HeurAgenix：運用大型語言模型解決複雜組合優化挑戰

摘要

啟發式演算法在解決組合優化（CO）問題中扮演著至關重要的角色，然而傳統設計高度依賴於人工專業知識，且難以在多樣化的實例中實現泛化。我們提出了HeurAgenix，這是一個由大型語言模型（LLMs）驅動的兩階段超啟發式框架，首先演化啟發式方法，然後自動從中進行選擇。在啟發式演化階段，HeurAgenix利用LLM比較初始啟發式解與更高質量的解，並提取可重用的演化策略。在問題求解過程中，它根據LLM的感知能力動態選擇每個問題狀態下最有前景的啟發式方法。為了靈活性，該選擇器可以是先進的LLM，也可以是經過微調的低推理成本的輕量級模型。為了緩解因CO複雜性導致的可靠監督稀缺問題，我們採用雙重獎勵機制對輕量級啟發式選擇器進行微調，該機制聯合利用選擇偏好和狀態感知的信號，從而在噪聲註釋下實現穩健的選擇。在經典基準上的大量實驗表明，HeurAgenix不僅超越了現有的基於LLM的超啟發式方法，還匹配或超越了專用求解器。代碼可在https://github.com/microsoft/HeurAgenix獲取。

English

Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce HeurAgenix, a two-stage hyper-heuristic framework powered by large language models (LLMs) that first evolves heuristics and then selects among them automatically. In the heuristic evolution phase, HeurAgenix leverages an LLM to compare seed heuristic solutions with higher-quality solutions and extract reusable evolution strategies. During problem solving, it dynamically picks the most promising heuristic for each problem state, guided by the LLM's perception ability. For flexibility, this selector can be either a state-of-the-art LLM or a fine-tuned lightweight model with lower inference cost. To mitigate the scarcity of reliable supervision caused by CO complexity, we fine-tune the lightweight heuristic selector with a dual-reward mechanism that jointly exploits singals from selection preferences and state perception, enabling robust selection under noisy annotations. Extensive experiments on canonical benchmarks show that HeurAgenix not only outperforms existing LLM-based hyper-heuristics but also matches or exceeds specialized solvers. Code is available at https://github.com/microsoft/HeurAgenix.

HeurAgenix：運用大型語言模型解決複雜組合優化挑戰

HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges

摘要

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