Mixed-integer linear programming (MILP) is one of the most popular mathematical formulations with numerous applications. In practice, improving the performance of MILP solvers often requires a large amount of high-quality data, which can be challenging to collect. Researchers thus turn to generation techniques to generate additional MILP instances. However, existing approaches do not take into account specific block structures -- which are closely related to the problem formulations -- in the constraint coefficient matrices (CCMs) of MILPs. Consequently, they are prone to generate computationally trivial or infeasible instances due to the disruptions of block structures and thus problem formulations. To address this challenge, we propose a novel MILP generation framework, called Block Structure Decomposition (MILP-StuDio), to generate high-quality instances by preserving the block structures. Specifically, MILP-StuDio begins by identifying the blocks in CCMs and decomposing the instances into block units, which serve as the building blocks of MILP instances. We then design three operators to construct new instances by removing, substituting, and appending block units in the original instances, enabling us to generate instances with flexible sizes. An appealing feature of MILP-StuDio is its strong ability to preserve the feasibility and computational hardness of the generated instances. Experiments on the commonly-used benchmarks demonstrate that using instances generated by MILP-StuDio is able to significantly reduce over 10% of the solving time for learning-based solvers.

翻译：混合整数线性规划（MILP）是最流行的数学规划形式之一，具有广泛的应用。在实际应用中，提升MILP求解器的性能通常需要大量高质量数据，而这些数据的收集往往具有挑战性。因此，研究者转向生成技术以产生额外的MILP实例。然而，现有方法未充分考虑MILP约束系数矩阵中与问题形式密切相关的特定块结构。这导致它们容易因破坏块结构（进而破坏问题形式）而生成计算上平凡或不可行的实例。为应对这一挑战，我们提出了一种新颖的MILP生成框架——块结构分解法（MILP-StuDio），通过保持块结构来生成高质量实例。具体而言，MILP-StuDio首先识别约束系数矩阵中的块结构，并将实例分解为块单元，这些块单元构成MILP实例的基础构件。随后，我们设计了三种操作符，通过移除、替换和追加原始实例中的块单元来构建新实例，从而能够生成规模灵活的实例。MILP-StuDio的一个突出特点是其能有效保持生成实例的可行性与计算难度。在常用基准测试上的实验表明，使用MILP-StuDio生成的实例能为基于学习的求解器显著减少超过10%的求解时间。