LLMs Evolve and Select Heuristics for Complex Optimisation Problems.

HeurAgenix, a novel hyper-heuristic framework utilising large language models, evolves and selects heuristics to solve combinatorial optimisation problems. It employs a dual-reward mechanism for robust heuristic selection, even with limited data, and demonstrably matches or surpasses the performance of specialised solvers on standard benchmarks.

Combinatorial optimisation problems, ubiquitous in fields ranging from logistics and finance to machine learning, often defy exact solutions and necessitate the use of heuristic algorithms. These algorithms, while effective, traditionally rely on substantial human expertise to design and adapt to varying problem instances.

Researchers at Microsoft Research Asia, alongside colleagues at Tsinghua University, present a novel approach to automating this process. Xianliang Yang, Ling Zhang, Haolong Qian, Lei Song, and Jiang Bian detail their work in “HeurAgenix: Leveraging LLMs for Solving Complex Combinatorial Optimisation Challenges”, introducing a framework that utilises large language models (LLMs) to both evolve and select heuristics, thereby reducing the reliance on manual intervention and achieving performance comparable to, or exceeding, specialised solvers. The system employs a two-stage process, first learning from comparisons between initial and improved solutions, and then dynamically choosing the most appropriate heuristic based on the current problem state.

HeurAgenix introduces a novel methodology for hyper-heuristic design, employing Large Language Models (LLMs) for both the evolution of problem-solving strategies, known as heuristics, and their dynamic selection during operation. This approach aims to overcome limitations inherent in traditional optimisation algorithms, which often struggle with the complexities of real-world combinatorial problems. Combinatorial problems involve finding the best solution from a finite set of possibilities, and are prevalent in fields like logistics, finance, and scheduling.

The framework functions through a two-stage process. Initially, an LLM analyses both initial and improved solutions to extract reusable strategies for heuristic evolution. This allows the system to learn from its successes and failures, progressively refining its ability to generate effective heuristics. Subsequently, during problem-solving, the LLM dynamically selects the most promising heuristic based on the current problem state, adapting the algorithm to the specific characteristics of each instance. A dual-reward mechanism further enhances robustness, combining signals from both selection preferences and state perception, enabling informed decisions even with incomplete or noisy data. The system is implemented using Python and TensorFlow, leveraging the capabilities of LLMs to drive both heuristic evolution and selection, and its modular design facilitates integration with other optimisation algorithms.

Extensive experimental evaluation demonstrates the framework’s performance across several benchmark problems. On the Minimum Knapsack Problem (MKP), a classic optimisation problem involving selecting items with maximum value within a weight limit, HeurAgenix frequently outperforms Particle Swarm Optimisation (PSO), Gravitational Search Algorithm (GWO), Ant Colony Optimisation (ACO), CirCut, and Variable Neighbourhood Search (VNSPR). However, on the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and Maximum Cut (MaxCut) instances, ReEvo+ACO consistently achieves superior results, indicating a relative weakness of HeurAgenix in these specific problem domains. Results for the Job Shop Scheduling Problem (JSSP) average between 2.54 ± 1.2 and 10.97 ± 2.9, and for the Traveling Salesperson Problem (TSP) range from 0.15 to 1.23 ± 0.8, establishing a baseline for future comparative studies.

The framework offers flexibility by allowing the use of either a state-of-the-art LLM or a fine-tuned, lightweight model for the selector, balancing performance with computational cost. Researchers conducted a comprehensive analysis of the framework’s performance, identifying areas for improvement and potential extensions, revealing that the performance of HeurAgenix on CVRPTW and MaxCut instances could be further enhanced by incorporating domain-specific knowledge and heuristics. Future work will focus on exploring the integration of such knowledge, as well as investigating more advanced LLM architectures and training techniques, to develop even more powerful and adaptable optimisation algorithms. Furthermore, researchers plan to extend the framework to address a wider range of combinatorial optimisation problems, including those arising in supply chain management, financial modelling, and machine learning.

The observed strengths in MKP suggest potential advantages in handling problems involving item selection and capacity constraints, with applications in resource allocation, portfolio optimisation, and logistics. The development of HeurAgenix represents a significant step towards creating truly intelligent optimisation algorithms, capable of learning and adapting to the complexities of real-world problems, demonstrating the potential of LLMs to drive advancements in the field of combinatorial optimisation. By automating the process of heuristic design and selection, HeurAgenix empowers researchers and practitioners to tackle challenging optimisation problems more effectively and efficiently, providing a solid foundation for future work in the area of intelligent optimisation.