Exact Methods and a Two-Stage Iterative Heuristic for the Carrier-Vehicle Traveling Salesman Problem
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The carrier-vehicle traveling salesman problem (CVTSP) aims to optimize the routes of a larger, but slower, carrier and a smaller, but faster, vehicle to minimize the maximum completion time for visiting a set of targets. This paper introduces an enhanced formulation for the CVTSP using a set of new valid inequalities derived from structural properties. A logic-based Benders decomposition method is tailored to solve the problem by introducing various types of Benders cuts. In particular, a new analytical cut is developed based on valid bounds of the travel time between any two consecutive visited nodes. To handle practical instances, we design a simple, yet effective, two-stage iterative heuristic, which repeatedly solves a traveling salesman problem using an updated approximate travel time matrix. We conduct numerical experiments on 529 benchmark instances. Results show that the proposed formulation and exact method perform well, especially for the instances with small vehicle endurance and distant targets. The heuristic quickly achieves optimality for all instances with known optimal values. It finds new best solutions for most open instances, outperforming state-of-the-art heuristics in solution quality and efficiency. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: Financial support from the National Natural Science Foundation of China [Grant 72201044] and [Grant 72571037] are gratefully acknowledged. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1140 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1140 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it