Applying a Hybrid Gray Wolf‐Enhanced Whale Optimization Algorithm to the Capacitated Vehicle Routing Problem
Bibliographic record
Abstract
The study presents a novel hybrid gray wolf and whale optimization algorithm (hGWOAM) for the capacitated vehicle routing problem (CVRP). By integrating the enhanced whale optimization algorithm (EWOA) and gray wolf optimizer (GWO) with tournament selection, opposition‐based learning, and mutation techniques, hGWOAM enhances routing efficiency under capacity constraints. Computational evaluations demonstrate its superior performance, achieving lower percentage deviations (%dev) compared to existing algorithms across multiple case studies and real‐world applications. In Case Study 1, hGWOAM achieved a mean percentage deviation (%dev) lower than EWOA (0.89%), GWO (0.74%), SCA (0.59%), DA (1.63%), ALO (2.26%), MHPSO (1.85%), PSO (1.96%), DPGA (2.85%), and SGA (4.14%). In Case Study 2, hGWOAM outperformed EWOA (12.05%), GWO (2.53%), ALO (21.07%), and DA (17.58%). In a real‐world application, it achieved the best %dev, surpassing EWOA (6.64%), GWO (6.34%), ALO (9.01%), and DA (12.24%). These findings highlight hGWOAM’s potential for optimizing logistics, reducing operational costs, and minimizing environmental impact while also paving the way for future advancements in metaheuristic optimization.
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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 | 0.000 | 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) | 0.001 | 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".