Modeling and Solving the Traveling Salesman Problem with Speed Optimization for a Plug-In Hybrid Electric Vehicle
Bibliographic record
Abstract
This paper investigates a variant of the traveling salesman problem (TSP) with speed optimization for a plug-in hybrid electric vehicle (PHEV), simultaneously optimizing the average speed and operation mode for each road segment in the route. Two mixed-integer nonlinear programming models are proposed for the problem: one with continuous speed decision variables and one with discretized variables. Because the models are nonlinear, we propose reformulation schemes and introduce valid inequalities to strengthen them. We also describe a branch-and-cut algorithm to solve these reformulations. Extensive numerical experiments are performed to demonstrate the algorithm’s performance in terms of computing time and energy consumption costs. Specifically, the proposed solution method can efficiently solve instances with a realistic number of customers and outperforms the benchmark approaches from the literature. Integrating speed optimization into the TSP of a PHEV can lead to significant energy savings compared with the fixed-speed TSP. In addition, the proposed model is extended to investigate the impact of the presence of charging stations, which makes the problem harder to solve but has the potential to further reduce energy consumption costs. Funding: F. Wu gratefully acknowledges the support of the National Natural Science Foundation of China [Grant 72271161]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0247 .
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".