{"id":"5345237e-1ab3-48bc-b19b-9185a0354a9c","arxiv_id":"2512.19340","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Classical ILP solves daily Silesian EMU circulation for 404 trips, while the direct QUBO reformulation becomes impractical beyond roughly 78 trips.","lead":"This paper builds a daily train-assignment model for Silesian Railways that adds bicycle-capacity limits to the usual seating and depot constraints, and solves it with a classical ILP solver. It then rewrites the model as a QUBO and shows quantum annealers and quantum-inspired solvers can currently handle only much smaller pieces.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (3a) swaps k and k' coefficients, so the printed ILP/QUBO does not conserve EMU flow at coupling/decoupling nodes; without code, Table 3's plans may be infeasible.","rationale":"The reader identified unreliable demand inputs as the weakest assumption. That is a reproducibility concern, but a more fundamental issue appears in the central mathematical formulation: Eq. (3a), as printed, does not balance EMU flow at nodes involving hyperarcs. The definitions of k and k' are unambiguous, and the toy's own Eq. (35) contradicts the general equation unless a typo is assumed. If the printed equation is what was implemented, the ILP solutions are not guaranteed to conserve rolling stock, which directly undermines the 'high-quality daily circulation plans' claim. If it is a typo, the paper still needs correction and code/data release to verify that the reported experiments used the correct equation. The reader's verdict of CONDITIONAL remains appropriate, but the condition must now explicitly include resolving this equation-level inconsistency, not just data availability. I therefore keep the verdict unchanged while disagreeing with the reader's identification of the most load-bearing weakness.","tokens_in":22375,"tokens_out":14425,"duration_ms":142242,"concrete_test":"Re-run instance 2a (which has 30 coupling-allowed trips) with the ILP encoded exactly as Eqs. (2)-(9) are printed, and compare against a run with corrected balance: sum_in k(h)x_h = sum_out k'(h)x_h. If the printed version produces a solution that violates per-node EMU conservation (or differs in objective/runtime from the corrected version), the reported Table 3 results depend on an unstated correction. Additionally, substitute the toy optimum x0=x2=x10=1 into the printed Eq. (3a) with k(x10)=2; the equation fails, confirming the inconsistency.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The flow-balance constraint (3a) is printed with the coefficients reversed. With k(h) defined as the EMU count that h points to and k'(h) as the EMU count h originates from, conservation at node v requires sum_{h in H(v)_in} k(h) x_h = sum_{h in H(v)_out} k'(h) x_h. The paper instead states sum_in k'(h) x_h = sum_out k(h) x_h. For simple arcs k=k'=1, so the error is invisible; it first appears on any coupling/decoupling hyperarc. Example: the toy hyperarc x10 points to v3 with two EMUs, so k(x10)=2, yet the authors' Eq. (35) for v1 uses x10 with coefficient 1 on the outgoing side. Thus the manuscript is internally inconsistent: either Eq. (3a) is a typo and the solved ILP uses the correct coefficients, or the printed model does not conserve EMU counts at every node. Because no code or data file is released, a reader cannot tell which form was actually solved. If the printed equation was implemented, the ILP results in Table 3 can assign two EMUs to a coupled trip while accounting for only one unit at the destination, so the claimed 'high-quality circulation plans' may violate physical flow conservation. The same swapped coefficients appear in the QUBO penalty P2 (Eq. 18), so the quantum and VeloxQ results inherit the issue.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies daily rolling-stock circulation planning for electric multiple units (EMUs) on the Silesian Railways network, with the distinctive features of predefined EMU coupling/decoupling, passenger seat capacity, bicycle capacity, and crew availability constraints. The authors formulate an acyclic ILP over a graph/hypergraph representation, solve it with SCIP on real timetable-based instances up to 404 trips and 11 EMU types, and compare against a QUBO reformulation solved by D-Wave quantum annealing and the quantum-inspired VeloxQ solver. The central claim is that the classical ILP approach produces high-quality daily plans in at most about 40 minutes on the largest instances, while direct QUBO approaches are limited to much smaller sub-instances because of quadratic term explosion and embedding constraints. The paper also outlines a hybrid classical-quantum architecture based on these observations.","tokens_in":22727,"tokens_out":12064,"duration_ms":106918,"significance":"If the central claim holds, the paper provides a useful, honest empirical characterization of the current frontier of QUBO-based methods for a realistic rolling-stock problem. The ILP model itself is clearly structured, the toy example is worked out in enough detail to be checked, and the scaling analysis of QUBO term growth is valuable for practitioners considering hybrid quantum-classical approaches. The inclusion of bicycle capacity as a demand-driven constraint is a novel operational detail. However, the paper's core claims currently overreach in a few specific places: a runtime claim contradicted by its own table, an internal inconsistency in the printed flow-conservation equation, and a lack of optimality gaps for the 'high-quality' assertion. These issues are fixable but require substantive revision.","major_comments":[{"comment":"The printed flow-conservation constraint is internally inconsistent with the parameter definitions. §2.1 defines k(h) as the number of EMUs that h points to and k'(h) as the number from which h originates. Conservation at a node then requires Σ_in k(h)x_h = Σ_out k'(h)x_h, not the reverse as printed in Eq. (3a). The toy equations (35) actually use the corrected form: x10 (a coupling hyperarc with k(x10)=2) enters the v1 and v2 outflow equations with coefficient 1, i.e., with k'(x10), not k(x10). The same swapped form is repeated in the QUBO penalty P2, Eq. (18). As written, the model does not enforce EMU conservation at coupling/decoupling nodes; a reader implementing Eqs. (3a)/(18) could obtain plans that create or destroy EMUs. Please correct the notation and state explicitly how k and k' are counted on each side for all three hyperarc types.","section":"2.1, Eq. (3a), Eq. (18), Eq. (35)"},{"comment":"The central claim that ILP yields plans 'within at most about 40 minutes' is contradicted by Table 3. For instance 8a with α=0.0, the reported computation time is 4852.04s ≈ 80.9 minutes. Even ignoring the α=0.0 case, the largest reported time is 698.92s, so the claim holds only for α>0. Please qualify the claim by objective weight or report all settings, and ensure the abstract matches the data.","section":"Abstract and Table 3"},{"comment":"The 'high-quality' characterization of the ILP solutions is not quantified. Table 3 reports objective values and computation times but no optimality gaps, dual bounds, or proof of optimality. For the largest instances (7/7a/8/8a) SCIP may stop with a heuristic solution; without a gap, the reader cannot assess the quality loss. Please report final MIP gaps or otherwise substantiate 'high-quality'.","section":"Section 3.2, Table 3"},{"comment":"Passenger and bicycle demand inputs are load-bearing for the practical capacity constraints, but Section 3.2 only says the timetable was supplied by Koleje Śląskie. It does not describe how per-trip passenger/bicycle demand or the acceptable shortage thresholds δp_h/δb_h were obtained, and no data file is provided. Without this, the case-study claims of feasible, high-quality plans are not auditable. Please provide the data (or a representative sample) and the estimation procedure, or clearly state the demand values as assumptions.","section":"Section 3.2, Eqs. (6)-(7)"}],"minor_comments":[{"comment":"The text says 'As in practical instances |T| is order of 10', but the instances in Table 2 have |T| up to 404. This should be 'order of 10^2' or similar.","section":"2.2, near Eq. (24)"},{"comment":"The statement that 'heuristic limitations of the Δ parameter reduce the computational time at a relatively small cost in the objective value' is not consistently supported: for α=0.01, instance 7 (Δ=300) is slower (378.37s) than instance 8 (Δ=960, 250.28s), while for α=0.0001 and α=0.0 the reverse holds. Please rephrase the caption to reflect the mixed behavior.","section":"Table 3 caption"},{"comment":"The term '#crew·{t1,t2,t3,t4,...}' should be '#crew × (number of time instants)'.","section":"Eq. (23)"},{"comment":"The caption says 'we report the computation time (...) together with the required number of runs to reach the optimal solution', but the figure only plots computation time; the number of runs is not shown. Please clarify what is displayed.","section":"Fig. 7 caption"},{"comment":"The paragraph on VeloxQ contains a stray '4095' before 'A key requirement from practice...' that appears to be an editing artifact. Please remove it.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"To the editor: the manuscript is primarily an operations-research case study with a quantum benchmark; the quantum contribution is a direct QUBO reformulation and hardware comparison rather than a new quantum algorithm. The authors' benchmarking of VeloxQ relies heavily on references from their own group (Refs. 23-27); an independent QUBO heuristic (e.g., simulated annealing or a general-purpose classical QUBO solver) would strengthen the comparison. The flow-conservation inconsistency in Eq. (3a) and the runtime overstatement in the abstract are fixable, but they currently undermine the precision of the paper's central claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one if you want a concrete, honest data point on where QUBO-based quantum optimization actually fails on a real rolling-stock problem. The central claim holds up: a standard ILP handles the Silesian instances up to 404 trips and 11 EMU types in about 40 minutes, while the direct QUBO reformulation becomes impractical from instance 3 onward (78 trips) because the number of QUBO terms explodes (~1.5×10^8 by instance 7). The paper's honest reporting—D-Wave can only embed the smallest instances, VeloxQ finds optima only where the QUBO is tractable—is more useful to the community than another benchmark with optimistic extrapolation.\n\nThe genuinely new bits are the bicycle-capacity constraint and the daily depot-balance treatment at terminal stations. The ILP itself is a fairly standard network-flow/hypergraph model, close to Fioole et al. and Borndörfer et al. The QUBO term-count scaling analysis is clean and is the real contribution for quantum-oriented readers.\n\nThe soft spots are fixable but real. The printed flow-balance constraint (Eq. 3a) and the QUBO penalty P2 (Eq. 18) have k and k' swapped. The toy model in Section 3.1 uses the opposite, correct coefficients (coefficient 1 for the coupling hyper-arc on the outgoing side), so the paper is internally inconsistent. That is almost certainly a typo, not a flaw in the method, but without code or data a reader cannot verify which form was actually solved, and the paper's own solution of the toy model would be infeasible under the printed equations. This needs an edit. Second, Table 3 reports runtimes and objective values but no optimality gaps, so 'high-quality' is asserted rather than quantified; SCIP either proved optimality or closed most of the gap, and the authors should say so. Third, the demand inputs and shortage thresholds δp_h/δb_h come from the operator, but the paper doesn't describe how they were set and no data file is provided. Those inputs determine feasibility, so this matters.\n\nNone of this kills the central claim. The ILP scalability result is plausible, and the quantum limitation story is consistent with the term counts. I would send this to peer review and require the typo fix, gap reporting, and a data/code release (or at least a detailed description of the demand generation) before acceptance. The useful readership is applied OR researchers working on rolling stock with real operator constraints, plus the QUBO/quantum-annealing benchmarking crowd. It deserves referee time.","headline":"Credible, honest applied study showing classical ILP wins on real Silesian instances; a swapped-coefficient typo in Eqs. (3a)/(18) and missing optimality gaps need fixing before publication.","tokens_in":23265,"tokens_out":6678,"would_cite":true,"duration_ms":55618,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C10","90B35","90B06"],"pacs":["03.67.Lx"],"model":"deepseek-v4-flash","headline":"A classical integer-programming model solves daily EMU circulation for 404-trip, 11-type regional instances in under 40 minutes; quantum and quantum-inspired QUBO solvers stall on far smaller sub-instances.","keywords":["rolling stock circulation","electric multiple units","integer linear programming","QUBO","quantum annealing","bicycle capacity","hypergraph flow","railway scheduling"],"falsifier":"Compare the ILP-generated circulation plan against measured passenger counts for the same day: if any trip in the executed plan has a seat shortage greater than the allowed threshold (or bicycle shortage greater than its threshold) despite the constraint being satisfied in the model, the demand-driven capacity claim is empirically falsified.","tokens_in":22271,"feed_emoji":"🚆","tokens_out":8550,"duration_ms":79499,"temperature":0.7,"pith_summary":"This paper aims to establish that a practical daily rolling-stock circulation plan for a regional railway operator can be produced by a classical integer linear program on real-world instances of hundreds of train trips, and that current quantum-annealing and quantum-inspired QUBO solvers are not yet competitive, being limited to tens of trips. The model adds a bicycle-capacity constraint requested by the operator and allows pairs of identical electric multiple units to couple on preselected trips. The authors show that the QUBO reformulation explodes in the number of quadratic terms (scaling as the fifth power of trip count), which is the main bottleneck, not the number of binary variables. If true, this quantifies the current frontier of QUBO-based methods for rolling stock and supports a hybrid architecture where quantum solvers address only local subproblems.","feed_headline":"Classical solver plans 404 railway trips in under 40 minutes","feed_subtitle":"Quantum and quantum-inspired QUBO solvers stall on tens of trips; the quadratic term blow-up sets the frontier.","key_machinery":"The load-bearing object is the hypergraph-flow model of trips as nodes and EMU transfers as arcs, with hyper-arcs encoding the coupling of two identical EMUs into a pair (and their decoupling). Each hyper-arc carries cost and capacity attributes, and the ILP enforces trip coverage, flow continuity, depot balance, seat/bicycle capacity, and driver availability. The QUBO version converts all constraints into penalty terms with slack variables, and the paper derives worst-case scaling bounds showing QUBO term counts scale as the fifth power of trip count times the square of EMU-type count, versus a lower-order polynomial for the ILP, which explains the practical gap.","core_discovery":"The central discovery is the empirical and analytical frontier: the integer linear programming (ILP) formulation, built on a hypergraph-flow representation of single and coupled EMU movements, solves real regional-railway instances with up to 404 train trips and 11 EMU types in at most about 40 minutes with a state-of-the-art open-source solver, while the QUBO reformulation of the same problem — solved by quantum annealing and by a physics-inspired classical QUBO solver — remains tractable only for instances up to roughly 50 trips. The analytical reason is that the QUBO's number of terms grows as the fifth power of the number of trips (and cubically in the number of EMU types), in contrast t","pith_inferences":["If demand data were replaced by measured per-trip passenger counts, the same ILP would likely produce plans that are feasible by the model but could reveal that the acceptable shortage thresholds are the real policy lever; setting them too high silently degrades service quality.","The paper's scaling analysis suggests a concrete research direction: design QUBO formulations with one-hot or domain-wall encodings that reduce quadratic term growth, which could shift the frontier for quantum solvers.","The observation that a physics-inspired classical QUBO solver finds optima on all tractable sub-instances in fractions of a second hints that, for sufficiently sparse subproblems, such solvers may already be practical workhorses.","The two-mode workflow (fast restricted-time-window solve, then larger-window refinement) could be generalized into an online rescheduling tool: solve a local neighborhood after a disruption with a small QUBO, and re-optimize globally with the ILP when time permits."],"forward_implications":["Route planners for regional operators can use the ILP model as a fast decision-support tool for daily circulation, including rescheduling during disruptions, with runtimes of minutes rather than hours.","The bicycle-capacity constraint shows that demand-driven capacity requirements can be incorporated without sacrificing tractability.","Because QUBO term explosion rather than variable count is the bottleneck, sparsifying the problem graph via tighter transfer-time windows is the key lever for making QUBO approaches work on larger instances.","Current quantum annealers and quantum-inspired solvers should be positioned as local subproblem optimizers within a hybrid classical-quantum planning architecture, not as end-to-end solvers for regional networks.","Multi-day circulation planning can be built on top of these daily plans via column-generation-style overnight transfer variables."],"fun_headline_variants":["Classical ILP handles 404 railway trips; quantum QUBO caps at ~50","ILP beats quantum: 404 trips in 40 min vs 50-trip QUBO limit","QUBO fifth-power blow-up limits quantum to 50 trips; ILP does 404","Railway planning: ILP solves 404 trips in 40 min, QUBO only ~50"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The passenger and bicycle demand figures (and the allowed shortage thresholds) are taken as given reliable inputs, but the paper never explains how they were set or provides the underlying data; if those numbers are wrong, a plan that satisfies the model can still put passengers on trains without enough seats or bike space.","fun_headline_variants_meta":{"raw":{"variants":["Classical ILP handles 404 railway trips; quantum QUBO caps at ~50","ILP beats quantum: 404 trips in 40 min vs 50-trip QUBO limit","QUBO fifth-power blow-up limits quantum to 50 trips; ILP does 404","Railway planning: ILP solves 404 trips in 40 min, QUBO only ~50"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000903,"raw_usage":{"total_tokens":3738,"prompt_tokens":777,"completion_tokens":2961,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":521,"completion_tokens_details":{"reasoning_tokens":2859}},"tokens_in":521,"tokens_out":2961,"duration_ms":18945,"temperature":1.0,"reasoning_tokens":2859,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T14:43:18.564740+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the ILP-generated circulation plan against measured passenger counts for the same day: if any trip in the executed plan has a seat shortage greater than the allowed threshold (or bicycle shortage greater than its threshold) despite the constraint being satisfied in the model, the demand-driven capacity claim is empirically falsified.","supporting_citations":[],"review_version":1}