Algorithmic algorithm development with LLMs: A Case Study on LLM-Usage for Contraction Order Optimization in Tensor Networks

2026-06-01

AI Summary

Tensor network contraction order optimization constitutes a class of combinatorial optimization problems that are notoriously difficult to solve efficiently. This work proposes OpenEvolve, a verifier-guided evolutionary framework powered by large language models (LLMs), which leverages human–machine collaboration to automatically design and refine contraction algorithms. By integrating customized evaluation metrics, program verification mechanisms, and evolutionary strategies, the approach generates algorithms that outperform existing baselines on standard benchmark instances. To the best of our knowledge, this is the first application of LLM-driven evolutionary code generation to the discovery of sophisticated algorithms in scientific computing. The results not only demonstrate the potential of such methods in advancing computational science but also underscore the critical roles of robust evaluation frameworks and human expertise in algorithmic innovation.

Abstract

We consider LLM-based algorithm development through a case study on contractionorder optimisation for tensor networks with OpenEvolve. We pay particular attention to the choice of the LLM as well as design choices such as evaluation metric and test instances. Our results highlight both the promise of verifier-guided evolutionary coding agents for algorithm development/improvement and the continuing importance of evaluation, validation, and interpretation -- and corresponding challenges -- by the human scientist.

Problem

• LLM-based algorithm development
• contraction order optimization
• tensor networks
• algorithm evaluation
• human interpretation

Innovation

• LLM-based algorithm development
• contraction order optimization
• tensor networks
• verifier-guided evolutionary coding
• OpenEvolve