## Chart: AlphaEvolve's Score vs. Optimal Score
### Overview
The image is a line chart comparing AlphaEvolve's score against an optimal score, plotted against the grid size (n). The chart shows how AlphaEvolve's performance compares to the theoretical optimal score as the grid size increases.
### Components/Axes
* **X-axis:** Grid Size (n), ranging from 0 to 100 in increments of 20.
* **Y-axis:** Number of Tiles, ranging from 0 to 120 in increments of 20.
* **Legend:** Located in the top-left corner.
* Blue line with circular markers: "AlphaEvolve's Score"
* Orange dashed line: "Optimal Score (n + [2√n] - 3)"
### Detailed Analysis
* **AlphaEvolve's Score (Blue Line):**
* Trend: Generally increases with grid size, but with significant upward spikes at irregular intervals.
* Data Points:
* At n=0, Score ≈ 4
* At n=20, Score ≈ 28
* At n=40, Score ≈ 44
* At n=60, Score ≈ 70
* At n=80, Score ≈ 124
* At n=100, Score ≈ 124
* **Optimal Score (Orange Dashed Line):**
* Trend: Increases linearly with grid size.
* Data Points:
* At n=0, Score ≈ 4
* At n=20, Score ≈ 28
* At n=40, Score ≈ 52
* At n=60, Score ≈ 70
* At n=80, Score ≈ 95
* At n=100, Score ≈ 115
### Key Observations
* AlphaEvolve's score closely follows the optimal score for smaller grid sizes (n < 60).
* For larger grid sizes (n > 60), AlphaEvolve's score exhibits significant spikes, exceeding the optimal score at certain points.
* The optimal score increases more smoothly and linearly compared to AlphaEvolve's score.
### Interpretation
The chart suggests that AlphaEvolve performs well in smaller grid sizes, closely matching the optimal score. However, as the grid size increases, its performance becomes more volatile, with occasional spikes indicating potentially successful strategies or configurations at specific grid sizes. The spikes suggest that AlphaEvolve is sometimes able to significantly outperform the expected optimal score, but its performance is not consistently above the optimal score. The optimal score line represents a theoretical upper bound, and AlphaEvolve's ability to exceed it at times indicates that the algorithm is finding solutions that are better than the average optimal solution.
