G-LNS：基於大型語言模型的生成式大鄰域搜尋自動啟發式設計

摘要

儘管大型語言模型（LLM）近期在自動啟發式設計（AHD）領域展現潛力，現有方法通常將AHD框架侷限於構造型優先規則或參數化局部搜索指導，從而將搜索空間限制在固定啟發式形式內。此類設計對結構性探索的能力有限，難以在複雜組合優化問題（COP）中逃離深度局部最優解。本研究提出G-LNS——一個生成式演化框架，將基於LLM的AHD擴展至大型鄰域搜索（LNS）算子的自動化設計。有別於以往孤立演化啟發式的方法，G-LNS利用LLM協同演化緊密耦合的破壞算子與修復算子對。通過合作式評估機制顯式捕捉算子間的互動，從而發現能共同實現有效結構破壞與重構的互補邏輯。在旅行商問題（TSP）和容量限制車輛路徑問題（CVRP）等具挑戰性的COP基準測試中，大量實驗表明G-LNS顯著優於基於LLM的AHD方法及強力經典求解器。所發現的啟發式不僅能以更少計算資源獲得接近最優的解，更在多元且未見過的實例分佈中展現出強健的泛化能力。

English

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

G-LNS：基於大型語言模型的生成式大鄰域搜尋自動啟發式設計

G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design

摘要

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