Rsf7 Benchmark Eval

---
name: rsf7-benchmark-eval
description: Evaluates the optimization capability of evolutionary algorithms on a highly multimodal, nonseparable benchmark function across low (d=5) and high (d=20) dimensional settings. It measures how effectively the algorithm navigates complex, multi-peaked likelihood surfaces to locate the global optimum within a fixed computational budget. Use when the user wants to benchmark on Rotated Schaffers F7 (RSF7), or asks about evaluating this task. Reports mean_max_function_value.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 1704.05761
  bibtex_key: liu2017maximum
  confidence: high
---

# rsf7-benchmark-eval

> Maximum Likelihood Estimation based on Random Subspace EDA: Application to Extrasolar Planet Detection — Liu et al. (2017) (arXiv:1704.05761, 2017)

## What this evaluates

Evaluates the optimization capability of evolutionary algorithms on a highly multimodal, nonseparable benchmark function across low (d=5) and high (d=20) dimensional settings. It measures how effectively the algorithm navigates complex, multi-peaked likelihood surfaces to locate the global optimum within a fixed computational budget.

## Datasets

- **Rotated Schaffers F7 (RSF7)** — total ?; splits: test (-1)

## Metrics

- `mean_max_function_value` **(primary)** — range: [0, 800]
  - Average of the maximum function value $g(\theta)$ found across 50 independent runs. The theoretical global maximum is 800.

## Input / output format

**Input**: A parameter vector $\theta$ of dimension $d$ (5 or 20) to be evaluated by the objective function $g(\theta) = -f(\theta)$.

**Output**: The estimated maximum function value $g(\theta)$ achieved by the algorithm within the evaluation budget.

## Scoring recipe

```python
def score(predictions, gold):
    # predictions: list of max values from 50 runs
    # gold: 800 (theoretical max)
    mean_val = sum(predictions) / len(predictions)
    return mean_val
```

## Common pitfalls

- The benchmark is originally a minimization function (RSF7) but is negated to $g(\theta)=-f(\theta)$ for maximization; the target value is 800, not 0.
- Evaluation budgets and population sizes scale significantly with dimension: $d=5$ uses $10^6$ evals and pop=20000, while $d=20$ uses $5\times10^6$ evals and pop=200000.
- Baseline comparisons rely on specific third-party implementations (e.g., CMA-ES diagonal option) with default parameters, making exact reproduction difficult without the cited code.

## Evidence (verbatim from paper)

> We ran each method for 50 times and calculated the mean of its estimate on the maximal function value. ... The maximum function value of $g(\theta)$ is 800, which is the target for the algorithm to search.

## Citation

```bibtex
@misc{liu2017maximum,
  title={Maximum Likelihood Estimation based on Random Subspace EDA: Application to Extrasolar Planet Detection},
  author={Liu et al. (2017)},
  year={2017},
  note={arXiv:1704.05761}
}
```

- arXiv: 1704.05761