LP Mining with LP2Graph: A Use Case for Railway Rescheduling

Railway rescheduling relies heavily on Mixed-Integer Linear Programming (MILP), yet the field's modeling knowledge is fragmented across hundreds of papers. These papers often use incompatible notations, and existing literature surveys are subjective, classifying models by domain vocabulary rather than by their underlying mathematical structure. This makes it difficult for practitioners to identify structurally similar models across different domains, such as job-shop scheduling or vehicle routing, which share fundamental mathematical properties with railway rescheduling.

The authors present LP2Graph, a method designed to transform published LP and MILP formulations into a canonical, typed variable-equation graph. By representing models as graphs, the method allows for structural analysis and feature extraction that are independent of the specific vocabulary or notation used in the original source. The pipeline follows a deterministic process: once a formulation is extracted into the canonical model, downstream tasks—including structural metric calculation, clustering, and taxonomy induction—are fully automated.

The mining pipeline operates through a multi-level, bottom-up clustering approach. It first clusters variables, then constraints and objectives, and finally whole-model structures. To ensure the representation is faithful to the original research, the authors perform a rigorous validation: they regenerate independent LaTeX formulations from the graphs and re-solve them using multiple solvers (CBC, HiGHS, and Gurobi). By comparing these results against the optima reported in the original papers, they confirm that the graph representation preserves the essential logic of the models.

This work provides a principled, reproducible foundation for automated model development. By moving away from subjective, vocabulary-based surveys toward an objective, structure-based taxonomy, the authors enable researchers to treat optimization models as a searchable, comparable dataset. This framework facilitates the systematic reuse of modeling knowledge across different domains, potentially accelerating the development of new optimization models in complex fields like railway operations.