RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search

2026-06-30

AI Summary

This work addresses the significant performance degradation of existing large language model (LLM)-based automated heuristic design methods under real-world distribution shifts, despite their strong in-distribution performance. The authors propose a novel bilevel optimization framework that formulates robust heuristic design as a constrained adversarial instance search problem: the outer loop evolves heuristic strategies using an LLM, while the inner loop efficiently generates worst-case instances within a neighborhood of the training distribution. Feasibility is ensured through base-distribution parameterization and boundary projection techniques. This approach is the first to integrate constrained adversarial search into LLM-driven heuristic evolution, substantially enhancing generalization robustness. Evaluated on online bin packing, job shop scheduling, and vehicle routing problems under five types of distribution shifts, the method consistently outperforms existing approaches, reducing performance degradation by up to 19-fold.

Abstract

Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods optimize heuristics for a fixed training instance set and may fail catastrophically when deployed under real-world distributional shifts. We propose Robust Adversary Instance Search (RAISE), a framework that integrates constrained worst-case instance search within a principled neighborhood of the training distribution into the LLM-based evolutionary search loop. RAISE treats robust AHD as a constrained adversarial instance search problem: the outer loop evolves heuristics via LLM operators, while an LLM-free inner loop efficiently identifies hard instances within an epsilon-ball around the training instance set using a basis distribution parameterization with boundary projection. Comprehensive experiments on Online Bin Packing (OBP), Online Job Shop Scheduling (OJSP), and Online Vehicle Routing (OVRP) across five distribution families demonstrate that existing LLM-based AHD methods degrade by up to 19 times under distribution shift, while RAISE consistently maintains strong performance across all tested distributions and problem scales

Problem

• Automated Heuristic Design
• Distribution Shift
• Robustness
• Adversarial Instance Search
• Large Language Models

Innovation

• Robust Heuristic Design
• Adversarial Instance Search
• Large Language Models
• Distributional Robustness
• Automated Algorithm Design