Pareto-based many-objective optimization using knee points
Bibliographic record
Abstract
Many real-world optimization problems contain multiple (often conflicting) goals to be optimized simultaneously, commonly referred to as multi-objective problems (MOPs). Currently, there exists a plethora of Pareto optimizers designed to solve MOPs. Previous literature has demonstrated that the performance of these optimizers degrade for problems which possess more than three objectives, known as many-objective problems (MaOPs). The downfall of the traditional Pareto approach is that the dominance-based selection strategy loses effectiveness in distinguishing desirable solutions as the number of objectives grows larger, inhibiting convergence to the true Pareto front. One potential solution to this problem is to utilize the concept of knee points as a secondary metric for optimization. Two new knee-driven algorithms are proposed within this work, namely the knee point driven particle swarm optimization (KnPSO) and knee point driven differential evolution (KnDE) algorithm. Due to the nature of the knee point identification mechanism used, both of these algorithms have the benefit of naturally producing a diverse set of solutions without having to incorporate additional criterion. The existing knee-driven evolutionary algorithm (KnEA) along with the proposed approaches are compared against several non-knee variants. Experimental results on nine challenging MaOPs demonstrate that knee points are a viable option for improving the performance of Pareto-based approaches. The knee point driven algorithms are shown to produce significantly higher inverted generational distance and hypervolume metric values in comparison to their non-knee counterparts.
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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 | 0.001 | 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".