HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimization Challenges (2506.15196v2)

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 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.

• The paper presents HeurAgenix, an LLM-powered framework that evolves and selects heuristics to tackle complex combinatorial optimization challenges.
• It employs a two-stage process combining heuristic evolution and adaptive selection, reinforced by a dual-reward mechanism for improved strategy development.
• Experimental results on TSP and CVRP demonstrate lower optimality gaps and enhanced efficiency, highlighting its potential for diverse industrial applications.

Leveraging LLMs for Combinatorial Optimization: The HeurAgenix Framework

Heuristic algorithms are indispensable tools in tackling combinatorial optimization (CO) dilemmas, famed for their efficacy in navigating high-dimensional search spaces where traditional methods exhibit computational limitations. However, the expertise-intensive nature of heuristic designs and their restricted adaptability remain noteworthy challenges. The paper presents HeurAgenix, an innovative two-stage hyper-heuristic framework powered by LLMs aiming to solve complex combinatorial optimization challenges.

Overview

HeurAgenix introduces a paradigm shift in heuristic development by harnessing LLMs to evolve and dynamically select heuristics. During heuristic evolution, the framework utilizes an LLM to derive improved strategies by comparing seed solutions against higher-quality ones. It intelligently extracts evolution strategies from these comparisons, aiming for adaptability across diverse problem instances. In problem-solving, HeurAgenix dynamically selects the most suitable heuristic based on current problem states, guided by either a state-of-the-art LLM or a lightweight model optimized for cost-effective inference. This selection process is bolstered by a fine-tuning strategy with a dual-reward mechanism, mitigating the scarcity of reliable supervision in complex CO environments.

Numerical Results and Claims

Extensive experiments demonstrate HeurAgenix's superiority over existing LLM-based hyper-heuristics, displaying performance that matches or exceeds specialized solvers. Notably for notable datasets and problems, like Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), HeurAgenix consistently achieves lower optimality gaps compared to traditional and other state-of-the-art methods. These results substantiate the framework's potential in automatically and effectively addressing CO problems without reliance on domain-specific solvers.

Implications

The practical implications of HeurAgenix are profound, promising advances in industries reliant on CO problem-solving, such as logistics, manufacturing, and financial optimization. By enabling autonomous heuristic evolution and dynamic selection, HeurAgenix reduces dependence on manual expertise, accelerating the adaptability of heuristics to emerging conditions. Theoretically, the framework enriches the discourse on hyper-heuristics by illustrating how LLMs can bolster traditional heuristic methods through evolution and real-time selection. Furthermore, it sets a precedent for leveraging dual-reward systems in training models to handle noisy data effectively, which is pivotal in decision-making processes plagued with imperfect supervision.

Future Directions

The versatility of HeurAgenix opens several avenues for future research. Exploring its applicability across a broader spectrum of CO problems could further cement its generality. Additionally, investigating methods to tailor the framework to work with varying computational resource constraints could expand its usability for different applications. Enhancements in dual-reward mechanisms may further optimize the learning process under noisy annotations, thus refining the heuristic selection model's robustness and efficiency.

In conclusion, HeurAgenix represents a significant step forward in the automated design and selection of heuristics for combinatorial optimization challenges. By harnessing LLMs, the framework not only elevates heuristic diversity and performance but also sets a foundational blueprint for future explorations into AI-driven optimization strategies.