New formulations for the electric vehicle routing problem with nonlinear charging functions
Bibliographic record
Abstract
Electric vehicle routing problems (E-VRPs) are receiving growing attention from the operations research community. Electric vehicles (EVs) differ substantially from internal combustion engine vehicles. In the routing context, the main difference is due to the limited EV autonomy, which can be recuperated at charging stations. These are rather scarce, thus EVs typically have to perform detours to reach them. Various assumptions on the charging policy and objective function{, among others}, have led to the definition of several variants E-VRPs. Modeling the charging functions is a focal point of the majority of these problems. The majority of the research has focused on constant or linear charging function. To account for the nonlinear relation between the times spent charging and the amount of energy charged, the electric vehicle routing problem with nonlinear charging function has been recently introduced. In this research we propose new formulations for this problem. We present an arc-based tracking of the time and the state of charge which, according to our experiments, outperform the classical node-based tracking of these values. We also propose alternative formulations of the piecewise linear approximation of the nonlinear charging function. To prevent the use of charging stations nodes replication, we propose a recharging path-based model. We present a labeling algorithm to generate a tractable number of these paths. This latter model overcomes the limits of the classical models presented in the literature and also outperforms them in our experiments.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".