An improved hybrid whale optimization algorithm for global optimization and engineering design problems
Bibliographic record
Abstract
The whale optimization algorithm (WOA) is a widely used metaheuristic optimization approach with applications in various scientific and industrial domains. However, WOA has a limitation of relying solely on the best solution to guide the population in subsequent iterations, overlooking the valuable information embedded in other candidate solutions. To address this limitation, we propose a novel and improved variant called Pbest-guided differential WOA (PDWOA). PDWOA combines the strengths of WOA, particle swarm optimizer (PSO), and differential evolution (DE) algorithms to overcome these shortcomings. In this study, we conduct a comprehensive evaluation of the proposed PDWOA algorithm on both benchmark and real-world optimization problems. The benchmark tests comprise 30-dimensional functions from CEC 2014 Test Functions, while the real-world problems include pressure vessel optimal design, tension/compression spring optimal design, and welded beam optimal design. We present the simulation results, including the outcomes of non-parametric statistical tests including the Wilcoxon signed-rank test and the Friedman test, which validate the performance improvements achieved by PDWOA over other algorithms. The results of our evaluation demonstrate the superiority of PDWOA compared to recent methods, including the original WOA. These findings provide valuable insights into the effectiveness of the proposed hybrid WOA algorithm. Furthermore, we offer recommendations for future research to further enhance its performance and open new avenues for exploration in the field of optimization algorithms. The MATLAB Codes of FISA are publicly available at https://github.com/ebrahimakbary/PDWOA.
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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 | 0.002 |
| 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 | 0.001 |
| 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".