Energy Estimation of Last Mile Electric Vehicle Routes

• EV lifecycle emissions are approximately 3x lower than those of ICE vehicles, making electrification a sustainability pillar for many last-mile carriers.Source: §1 · p. 1
• EV adoption complicates last-mile route planning, so the paper develops deep-learning energy estimators and presents RET, comparing them with distance- and physics-based benchmarks.The paper also explores increasing model capacity using Chinchilla scaling laws and the Transformer architecture.Source: §1 · p. 1

• At the same normalized EV distance of 0.5, returning state of charge varied from 0% to 70% across routes, with variation highly correlated with ambient temperature.Energy use on the exact same route can vary by more than 100% depending on ambient temperature; topography, stationary time, and acceleration profile also matter.Source: §2 · p. 1
• Delivery routes include frequent stops and substantial parked time, making HVAC consumption disproportionately impactful compared with consumer EV driving.Source: §2 · pp. 1–2
• Battery capacity and charging speed constrain EV route planning; fast charging reduces charging time but can deteriorate batteries faster and increase delivery-station power load.EV charging is approximately two orders of magnitude slower than refueling a comparable ICE vehicle.Source: §2 · p. 2
• Public charging is limited, scattered, and often unavailable where energy risk is greatest, while on-road charging is impractical given charging speed and routing time.Source: §2 · p. 2
• Because route feasibility depends on factors including weather and elevation, an energy-infeasible assignment can harm drivers, customers, and carriers when charging recourse is limited.Source: §2 · p. 2
• An energy constraint reduces the feasible route space and can lower productivity and route quality, while omitting it risks range anxiety or vehicles returning before completing routes.Source: §2 · p. 2

• Physics models estimate energy from signals including time, distance, HVAC use, temperature, acceleration, vehicle mechanics, and road characteristics.The paper distinguishes its setting because planning-time information is imperfect, including traffic predictions and fine-grained route elevation and slope.Source: §3 · p. 2
• Direct machine-learning methods have also predicted energy [3] [18], but the paper identifies planning-time information and latency requirements as differences in its setting.Source: §3 · p. 2
• Route energy prediction is related to time-series estimation, where a sequence of energy estimates is predicted from features and prior predicted energy.Source: §3 · p. 2

4 MODELING ENERGY CONSUMPTION WITH DEEP LEARNING

• The modeling approach introduces features and two deep-learning models: a feed-forward NN for individual segments and an RNN for routes represented as segment sequences.Source: §4 · p. 2

4.1 Features.

• Features span route characteristics, traveled path, environment, vehicle, and other factors, with selection based mainly on availability and exploratory analysis of route impact.Package weight is treated as insignificant relative to vehicle weight, while temperature is included because it varies across routes and affects energy consumption.Source: §4.1 · p. 2

4.2 Predicting individual segments with a Fully Connected Model.

• The fully connected model predicts each route segment’s energy independently and aggregates segment predictions to the route level.The segment-level network uses two fully connected layers of 32 units each.Source: §4.2 · pp. 2–3

4.3 Predicting entire routes with a Recurrent Neural Network.

• The route-level RNN uses a unidirectional GRU to capture correlations between segments and predicts each segment’s energy in the context of the whole route.It embeds features and sequence steps, then sums predicted segment consumption for the route.Source: §4.3 · p. 3

5 TRAINING A COMPUTE OPTIMAL TRANSFORMER

• RET is a decoder-only Transformer with hand-crafted route features, per-step energy predictions, and mean absolute error loss.Its design is mostly consistent with GPT2, but the smaller dataset motivates substantially smaller models.Source: §5 · p. 3
• Using Chinchilla scaling laws [12], the authors fit model size to available data and estimate a 3M-parameter optimum.Figure 2 compares data size with parameter count and predicts an optimal model orders of magnitude larger than the Feed Forward NN and RNN.Source: §5 · p. 3, Figure 2 · p. 3
• Because inference compute also matters, the authors train two smaller RET models to test whether they retain some accuracy benefits with lower inference time.Chinchilla optimality is framed as maximizing accuracy for a given compute budget [12].Source: §5 · p. 3

6 MODELING RESULTS

• The evaluation covers overall, hot- and cold-route MAPE, and inference speed; RET-20k matches the RNN's parameter count, while RET-300k is a middle ground for lower latency.The evaluation uses MAPE and a hold-out subset of hot and cold routes.Source: §6 · p. 3, Table 2 · p. 4, §6.1 · p. 4

6.1 Accuracy

• The NN improves MAPE by +1117 bps over Distance and +260 bps over Physics, while the RNN adds +112 bps over the NN.The authors attribute the RNN gain likely to sequence modeling and larger model size.Source: §6.1 · p. 4
• RET-3M improves MAPE by +217 bps versus NN and +105 bps versus RNN overall, with +753 bps on hot routes and 167 bps on cold routes.The authors note that cold routes were relatively lacking in training data.Source: Table 3 · p. 4, §6.1 · p. 4

6.2 Inference Speed

• RET-3M is 4x slower than RET-300k on CPU and GPU, although RET-300k approaches its overall and cold-route MAPE and slightly edges it on hot routes.Inference speed matters because routing optimization may evaluate several orders of magnitude more routes than are ultimately needed.Source: §6.2 · p. 4, Table 4 · p. 4

7 FINAL REMARKS

• Deep-learning solutions, including compute-optimal RET, predict energy consumption for EV-aware route planning.The paper presents this as a benefit of its range of approaches.Source: §7 · p. 4
• Battery-capacity constraints create a route quality–route-risk trade-off because energy predictions are not perfectly accurate.The routing constraint’s conservativeness must be chosen explicitly.Source: §7 · p. 4
• Energy estimates apply beyond routing to upstream vehicle assignment and on-road route-feasibility support under changing weather or traffic.Assigning larger-battery vehicles to higher-consumption areas can limit effects on route quality.Source: §7 · p. 5
• Future work could combine physics predictions with a learned estimate of the difference between predicted and actual energy use.This approach is proposed to make the model learn signals not captured by the physics model.Source: §7 · p. 5
• Explicit uncertainty modeling remains an improvement area, while common distribution- or ensemble-based approaches increase inference time.The paper identifies uncertainty methods as a direction for future work.Source: §7 · p. 5

A GLOSSARY

• DS means Delivery Station, while EV and ICE mean Electric Vehicle and Internal Combustion Engine.Source: A GLOSSARY · p. 5
• GRU, HVAC, and SOC mean Gated Recurrent Unit, Heating, Ventilation, and Air Conditioning, and State of Charge.Source: A GLOSSARY · p. 5
• MAPE, NN, RNN, and RET mean Mean Absolute Percentage Error, Neural Network, Recurrent Neural Network, and Route Energy Transformer.Source: A GLOSSARY · p. 5