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

TL;DR

G-LNS introduces a generative evolutionary framework that uses large language models to co-evolve destroy and repair heuristics, significantly improving solution quality and generalization in complex combinatorial optimization problems.

Contribution

It extends LLM-based automated heuristic design to the joint evolution of destroy and repair operators, enabling more effective structural exploration in large neighborhood search.

Findings

Outperforms existing LLM-based AHD methods and classical solvers.

Achieves near-optimal solutions with less computation.

Generalizes well across diverse problem instances.

Abstract

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.