/2310.09748/) (2023)
- [Source-Aware Training Enables Knowledge Attribution in Language Models](https://mlsanity.com/paper/2404.01019/) (2024)
- [When Large Language Model Meets Optimization](https://mlsanity.com/paper/2405.10098/) (2024)
- [Metaheuristics and Large Language Models Join Forces: Toward an Integrated Optimization Approach](https://mlsanity.com/paper/2405.18272/) (2024)
- [Explaining Genetic Programming Trees using Large Language Models](https://mlsanity.com/paper/2403.03397/) (2024)
- [Large Language Models for the Automated Analysis of Optimization Algorithms](https://mlsanity.com/paper/2402.08472/) (2024)
- [Investigating the Role of Prompting and External Tools in Hallucination Rates of Large Language Models](https://mlsanity.com/paper/2410.19385/) (2024)
- [Improving Existing Optimization Algorithms with LLMs](https://mlsanity.com/paper/2502.08298/) (2025)
- [An Empirical Investigation of Correlation between Code Complexity and Bugs](https://mlsanity.com/paper/1912.01142/) (2019)

## Built on by (most cited first, 7 of 7)

- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selection](https://mlsanity.com/paper/2512.13374/) (2025)
- [LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithm](https://mlsanity.com/paper/2509.09707/) (2025)
- [Reasoning with Preference Constraints: A Benchmark for Language Models in Many-to-One Matching Markets](https://mlsanity.com/paper/2509.13131/) (2025)
- [Constraint-aware Path Planning from Natural Language Instructions Using Large Language Models](https://mlsanity.com/paper/2603.19257/) (2026)
- [From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorial](https://mlsanity.com/paper/2609.31649/) (2026)
- [LYNX: Analytical Program Synthesis via Grounding and Closed-Loop Refinement](https://mlsanity.com/paper/2610.14777/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have shown notable potential in code generation for optimization algorithms, unlocking exciting new opportunities. This paper examines how LLMs, rather than creating algorithms from scratch, can improve existing ones without the need for specialized expertise. To explore this potential, we selected 10 baseline optimization algorithms from various domains (metaheuristics, reinforcement learning, deterministic, and exact methods) to solve the classic Travelling Salesman Problem. The results show that our simple methodology often results in LLM-generated algorithm variants that improve over the baseline algorithms in terms of solution quality, reduction in computational time, and simplification of code complexity, all without requiring specialized optimization knowledge or advanced algorithmic implementation skills.