A hybrid matheuristic approach for the vehicle routing problem with three-dimensional loading constraints
Bibliographic record
Abstract
This paper proposes a matheuristic algorithm based on a column generation structure for the capacitated vehicle routing problem with three-dimensional loading constraints (3L–CVRP). In the column generation approach, the master problem is responsible for managing the selection of best-set routes. In contrast, the slave problem is responsible for solving a shorter restricted route problem (CSP, Constrained Shortest Path) for generating columns (feasible routes). The CSP is not necessarily solved to optimality. In addition, a greedy randomized adaptive search procedure (GRASP) algorithm is used to verify the packing constraints. The master problem begins with a set of feasible routes obtained through a multi-start randomized constructive algorithm (MSRCA) heuristic for the multi-container loading problem (3D–BPP, three-dimensional bin packing problem). The MSRCA consists of finding valid routes considering the customers' best packing (packing first-route second). The efficiency of the proposed approach has been validated by a set of benchmark instances from the literature. The results show the efficiency of the proposed approach and conclude that the slave problem is too complex and computationally expensive to solve through a MIP.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".