Reducing Complexity for Quantum Approaches in Train Load Optimization

Railcar shunting is a core planning task in freight railyards, where yard planners need to disassemble and reassemble groups of railcars to form outbound trains. Classification tracks with access from one side only can be considered as stack structures, where railcars are added and removed from only one end, leading to a last-in-first-out (LIFO) retrieval order. In contrast, two-sided tracks function like queue structures, allowing railcars to be added from one end and removed from the opposite end, following a first-in-first-out (FIFO) order. We consider a problem requiring assembly of multiple outbound trains using two locomotives in a railyard with two-sided classification track access. To address this combinatorially challenging problem class, we decompose the problem into two subproblems, each with one-sided classification track access and a locomotive on each side. We present a novel Hybrid Heuristic-Reinforcement Learning (HHRL) framework that integrates railway-specific heuristic solution approaches with a reinforcement learning method, specifically Q-learning. The proposed framework leverages methods to decrease the state-action space and guide exploration during reinforcement learning. The results of a series of numerical experiments demonstrate the efficiency and quality of the HHRL algorithm in both one-sided access, single-locomotive problems and two-sided access, two-locomotive problems.

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.

Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations. While recent works have leveraged LLMs to automate optimization modeling, current frameworks predominantly rely on a rigid mixed-integer linear programming (MILP) paradigm. In this paper, we argue that not all problems are best modeled as MILP, as forcing complex domains into linear constraints can induce prohibitive modeling complexity and severely restrict solver flexibility. To address this, we propose OptiDSL, a framework that shifts the focus from rigid MILP formulations to domain-specific language (DSL) representations. By utilizing LLMs to map natural language onto standardized, domain-accepted structures, OptiDSL decouples problem formulation from execution. This paradigm enables seamless integration with a diverse library of specialized solvers, ranging from traditional heuristics to modern learning-based methods. Experimental results on the comprehensive benchmark of 44 COP types show that OptiDSL significantly surpasses MILP-based pipelines, yielding a 51.66% gain in formulation accuracy and a 91.71% decrease in modeling time. Notably, it also outperforms MILP-based pipelines on the existing benchmark, achieving a 23.09% higher formulation accuracy. Our code is available at https://anonymous.4open.science/r/OptiDSL.