BEACON: Continuous Bi-objective Benchmark problems with Explicit Adjustable COrrelatioN control
Bibliographic record
Abstract
This paper presents BEACON, a novel methodology for generating bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Although numerous benchmark problems exist, continuous benchmarks lack systematic mechanisms to control objective correlations, critical in real-world optimisation. Our approach utilises Gaussian Process samples approximated via Random Fourier Features and a Cholesky-based correlation transformation to generate problems with tunable correlation values ranging from perfectly negative to perfectly positive. Experiments with three popular multi-objective evolutionary algorithms (NSGA-II, SMS-EMOA, MOEA/D) across varying correlation levels and decision space dimensions reveal that algorithm performance depends on the interplay between correlation structure and dimensionality rather than either factor in isolation. Our framework bridges the gap between discrete benchmarks with correlation control and continuous benchmarks without it, enabling systematic study of correlation effects on optimisation dynamics and supporting the development of algorithms that can adapt to different correlation structures found in real-world problems.
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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 | 0.002 | 0.008 |
| 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 | 0.002 |
| 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".