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Joint Optimisation of Electric Vehicle Routing and Scheduling: A Deep Learning-Driven Approach for Dynamic Fleet Sizes

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A CNN that predicts the binary variables of an EV fleet's day-ahead routing-and-scheduling problem lets a MIP solver finish 97.8% faster, with 99.5% feasibility, under 0.01% optimality loss, and no retraining for fleet sizes between 20…

desk verdict Solid ML-for-MIP acceleration with a genuinely useful padding trick, but the near-optimality claim rests on a 0.1%-gap baseline and should be restated or re-benchmarked. read the letter →

arxiv 2507.15307 v1 pith:VPOYEKVU submitted 2025-07-21 eess.SY cs.SY

Jun Kang Yap , Vishnu Monn Baskaran , Wen Shan Tan , Ze Yang Ding , Hao Wang , David L. Dowe This is my paper · ORCID
classification eess.SYcs.SY
keywords ElectricVehiclesPowersystemsimulationOptimizationNeuralnetworksjointroutingandschedulingmixed-integerprogrammingvariablefleetsize
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that a deep convolutional network can take over the hard binary decisions in a day-ahead electric-vehicle routing-and-scheduling problem, converting a mixed-integer program that is slow into one a solver can handle quickly. The network is trained on single-scenario problems but applied per scenario at run time, with a zero-padding scheme that lets it accept any fleet size between 20 and 100 without retraining. If correct, this gives grid operators a way to coordinate EV charging, discharging, and routing with renewable generation inside the clearing window of a day-ahead energy market. The paper reports a 97.8% runtime reduction against an unassisted MIP solver while keeping 99.5% of test instances feasible and deviating less than 0.01% from the optimal cost.

What carries the argument

The load-bearing object is a convolutional neural network that takes the solar, load, and job-schedule time series as input and outputs probabilities for every binary variable of the MIP. A thresholding step keeps only variables the network predicts with high confidence, passing the rest to the solver, while a padding mechanism sizes the network for a maximum fleet size $e_{\max}$ and zero-fills missing EV rows so the same weights serve any fleet size from 20 to 100. This combination lets one trained model serve the tested fleet range and hands the solver only the genuinely ambiguous binaries. The formulation side is carried by a modified time-space network with virtual congestion nodes (VCNs) that allow arc travel times to lengthen or shorten with traffic conditions, so the routing variables the CNN predicts are time-dependent.

What would settle it

Generate test instances where the optimal binary routing decision in one solar scenario conflicts with another scenario's optimal decision at the same timespan, then run the paper's training and inference pipeline; if feasibility falls well below 99.5% or the optimality loss rises above 0.01%, the concatenated-prediction assumption is the bottleneck.

Watch

Extended reading notes

Core claim

The central claim is that a CNN trained to predict the binary variables of the EV joint routing and scheduling (JRS) MIP can be used as a warm start for the solver, shrinking the search space so that the remaining variables are found quickly. The paper introduces a deterministic-training, stochastic-inference workflow: because labelling full stochastic instances is prohibitively expensive, the CNN is trained on deterministic versions and then applied to each of the five solar scenarios independently, concatenating the predicted binaries into a single solution. A padding mechanism zero-fills the input and output rows of missing EVs, so the same network handles fleets of size 20 to 100 with no retraining. On the IEEE 33-bus distribution system combined with the Nguyen-Dupuis transportation network, the assisted solver achieves 97.8% runtime reduction, 99.5% feasibility, and a mean optimality deviation of -0.01% relative to the unassisted MIP baseline.

Load-bearing premise

The whole speed-up rests on the assumption that a network trained on simplified single-scenario problems can still propose binary decisions that, when pasted together across five solar scenarios, remain jointly feasible and near-optimal for the full stochastic problem, without any explicit justification or ablation in the paper.

Editorial extensions

If this is right

  • Runtimes for day-ahead EV coordination drop from hours to minutes, putting the problem inside the typical 3-4 hour clearing window of day-ahead energy markets.
  • A single trained model covers EV fleet sizes from 20 to 100, so operators avoid generating a fresh labelled dataset and retraining for each new fleet count.
  • The 99.5% feasibility rate, together with the threshold-raising retry loop in the paper, gives a practical fallback when the predicted binary solution is infeasible.
  • The near-zero optimality loss indicates that the binary structure of the JRS problem can be learned from local input features, which is a prerequisite for using learned warm starts in other power-system MIPs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The deterministic-to-stochastic transfer is the most fragile link; comparing against a model trained on a handful of full stochastic labels would reveal how much of the reported 0.01% gap is transfer loss rather than network capacity.
  • The zero-padding scheme is generic: any MIP with a variable number of homogeneous agents whose binary variables scale linearly with the agent count could reuse it, so the method may carry over to unit commitment with flexible generator counts or to multi-robot task allocation.
  • The paper states that the computational burden shifts to labelling; that suggests reinforcement learning or self-supervised pretraining on MIP dual information could replace some supervised labelling and improve scalability.
  • Because the optimality loss is so small, operators might skip the feasibility-retry loop and accept the CNN's binaries outright, trading a tiny cost penalty for predictable, near-constant solve times.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This paper proposes a deep learning-assisted approach to accelerate the solution of a day-ahead electric vehicle (EV) joint routing and scheduling (JRS) problem. The problem is formulated as a stochastic mixed-integer program (MIP) with scenario-based solar uncertainty, and the routing component uses a time-space network extended with virtual congestion nodes (VCNs) to model time-varying travel times. A convolutional neural network (CNN) is trained to predict the binary routing and charging variables, using a padding mechanism so that a single model can handle varying fleet sizes without retraining. The predicted binaries are thresholded and then fixed, and Gurobi solves the reduced problem. In a case study on the IEEE 33-bus distribution network coupled with the Nguyen-Dupuis transportation network, the best model (CNN5) achieves a 97.83% average runtime reduction, a 99.5% feasibility rate, and an average optimality loss of -0.01% relative to a Gurobi baseline.

Significance. The paper addresses a timely and practically important problem—fast, near-optimal scheduling of EV fleets for grid support. The proposed CNN-assisted solution with padding for variable EV counts is a sensible approach to a real obstacle in applying learning-based acceleration to problems with changing dimensions. The VCN modification to the time-space network is a useful modeling contribution. The experimental study is comprehensive in terms of model variants (four training intervals) and includes an ablation of the padding mechanism. However, the headline near-optimality claim is not supported by the experimental design, because the reference 'optimal' solutions are themselves only approximated to a 0.1% MIP gap. This limits the strength of the paper's central contribution until the claim is either re-scoped or replaced with a certified optimality evaluation.

major comments (2)
  1. [Abstract; Section IV-A; Table I] The abstract claims that the approach deviates 'less than 0.01% from the optimal solution,' but this is not established by the experiments. Section IV-A states that Gurobi labels the datasets with a MIPGap of 0.1% or a 120-minute timeout, so the reference solutions are approximate to within 0.1% of the true optimum. Table I reports an optimality loss l-bar of -0.01% for CNN5, which means the assisted solution is 0.01% better than this approximate reference, not that it is within 0.01% of the true optimum. Moreover, fixing CNN-predicted binaries restricts the feasible region, so even solving the reduced MIP to a 0.1% gap does not bound the gap to the original optimum. Please either solve a subset of test instances to certified optimality (or with a much tighter MIPGap) and report the resulting suboptimality, or revise the abstract and conclusion to state that the solution is 'within 0.1% of the solver reference' rather than 'within 0.01% of the optimal solution.'
  2. [Section IV-C; Fig. 6] The runtime comparison is incompletely specified. The paper does not state the termination criterion used for the unassisted Gurobi baseline in the runtime experiments. If the baseline is not given the same MIPGap=0.1% and 120-minute time limit used for labelling, the reported 97.8% speedup could be inflated by instances where the baseline hits the time limit. If the baseline does use the same limits, then the comparison is between two approximate solves and should be described accordingly. Please specify the exact solver parameters for the baseline and, ideally, report time-to-given-optimality-gap curves for both the assisted and unassisted solvers.
minor comments (5)
  1. [Abstract] The abstract reports a 99.5% feasibility rate, but this is achieved by only one of the four trained models (CNN5); Table I shows CNN10, CNN15, and CNN20 have feasibility rates of 97.5%, 95.5%, and 77.0%, respectively. The abstract should either qualify this as the best-case result or acknowledge the sensitivity of feasibility to the training interval.
  2. [Section III-C; Algorithm 1] The thresholding logic in Algorithm 1 is unclear. The condition 'if p_t0 >= y_hat >= p_t1 then Dispose' uses scalar threshold values p_t0 and p_t1, but the text describes 'extracting predictions with probabilities above or below a threshold.' With p_t0≈0.99 and p_t1≈0.70, the condition disposes predictions in [0.70, 0.99], which would include many high-confidence positive predictions, while predictions below 0.70 are rounded to 0. Please clarify whether the intended comparison is y_hat > p_t1 for rounding to 1 and (1 - y_hat) > p_t0 for rounding to 0, and correct the pseudocode accordingly.
  3. [Section II-C, Eq. (11)] In equation (11), the summation range is written as 't = 2, ..., t', which should be 't = 2, ..., |T|'.
  4. [Section II-A] The description of virtual congestion nodes (VCNs) would benefit from a small illustrative example or figure showing how a VCN extends a trip time by one or more timespans. As written, the distinction between 'destination nodes', 'virtual nodes', and 'VCNs' is easy to lose.
  5. [Section IV-A] The paper states that 'Code for reproducing experiments will be available at' a GitHub URL. The repository was not available at the time of review. Please ensure the code is released before publication to support reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; CNN suggestions are solver-verified and the stochastic problem is scenario-separable.

full rationale

The claimed derivation is not circular. The CNN is a supervised approximator trained on solver-generated binary labels (Sections III-A and III-B); at inference it only proposes binary assignments, and the final solution is obtained by Gurobi solving the reduced MIP (Algorithm 1, line 14), so feasibility and optimality of the remaining variables are solver-enforced rather than defined by the fitted parameters. The stochastic test problem is scenario-separable: objective (1) and constraints (2)-(20) are all indexed by sc and contain no cross-scenario or non-anticipativity constraints, so the per-scenario prediction and concatenation in Algorithm 1 is structurally exact rather than a hidden reduction. The self-references ([2], [12]) are related-work citations and are not load-bearing for the method. The only caveat is that the abstract's 'deviating less than 0.01% from the optimal solution' is not strictly established because the Gurobi reference and training labels use MIPGap=0.1% or a 120-minute timeout (Section IV-B), so the comparison is to an approximate baseline rather than a certified optimum; this is a benchmark-precision/correctness issue, not a circularity of derivation.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The central claim rests on a specific synthetic problem generator, a linearized power flow model, a scenario-based uncertainty representation, and a CNN trained on deterministic instances but applied per scenario. The VCN routing construct is an unvalidated modeling addition.

free parameters (1)
  • Post-processing thresholds (mean prediction probabilities) = bar_p0=99.58%, bar_p1=71.64% (CNN5)
    Computed from CNN training/validation predictions to decide which binary variables are confidently predicted and fixed before Gurobi solves the remaining problem. These thresholds directly control the feasibility-runtime trade-off and are fitted to the training distribution.
assumptions (5)
  • domain assumption LinDistFlow linearized power flow equations accurately model the distribution network
    Used in constraints (17)-(19) to represent line flows and voltages; a standard approximation for radial networks that ignores reactive losses and angle differences.
  • domain assumption Five equally probable Monte Carlo scenarios capture solar generation uncertainty
    Section IV-A sets |SC|=5; the paper assumes this small scenario set is sufficient for day-ahead decision quality.
  • domain assumption Synthetic data generation (historical solar PDF sampling, random load scaling, random job schedules) produces instances representative of real day-ahead operations
    Section III-A constructs all training and test data synthetically; the measured speedups are only shown for this synthetic distribution.
  • domain assumption EV routing and charging binary variables may be scenario-dependent
    Constraints (2)-(11) index I, Ic, Id by sc, meaning decisions can differ by solar scenario; the paper never discusses non-anticipativity or two-stage decision structure, an implicit modeling choice.
  • ad hoc to paper Virtual congestion nodes correctly model time-varying travel times without distorting the time-space network
    Section II-A introduces VCNs as a new construct; no validation against traffic data or comparison with alternative time-expanded networks is provided.
invented entities (1)
  • Virtual congestion nodes (VCNs)
    purpose: To extend the time-space network with alternate congestion paths so EV travel times can vary between time periods (Section II-A)
    VCNs are an internal modeling device with no calibration to real congestion data and no falsifiable prediction outside the model.

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Pith. "Pith review of Joint Optimisation of Electric Vehicle Routing and Scheduling: A Deep Learning-Driven Approach for Dynamic Fleet Sizes." pith.science (2026). https://pith.science/paper/VPOYEKVU

@misc{pith2026250715307,
  author       = {Pith},
  title        = {Pith review of: Joint Optimisation of Electric Vehicle Routing and Scheduling: A Deep Learning-Driven Approach for Dynamic Fleet Sizes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VPOYEKVU}},
  note         = {Machine review of arXiv:2507.15307}
}
read the original abstract

Electric Vehicles (EVs) are becoming increasingly prevalent nowadays, with studies highlighting their potential as mobile energy storage systems to provide grid support. Realising this potential requires effective charging coordination, which are often formulated as mixed-integer programming (MIP) problems. However, MIP problems are NP-hard and often intractable when applied to time-sensitive tasks. To address this limitation, we propose a deep learning assisted approach for optimising a day-ahead EV joint routing and scheduling problem with varying number of EVs. This problem simultaneously optimises EV routing, charging, discharging and generator scheduling within a distribution network with renewable energy sources. A convolutional neural network is trained to predict the binary variables, thereby reducing the solution search space and enabling solvers to determine the remaining variables more efficiently. Additionally, a padding mechanism is included to handle the changes in input and output sizes caused by varying number of EVs, thus eliminating the need for re-training. In a case study on the IEEE 33-bus system and Nguyen-Dupuis transportation network, our approach reduced runtime by 97.8% when compared to an unassisted MIP solver, while retaining 99.5% feasibility and deviating less than 0.01% from the optimal solution.

Figures

Figures reproduced from arXiv: 2507.15307 by the authors.

Figure 1
Figure 1. A variation of an EV charging coordination problem. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (Top) Overview of the proposed training and (Bottom) inference framework. The simplified problem model shows EVs’ interaction with DN and TN, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Structure of CNN in this work, where emax is the estimated maximum number of EVs and the input and output shapes shown are compressed. variable is calculated with (21) proposed in [27], where pt 1/0 are the PPs of each binary variable, yˆ is the prediction of the CNN and y is the actual label. p 1/0 t = ˆy · 1{y=1} + (1 − yˆ) · 1{y̸=1}. (21) This method involves extracting predictions with probabilities above or bel… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: IEEE 33-bus system and Nguyen-Dupuis transportation network. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Number of EVs of problem instances in training and testing dataset. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Solution time and feasibility rate of each CNN trained on different [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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