Pareto-optimality and a search for robustness: choosing solutions with desired properties in objective space and parameter space
Bibliographic record
Abstract
Multi-objective genetic algorithms are increasingly being applied to calibrate hydrological models by generating several competitive solutions usually referred to as a Pareto-optimal set. The Pareto-optimal set comprises non-dominated solutions at the calibration phase but it is usually unknown whether all or only a subset of non-dominated solutions at the calibration phase remains non-dominated at the validation phase. In practice, users would like to know solutions (and their associated properties) which remain non-dominated at both the calibration and validation phases. This study investigates robustness of the Pareto-optimal set by developing a model characterization framework (MCF). The MCF uses cluster analysis to examine the distribution of solutions in parameter space and objective space, and conditional probability to combine linkages between the distributions of solutions in both spaces. The MCF has been illustrated for calibration output generated from application of the Non-dominated Sorting Genetic Algorithm-II to calibrate the Soil and Water Assessment Tool for streamflow in the Fairchild Creek watershed in southern Ontario. Our results show that not all non-dominated solutions found at the calibration phase perform the same for different validation periods. The MCF illustrates that robust solutions – non-dominated solutions which cluster in similar locations in parameter space and objective space – performed consistently well for several validation periods.
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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 | 0.012 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 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".