{"id":"f732ded2-8cff-4a9c-8778-46633e932fd0","arxiv_id":"2506.04968","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"An ILP-based detour planner that guides partially occupied ride-pooling vehicles through high-demand, low-competition edges to increase the probability of a second pickup, with modest simulated gains.","lead":"This paper introduces a route-planning method for partially occupied ride-pooling vehicles, choosing detours that maximize the chance of picking up a second passenger while still serving the current one. The authors test it in a Shenzhen simulation and report slightly higher answer rates and lower waiting times than the shortest-path baseline.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"ILP (11) does not enforce a simple OA–DA path: with slack in (11f), positive P_ij rewards adding disjoint or endpoint cycles, so the optimized edge set is not necessarily the route evaluated in Table I; subtour elimination is missing.","rationale":"The paper's central contribution is an ILP whose optimum is claimed to be a route. The subtour flaw is load-bearing because it breaks the link between the mathematical object being optimized and the trajectory actually evaluated. Unlike the independence assumption in Eq. (6), which only affects the quality of the probability estimates, or the log-linear approximation in Eq. (10), whose bias can be bounded, the missing connectivity constraints make Eq. (11) not a path-planning formulation at all. Positive edge scores guarantee that a solver will fill any slack in the detour budget with cycles, so this is not a corner case. The reader's report lists 'add subtour elimination' among its conditions, so the verdict does not move; it remains conditional. However, the paper should be required to either add a correct subtour-elimination constraint or prove connectivity is implied, and to verify that the solutions used in Table I contain no extra components. I disagree with the reader's choice of weakest assumption: independence of matching events is a modeling approximation, but the subtour issue is a definite formal defect in the stated algorithm and must be settled before any simulation claim can be trusted.","tokens_in":8834,"tokens_out":9326,"duration_ms":124111,"concrete_test":"Construct a six-node instance with OA=S, DA=T, path S->A->T, and a disjoint cycle C->D->E->C, all P_ij=1 and length budget L(S,T)+epsilon. Solving Eqs. (11a)–(11f) will return the cycle as part of the optimum, proving the constraint set admits non-path solutions. Then instrument the Shenzhen simulator: for every ILP solve, check whether the Gurobi solution contains a connected component other than the OA–DA path, or a cycle through OA or DA. If so, add subtour-elimination constraints (e.g., requiring a path or using Miller–Tucker–Zemlin cuts) and rerun the three-hour simulation. If the Table I gaps (81.4 vs 80.0 answer rate, 656 vs 614 shared orders) persist, the finding survives; if they vanish or reverse, the central claim is an artifact of the invalid formulation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Constraints (11c)–(11e) do not enforce a single OA-to-DA path. Equation (11d) imposes flow balance only at intermediate nodes, and (11e) bounds each node's in/out degree by one, but nothing rules out one or more disjoint directed cycles, or a cycle that passes through OA or DA. Since the objective (10) sums nonnegative edge probabilities (typically positive), adding such a cycle never decreases the objective; whenever the detour budget (11f) has slack, the ILP optimum will include extra cycle edges that are not on the OA–DA route. Section III-B's claim that (11e) 'prevent[s] cycles in the path' is therefore incorrect: it only prevents a node from having degree greater than one, not disconnected cycles or cycles attached at the endpoints. The 'route constructed by sequentially connecting the selected edges' is thus not well-defined. If the simulator discards the extra edges, the realized trajectory is not the ILP optimum; if it follows them, the vehicle loops. Either way, Table I is not testing the algorithm as stated.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an en-route path-planning algorithm for partially occupied vehicles in ride-pooling systems. A matching probability model is introduced that combines \"attractiveness\" of demand and \"repulsiveness\" of competing vehicles, and the route choice is formulated as an integer linear program (ILP) maximizing the sum of edge-level match probabilities under a detour budget. The method is evaluated in an agent-based simulator on a Shenzhen road network, with results reported in Table I. The central claim is that the proposed ILP-based routing yields higher answer rates, shorter waiting times, and more shared trips than a shortest-path policy.","tokens_in":9076,"tokens_out":4106,"duration_ms":49685,"significance":"If the central claim held, the paper would offer a practical and computationally tractable approach to real-time detour planning for ride-pooling, and the joint modeling of passenger demand and vehicle competition is a reasonable idea worth exploring. The use of a realistic simulator on a real urban network is a strength. However, the current manuscript does not yet support the central claim because the ILP as stated may not produce a valid path, the linearization underlying the objective is not justified, and the calibration/evaluation setup may bias the reported improvements. These issues are load-bearing for the claim that the proposed method outperforms the shortest-path baseline.","major_comments":[{"comment":"The ILP formulation does not enforce that the selected edges form a single simple path from OA to DA. Constraint (11d) imposes flow balance only at intermediate nodes, and (11e) bounds the in-degree and out-degree of each node by one, but this does not rule out directed cycles that are disjoint from the main path, or cycles attached at OA or DA, or a cycle passing through OA or DA. Since the objective coefficients P^t_ij are nonnegative, adding such a cycle never decreases the objective and, whenever the detour budget (11f) has slack, the ILP optimum will include extra cycle edges that are not on the OA-DA route. The statement in Section III-B that (11e) \"prevent[s] cycles in the path\" is therefore incorrect, and the claim that the route rcurrent is \"constructed by sequentially connecting these selected edges\" is not well-defined. Consequently, Table I may be evaluating a trajectory that differs from the ILP optimum, so the reported performance of the proposed method is not attributable to the algorithm as stated. Subtour-elimination constraints or an explicit path-based formulation are needed.","section":"Section III-B, Eqs. (11c)-(11e)"},{"comment":"The transformation from the multiplicative objective (8) to the linear objective (10) relies on the approximation log(1-y) ≈ -y, which is valid only when all P^t_ij · x_ij are close to zero. The paper does not report typical values of P^t_ij for the Shenzhen case study, and if some edge probabilities are not small (e.g., above 0.1), this approximation can change the ranking of candidate routes and hence the optimal solution. The authors should either justify the small-probability regime using the actual data, solve the exact nonlinear objective (8), or provide a sensitivity analysis comparing the solutions of (8) and (10). Without this, the claim that the ILP maximizes the likelihood of picking up a second passenger is unsupported.","section":"Section III-A, Eqs. (9)-(10)"},{"comment":"The hyperparameters ζ and η are selected via grid search to maximize the answer rate, which is also the primary metric used for comparison in Table I. The paper does not describe a separate calibration/validation split or report how sensitive the comparative results are to ζ and η. As a result, the reported improvement of the proposed method over the shortest-path policy could be at least partly an artifact of tuning to the evaluation metric rather than a genuine advantage of the routing mechanism. Please clarify whether the tuning was performed on a period disjoint from the evaluation scenarios, or report results across a range of hyperparameter values.","section":"Section IV-B, Experimental setup"},{"comment":"The route-level probability of no match is computed as the product of per-edge no-match probabilities, which assumes that match opportunities on different edges are statistically independent. In the simulator, however, requests arrive in the network and the matching process is centralized and sequential (Section IV-A), and the presence of other vehicles creates spatial and temporal correlation in match opportunities. Under such correlation, the product form is not the true probability and can mis-rank routes. The authors should justify the independence assumption or test its impact, for example by comparing the optimized routes with routes selected using a simulator-based estimate of the actual route-level match probability.","section":"Section II-C, Eq. (6)"}],"minor_comments":[{"comment":"The sentence \"Constraint (11e) ensures that each node is visited at most once, preventing cycles in the path\" should be revised, since (11e) only bounds degrees and does not prevent disconnected or attached cycles; this is already covered in the major comments but the wording should be corrected.","section":"Section III-B, after Eq. (11f)"},{"comment":"The caption describes Path 3 as having passengers traveling \"in the opposite direction of the current trip, from OA to DA\"; the phrase \"from OA to DA\" appears to mean the opposite direction of the current origin-destination pair, but the wording is confusing and should be clarified.","section":"Fig. 1 caption"},{"comment":"The row label \"No share ( f leet+ 20%)\" should be typeset as \"No share (fleet + 20%)\" for consistency, and the meaning of the +20% fleet scenario could be spelled out explicitly in the table caption.","section":"Table I"},{"comment":"In Algorithm 1, the update step augments R with rcurrent but does not specify when routes are removed; a brief comment on the lifecycle of planned routes would improve reproducibility.","section":"Section IV-B, Algorithm 1"}],"recommendation":"major_revision","confidential_remarks":"The central idea is reasonable and the simulation study is substantial, but the ILP formulation's failure to enforce a single path is a technical flaw that must be fixed before the results can be trusted. The calibration/evaluation overlap is also a concern that the authors will need to address explicitly. This is a major-revision situation rather than a reject: the flaws are fixable within the scope of the manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The core idea is sensible: formulate en-route detour planning for a partially occupied vehicle as an Arc Orienteering Problem, with a trip-specific match probability that accounts for both demand attractiveness and competition from other vehicles. That specific combination is new, and the motivation—why the shortest path is not always best—is clearly argued. The writing is clean, the Shenzhen case study uses a real road network, and the comparison with shortest-path and no-sharing baselines is standard. I'd credit the authors for assembling these ingredients into a coherent model.\n\nThe soft spots, however, are not minor. The stress-test note is correct: constraints (11c)–(11e) do not rule out disjoint directed cycles. Since the objective (10) sums nonnegative edge probabilities and the detour budget (11f) often has slack, an optimal ILP solution can include extra cycle edges that are not on any OA–DA route. The claim in Section III-B that (11e) prevents cycles is simply wrong. This means the \"route\" constructed from the ILP output is not well-defined, and the simulator is likely evaluating something other than the ILP optimum. That is a load-bearing flaw in the optimization model as written.\n\nTwo other concerns, in proportion. The log-linearization in (9)–(10) assumes per-edge match probabilities are small; no error bound or empirical check is provided. And the parameters ζ and η are tuned by grid search to maximize the same answer rate used in the evaluation table, on a single simulation run, so the reported 1.4 pp answer-rate gain and 2.5 s waiting-time reduction are not statistically grounded. The independence assumption across edges (Eq. 6) is also questionable under bursty demand, but that is a modeling choice rather than a bug.\n\nWho is this for? Researchers in OR/transportation, especially those working on ride-pooling fleet operations. They would get a useful formulation sketch and a plausible starting point, but they should not treat the numerical results as evidence of operational improvement until the ILP is fixed and the evaluation is strengthened.\n\nMy recommendation: send it to peer review, but with a clear expectation of major revision. The formal subtour issue is fixable with standard subtour-elimination constraints, and the validation can be improved with multi-seed statistics and a hold-out parameter choice. If those are addressed, the paper could become a solid contribution. As is, it is not there yet.","headline":"A plausible ride-pooling detour planner with a real formal flaw: the ILP does not enforce a single path, and the validation is too thin to support the claims.","tokens_in":9592,"tokens_out":2570,"would_cite":false,"duration_ms":33656,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For partially occupied ride-pooling vehicles, the route that maximizes the chance of an en-route second pickup is not the shortest path; the paper plans it as an integer linear program and shows it improves service in simulation.","keywords":["ride-pooling","en-route path planning","integer linear programming","matching probability","detour routing","vehicle coordination","demand responsiveness","Arc Orienteering Problem"],"falsifier":"Run the same Shenzhen simulator with demand arriving in short bursts or with vehicles clustering, and compare the realized fraction of trips that gain a second passenger under routes chosen by the ILP versus routes chosen by shortest path. If the ILP routes do not yield a higher realized match rate, the independence product (Eq. (6) and (8)) mis-ranks routes and the central claim is not robust.","tokens_in":8615,"feed_emoji":"🚕","tokens_out":5309,"duration_ms":57985,"temperature":0.7,"pith_summary":"This paper addresses the routing problem for ride-pooling vehicles that have already picked up one passenger and have a free seat. It argues that following the shortest path to the current passenger's destination is often not the best choice: a slightly longer route through areas with many compatible requests and few competing vehicles raises the chance of picking up a second passenger. The authors build a trip-specific matching-probability model for each road edge, approximate the route-level objective in linear form, and cast the planning task as an integer linear program with a detour budget. Simulation on a realistic Shenzhen road network indicates that this policy outperforms shortest-path routing on answer rate, waiting time, shared orders, and empty distance.","feed_headline":"Smarter detours help ride-pool cars find second passengers","feed_subtitle":"An ILP-based route planner beats shortest paths on answer rate, waiting time, and shared rides in a Shenzhen simulation.","key_machinery":"The load-bearing mechanism is the per-edge match probability of Eq. (6): $P^t_{ij} = 1 - (1 - p^t_{\\mathrm{edge}}(i,j,O_A,D_A))^{\\hat{T}(i,j)}$, where $p^t_{\\mathrm{edge}}$ is the average of the node-level match probabilities at the two endpoints. The node-level probability (Eq. (1)) is $1 - \\zeta \\exp(-\\lambda_{\\mathrm{Att}} / (\\eta n_t(i)))$, in which $\\lambda_{\\mathrm{Att}}$ is the expected compatible passenger demand weighted by how efficiently the two trips can be pooled, and $n_t(i)$ counts nearby empty, dropping-off, and partially occupied vehicles. By assuming match opportunities occur independently over time, the route-level probability of no match becomes the product over edges of $(1 - P^t_{ij})$, and the small-probability logarithm approximation turns the objective into a linear sum, making the planning problem an instance of the Arc Orienteering Problem cast as ILP (11), whose optimal path is the route that most improves the chance of a second pickup within the detour budget.","core_discovery":"The central claim is that en-route path planning for partially occupied vehicles should maximize the sum of edge-level match probabilities, subject to flow and detour constraints, and that solving this ILP yields routes that measurably improve service. Specifically, the paper solves $\\max \\sum_{(i,j)\\in E} P^t_{ij} x_{ij}$ with binary edge variables, start/end constraints, flow conservation, no cycles, and total length at most $\\alpha$ times the shortest-path length. The probabilities $P^t_{ij}$ combine a passenger-demand attractiveness term with a vehicle-competition repulsiveness term. In the reported Shenzhen case study, the proposed policy achieves an 81.4% answer rate versus 80.0% for the shortest-path policy, a shorter average waiting time (151.3 s versus 153.8 s), more shared orders (656 versus 614), longer total shared distance, and lower empty distance. A corollary emphasized by the authors is that serving the same share of requests without ride-pooling would need a fleet about 20% larger, with much more empty driving.","pith_inferences":["Editorial inference: the independence assumption is the most exposed part of the model; a natural test is to compute route-level no-match probabilities by simulation instead of by multiplication and see whether the ILP's ranking of candidate routes changes.","Editorial inference: the same attractiveness/repulsiveness machinery could be applied to empty-vehicle repositioning or to the final drop-off leg, not only to partially occupied vehicles; the paper does not explore these.","Editorial inference: the reported gains are obtained under a first-come-first-served matching policy that does not itself optimize for pooling, so the benefits might change under a proactive matching policy; extending the comparison would clarify how much of the gain is routing versus matching.","Editorial inference: using an online predictor of demand instead of historical averages, as the paper notes as future work, could make the edge probabilities time-consistent with bursty arrivals; such an extension is testable with the same ILP."],"forward_implications":["Ride-pooling fleets can raise the share of trips that become shared without waiting for passive batch matching: the planned detour is computed at pickup time and can be updated as conditions change.","Because routes avoid areas already crowded with other partially occupied vehicles, the method acts as a lightweight coordination mechanism across the fleet, reducing oversupply and undersupply.","The detour budget adapts to demand: in the case study the planned path is longer in the low-demand hour (10.39 km) than in the high-demand hour (10.29 km), both within the 20% threshold.","Without ride-sharing, matching the same answer rate requires about 20% more vehicles and much more empty driving, so the routing gains translate directly into fleet-size and congestion savings."],"supporting_citations":[{"why":"Frames the problem as an Arc Orienteering Problem, giving the scored-edges-within-budget formulation used in ILP (11).","marker":"[17]"},{"why":"Supplies the base matching function that Eq. (1) adapts to pooling by adding compatible-demand weighting.","marker":"[18]"},{"why":"Provides the empirical pooling-matching probability law and detour-distance relations that motivate the trip-specific probability model.","marker":"[7]"},{"why":"Provides the shared-mobility simulator and the macroscopic fundamental diagram used for the Shenzhen case study and travel-time inputs.","marker":"[22]"},{"why":"Gives the shortest-path distances used in $L_s$ and $L_p$ for the compatibility ratio.","marker":"[20]"},{"why":"Supplies travel-time estimation methods used to set edge travel times $\\hat{T}(i,j)$.","marker":"[21]"}],"fun_headline_variants":["ILP route planner boosts ride-pool pickups without delaying riders","Maximize ride-pool matches with probability-optimized detours","Smarter detours: ILP path-planning lifts ride-pool answer rates","Ride-pooling: dynamic path planning finds extra passengers en route","Detour optimization in ride-pooling cuts wait times, adds shared rides"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The decisive assumption is that the chance of failing to find a match on one road edge is independent of the chance on every other edge, so the route-level probability is just the product of per-edge probabilities; in reality nearby matching opportunities are correlated in time and space.","fun_headline_variants_meta":{"raw":{"variants":["ILP route planner boosts ride-pool pickups without delaying riders","Maximize ride-pool matches with probability-optimized detours","Smarter detours: ILP path-planning lifts ride-pool answer rates","Ride-pooling: dynamic path planning finds extra passengers en route","Detour optimization in ride-pooling cuts wait times, adds shared rides"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00079,"raw_usage":{"total_tokens":3464,"prompt_tokens":909,"completion_tokens":2555,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":525,"completion_tokens_details":{"reasoning_tokens":2458}},"tokens_in":525,"tokens_out":2555,"duration_ms":21154,"temperature":1.0,"reasoning_tokens":2458,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:28:53.313184+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same Shenzhen simulator with demand arriving in short bursts or with vehicles clustering, and compare the realized fraction of trips that gain a second passenger under routes chosen by the ILP versus routes chosen by shortest path. If the ILP routes do not yield a higher realized match rate, the independence product (Eq. (6) and (8)) mis-ranks routes and the central claim is not robust.","supporting_citations":[{"cited_title":"The planning of cycle trips in the province of east flanders,","cited_arxiv_id":null,"evidence_quote":"Frames the problem as an Arc Orienteering Problem, giving the scored-edges-within-budget formulation used in ILP (11)."},{"cited_title":"Spatial Equilibrium, Search Frictions, and Dynamic Efficiency in the Taxi Industry,","cited_arxiv_id":null,"evidence_quote":"Supplies the base matching function that Eq. (1) adapts to pooling by adding compatible-demand weighting."},{"cited_title":"Data-driven analysis on match- ing probability, routing distance and detour distance in ride-pooling services,","cited_arxiv_id":null,"evidence_quote":"Provides the empirical pooling-matching probability law and detour-distance relations that motivate the trip-specific probability model."},{"cited_title":"On the inefficiency of ride- sourcing services towards urban congestion,","cited_arxiv_id":null,"evidence_quote":"Provides the shared-mobility simulator and the macroscopic fundamental diagram used for the Shenzhen case study and travel-time inputs."},{"cited_title":"Algorithm 97: Shortest path,","cited_arxiv_id":null,"evidence_quote":"Gives the shortest-path distances used in $L_s$ and $L_p$ for the compatibility ratio."},{"cited_title":"Travel time estimation of a path using sparse trajectories,","cited_arxiv_id":null,"evidence_quote":"Supplies travel-time estimation methods used to set edge travel times $\\hat{T}(i,j)$."}],"review_version":1}