Mixed-integer linear programming (MILP) is a cornerstone of optimization with applications across numerous domains. However, the development and evaluation of MILP-solving algorithms are hindered by existing benchmark datasets, which are often limited in scale, lack diversity, and are poorly structured, making them inadequate for systematic testing across different solving approaches, especially for machine learning (ML)-based methods. To address these issues, we introduce MILPBench, a large-scale benchmark suite comprising 100,000 MILP instances organized into 60 well-categorized classes. Using structural properties and embedding similarity metrics, we developed a novel classification framework to ensure both intra-class homogeneity and inter-class diversity. In addition to the dataset, MILPBench includes a comprehensive baseline library featuring 15 mainstream solving methods, spanning traditional solvers, heuristic algorithms, and ML-based approaches. This design enables rigorous and standardized evaluation of MILP-solving algorithms under diverse conditions. Extensive benchmarking demonstrates the utility of MILPBench as a scalable and versatile testbed for advancing MILP research, fostering innovation in solver development, and bridging the gap between optimization and machine learning.

Large Neighborhood Search (LNS) is a widely used method for solving large-scale Mixed Integer Linear Programming (MILP) problems. The effectiveness of LNS crucially depends on the choice of the search neighborhood. However, existing strategies either rely on expert knowledge or computationally expensive Machine Learning (ML) approaches, both of which struggle to scale effectively for large problems. To address this, we propose LLM-LNS, a novel Large Language Model (LLM)-driven LNS framework for large-scale MILP problems. Our approach introduces a dual-layer self-evolutionary LLM agent to automate neighborhood selection, discovering effective strategies with scant small-scale training data that generalize well to large-scale MILPs. The inner layer evolves heuristic strategies to ensure convergence, while the outer layer evolves evolutionary prompt strategies to maintain diversity. Experimental results demonstrate that the proposed dual-layer agent outperforms state-of-the-art agents such as FunSearch and EOH. Furthermore, the full LLM-LNS framework surpasses manually designed LNS algorithms like ACP, ML-based LNS methods like CL-LNS, and large-scale solvers such as Gurobi and SCIP. It also achieves superior performance compared to advanced ML-based MILP optimization frameworks like GNN&GBDT and Light-MILPopt, further validating the effectiveness of our approach.