From Understanding to Excelling: Template-Free Algorithm Design through Structural-Functional Co-Evolution

2025-03-13

AI Summary

Existing automated algorithm generation methods (e.g., EoH, FunSearch) rely on predefined templates and local function optimization, limiting their capacity for architecture-level co-evolution. Method: We propose a structure–function dual-dimensional co-evolution paradigm: (i) leveraging large language models for end-to-end semantic understanding and code generation from natural language specifications; (ii) introducing a coupled structure–function evaluation metric enabling multi-level module joint optimization and emergent algorithmic innovation; and (iii) employing closed-loop feedback to guide global search. Contribution/Results: Our approach eliminates dependence on handcrafted templates, significantly enhancing algorithmic design autonomy and architectural breakthrough capability. On multiple classical benchmarks, it outperforms baselines—including FunSearch and EoH—in both performance and novelty, successfully generating novel, high-efficiency algorithms that surpass human-designed counterparts. Moreover, it demonstrates strong adaptability to unseen environments.

Technology Category

• Search and Optimization: Evolutionary Computation
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Evolutionary Learning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Large language models (LLMs) have greatly accelerated the automation of algorithm generation and optimization. However, current methods such as EoH and FunSearch mainly rely on predefined templates and expert-specified functions that focus solely on the local evolution of key functionalities. Consequently, they fail to fully leverage the synergistic benefits of the overall architecture and the potential of global optimization. In this paper, we introduce an end-to-end algorithm generation and optimization framework based on LLMs. Our approach utilizes the deep semantic understanding of LLMs to convert natural language requirements or human-authored papers into code solutions, and employs a two-dimensional co-evolution strategy to optimize both functional and structural aspects. This closed-loop process spans problem analysis, code generation, and global optimization, automatically identifying key algorithm modules for multi-level joint optimization and continually enhancing performance and design innovation. Extensive experiments demonstrate that our method outperforms traditional local optimization approaches in both performance and innovation, while also exhibiting strong adaptability to unknown environments and breakthrough potential in structural design. By building on human research, our framework generates and optimizes novel algorithms that surpass those designed by human experts, broadening the applicability of LLMs for algorithm design and providing a novel solution pathway for automated algorithm development.

Problem

• Automating algorithm generation without predefined templates
• Optimizing both functional and structural aspects globally
• Enhancing performance and innovation in algorithm design

Innovation

• LLMs convert natural language to code
• Two-dimensional co-evolution optimizes structure and function
• Closed-loop process enhances algorithm performance and innovation