Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization

• URL: http://arxiv.org/abs/2505.20881v1
• Date: Tue, 27 May 2025 08:26:27 GMT
• Title: Generalizable Heuristic Generation Through Large Language Models with Meta-Optimization
• Authors: Yiding Shi, Jianan Zhou, Wen Song, Jieyi Bi, Yaoxin Wu, Jie Zhang,
• Abstract summary: Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling optimization problems.<n>Existing approaches often rely on manually predefined evolutionary generalizations and single-task training schemes.<n>We propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the level of meta-learning.
• Score: 14.919482411153185
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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