HeurAgenix: A Multi-Agent LLM-Based Paradigm for Adaptive Heuristic Evolution and Selection in Combinatorial Optimization
Keywords: Combinatorial Optimization; Heuristic Evolution; Heuristic Selection; Large Language Models
Abstract: Combinatorial Optimization (CO) is a class of problems where the goal is to identify an optimal solution from a finite set of feasible solutions under specific constraints. Despite its ubiquity across industries, existing heuristic algorithms struggle with limited adaptability, complex parameter tuning, and limited generalization to novel problems. Recent approaches leveraging machine learning have made incremental improvements but remain constrained by extensive data requirements and reliance on historical problem-specific adjustments. Large Language Models (LLMs) offer a new paradigm to overcome these limitations due to their ability to generalize across domains, autonomously generate novel insights, and adapt dynamically to different problem contexts. To harness these capabilities, we introduce $\textbf{HeurAgenix}$, a novel multi-agent hyper-heuristic framework that leverages LLMs to generate, evolve, evaluate, and select heuristics for solving CO problems. Our framework comprises four key agents: heuristic generation, heuristic evolution, benchmark evaluation, and heuristic selection. Each agent is designed to exploit specific strengths of LLMs, such as their capacity for synthesizing knowledge from diverse sources, autonomous decision-making, and adaptability to new problem instances. Experiments on both classic and novel CO tasks show that HeurAgenix significantly outperforms state-of-the-art approaches by enabling scalable, adaptable, and data-efficient solutions to complex optimization challenges.
Primary Area: optimization
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Submission Number: 9803
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