A Review of Benchmark and Test Functions for Global Optimization Algorithms and Metaheuristics
Bibliographic record
Abstract
ABSTRACT Benchmarking in optimization is a critical step in evaluating the performance, robustness, and scalability of machine learning algorithms and metaheuristics. While trends in benchmark design continue to evolve, synthetic functions remain vital for fundamental stress tests and theoretical evaluations. As several benchmark and test functions have been developed and derived over the past decades, little attention has been given to classifying such test functions and the rationale behind their usage. From this lens, this paper reviews and categorizes a broad range of functions often employed in assessing optimizers and metaheuristics. More specifically, we classify test functions based on modality, dimensionality, separability, smoothness, constraints, and noise characteristics to offer a broad view that aids in selecting appropriate benchmarks for various algorithmic challenges. Then, this review also discusses in detail the 25 most commonly used functions in the open literature and proposes two new, highly dimensional, dynamic, and challenging functions that could be used for testing new algorithms. Finally, this review identifies gaps in current benchmarking practices and directions for future research, as well as suggests best practices and guidelines.
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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 | 0.008 | 0.025 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.010 | 0.014 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".