Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization

2025-05-27

AI Summary

Existing LLM-driven heuristic design relies on predefined evolutionary operators and single-task training, limiting algorithmic diversity and generalization across problem scales. Method: We propose Meta-Optimization of Heuristics (MoH), the first framework to integrate meta-learning into the optimizer-design layer for heuristic generation—enabling LLMs to autonomously discover, construct, and iteratively refine diverse optimizers at the meta-optimization level. MoH introduces a self-referential mechanism for interpretable, self-generated optimizers and employs multi-task reinforcement learning to enhance cross-scale generalization. The method synergistically combines LLMs, meta-learning, self-reference, multi-task RL, and evolutionary search. Contribution/Results: MoH achieves state-of-the-art performance on classical combinatorial optimization benchmarks, significantly outperforming baselines in zero-shot transfer across problem scales. Generated optimizers exhibit both high interpretability and strong cross-scale transferability.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.

Problem

• Overcoming reliance on predefined evolutionary computation optimizers
• Enhancing heuristic generalization in combinatorial optimization problems
• Eliminating single-task training limitations for diverse heuristic exploration

Innovation

• LLMs generate heuristic algorithms autonomously
• Meta-learning refines optimizers without predefined EC
• Multi-task training enhances generalization capability