mlsanityData to 14 Oct 2026

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

arXiv 2503.10968 ↗First posted 14 Mar 2025cs.AI cs.CL cs.LGcited by 7

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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.

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

21 of 54 references.

References · 21

  1. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  2. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,986
  3. 2023Large Language Models as Optimizerscited by 864
  4. 2023Large Language Modelscited by 780
  5. 2024ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolutioncited by 276
  6. 2024Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Modelcited by 268
  7. 2023Better Zero-Shot Reasoning with Role-Play Promptingcited by 223
  8. 2023Large Language Models as Evolutionary Optimizerscited by 124
  9. 2024The Prompt Report: A Systematic Survey of Prompt Engineering Techniquescited by 121
  10. 2024LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristicscited by 97
  11. 2023At Which Training Stage Does Code Data Help LLMs Reasoning?cited by 82
  12. 2024HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMscited by 73
9 more
  1. 2023Large Language Model-Aware In-Context Learning for Code Generationcited by 43
  2. 2024Source-Aware Training Enables Knowledge Attribution in Language Modelscited by 30
  3. 2024When Large Language Model Meets Optimizationcited by 22
  4. 2024Metaheuristics and Large Language Models Join Forces: Toward an Integrated Optimization Approachcited by 7
  5. 2024Explaining Genetic Programming Trees using Large Language Modelscited by 6
  6. 2024Large Language Models for the Automated Analysis of Optimization Algorithmscited by 5
  7. 2024Investigating the Role of Prompting and External Tools in Hallucination Rates of Large Language Modelscited by 4
  8. 2025Improving Existing Optimization Algorithms with LLMscited by 4
  9. 2019An Empirical Investigation of Correlation between Code Complexity and Bugscited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 3.

7 papers.

  1. 2025Large Language Models in Operations Research: Methods, Applications, and Challengescited by 6
  2. 2025Behavior and Representation in Open-Weight Large Language Models for Combinatorial Optimization: From Feature Extraction to Algorithm Selectioncited by 1
  3. 2025LLM-Based Instance-Driven Heuristic Bias In the Context of a Biased Random Key Genetic Algorithmcited by 0
  4. 2025Reasoning with Preference Constraints: A Benchmark for Language Models in Many-to-One Matching Marketscited by 0
  5. 2026Constraint-aware Path Planning from Natural Language Instructions Using Large Language Modelscited by 0
  6. 2026From Hand-Crafted to LLM-Based Variation Operators in Metaheuristics: A Tutorialcited by 0
  7. 2026LYNX: Analytical Program Synthesis via Grounding and Closed-Loop Refinementcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving
  2. 2024Exploring Combinatorial Problem Solving with Large Language Models: A Case Study on the Travelling Salesman Problem Using GPT-3.5 Turbo
  3. 2025LLMize: A Framework for Large Language Model-Based Numerical Optimization
  4. 2026DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization
  5. 2025Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning
  6. 2025Large Language Models as End-to-end Combinatorial Optimization Solvers
  7. 2026FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization
  8. 2025Fine-tuning Large Language Model for Automated Algorithm Design