PADDS Algorithm Assessment for Biobjective Water Distribution System Benchmark Design Problems
Bibliographic record
Abstract
Two implementations of the Pareto archived dynamically dimensioned search (PADDS) algorithm using different selection metrics are applied to 12 water distribution network (WDN) design benchmark problems from the literature. Convex hull contribution (CHC) and hypervolume contribution (HVC) are used as selection metrics for PADDS making this study the first to assess their relative performance on WDN design problems. Past research applied five state-of-the-art multiobjective evolutionary algorithms (MOEAs) to these 12 benchmark problems to generate the best-known Pareto fronts (PFs). The PADDS-CHC and PADDS-HVC both find all solutions on the known true PFs of the first three problems. Together, both PADDS results augment the previously best-known PFs in the nine other benchmark problems with new PF solutions, some of which dominate previous best-known PF solutions, to define updated best-known PFs. Comparative results against five state-of-the-art MOEAs show PADDS derived best-known PFs are equal or better than all other algorithms in 11 of 12 WDN design problems. A comprehensive comparison between PADDS-CHC and PADDS-HVC performance on the largely convex benchmark problem Pareto fronts reveals the different responses of PADDS algorithm to increment of computational budget. An innovative measure called effective archive size (EAS) is introduced to quantify the portion of PADDS archived solutions that play the dominant role in directing PADDS toward the final PF. Tracking the EAS value throughout the search revealed that compared with PADDS-HVC, the EAS of PADDS-CHC is typically close to an order of magnitude smaller. In fact, the PADDS-CHC algorithm generates candidate solutions from a surprisingly small effective archive size that ranges from only 16 to 73 solutions across the 12 benchmark WDN problems while being only 24 for the largest problem.
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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 | 0.004 | 0.009 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".