LP Mining with LP2Graph: A Use Case for Railway Rescheduling

2026-07-13

AI Summary

This work addresses the lack of a unified, structured representation and reproducible taxonomy for existing mixed-integer linear programming (MILP) models in railway rescheduling. It proposes LP2Graph, a novel framework that transforms linear programming models into standardized variable-equation graph structures through formal grammar parsing. By integrating graph representation learning, bottom-up hierarchical clustering, and a rule-guided classifier, LP2Graph establishes the first automatic classification system based on model structure rather than terminology. The approach validates solution consistency across multiple solvers (CBC, HiGHS, Gurobi) for representative models within each cluster, achieving the first objective, structure-driven categorization and mining of LP/MILP models. Furthermore, the study releases a reproducible dataset of LP models to support future research in automated modeling.

Abstract

Like many optimization-driven domains, railway rescheduling relies on Mixed-Integer Linear Programming (MILP), yet the field's modeling knowledge is scattered across hundreds of papers in incompatible notations, and narrative surveys organize it subjectively: they classify models by vocabulary rather than by structure, and reproduce neither. We present LP Mining with LP2Graph, a method that mines the structure of published LP and MILP formulations into a reproducible dataset and an induced taxonomy. Its core, LP2Graph, represents each formulation admitted by its canonical grammar as a typed variable--equation graph derived from a single canonical model; once a source is extracted into that model, everything downstream is deterministic. Each source is parsed into this model, homologized, and clustered bottom-up (over variables, then constraints and the objective, then whole-model structure) and, separately, by application domain and solution approach; the resulting groups are labeled by a rule-seeded, self-updating classifier. We validate the representation rather than assume it: per-cluster representatives are regenerated as independent LaTeX and re-solved across CBC, HiGHS and Gurobi against the optimum reported in the source paper. The outcome is an objective, repeatable taxonomy of variables, constraints and model types: the principled foundation on which our raiLPminer line of automated railway-rescheduling model development builds.

Problem

• railway rescheduling
• Mixed-Integer Linear Programming
• model taxonomy
• reproducibility
• LP formulation

Innovation

• LP2Graph
• MILP mining
• structured taxonomy
• canonical modeling
• railway rescheduling