An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows
Bibliographic record
Abstract
This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality initial solutions are generated by means of a savings-based heuristic that combines diversification strategies with learning mechanisms. In Phase 2, an attempt is made to reduce the number of routes in the initial solution with a new local search procedure. In Phase 3, the solution from Phase 2 is further improved by a set of four local search operators that are embedded in a deterministic annealing framework to guide the improvement process. Some new implementation strategies are also suggested for efficient time window feasibility checks. Extensive computational experiments on the 168 benchmark instances have shown that the suggested method outperforms the previously published results and found 167 best-known solutions. Experimental results are also given for the new problem variant.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".