HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges

TL;DR

HeurAgenix introduces a two-stage hyper-heuristic framework utilizing large language models to automatically evolve and select heuristics, significantly improving performance on combinatorial optimization problems compared to existing methods.

Contribution

The paper presents a novel LLM-powered hyper-heuristic framework that automatically evolves and selects heuristics, enhancing generalization and efficiency in solving combinatorial optimization challenges.

Findings

Outperforms existing LLM-based hyper-heuristics

Matches or exceeds specialized solvers on benchmarks

Uses a dual-reward fine-tuning mechanism for robust heuristic selection

Abstract

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 \textbf{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.