The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve problems with large-scale instance sizes, which significantly diminishes their usefulness for real-world applications. In this work, we propose a novel Light Encoder and Heavy Decoder (LEHD) model with a strong generalization ability to address this critical issue. The LEHD model can learn to dynamically capture the relationships between all available nodes of varying sizes, which is beneficial for model generalization to problems of various scales. Moreover, we develop a data-efficient training scheme and a flexible solution construction mechanism for the proposed LEHD model. By training on small-scale problem instances, the LEHD model can generate nearly optimal solutions for the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 1000 nodes, and also generalizes well to solve real-world TSPLib and CVRPLib problems. These results confirm our proposed LEHD model can significantly improve the state-of-the-art performance for constructive NCO.

It is often very tedious for human experts to design efficient algorithms. Recently, we have proposed a novel Algorithm Evolution using Large Language Model (AEL) framework for automatic algorithm design. AEL combines the power of a large language model and the paradigm of evolutionary computation to design, combine, and modify algorithms automatically. In this paper, we use AEL to design the guide algorithm for guided local search (GLS) to solve the well-known traveling salesman problem (TSP). AEL automatically evolves elite GLS algorithms in two days, with minimal human effort and no model training. Experimental results on 1,000 TSP20-TSP100 instances and TSPLib instances show that AEL-designed GLS outperforms state-of-the-art human-designed GLS with the same iteration budget. It achieves a 0% gap on TSP20 and TSP50 and a 0.032% gap on TSP100 in 1,000 iterations. Our findings mark the emergence of a new era in automatic algorithm design.