## Line Chart: Ratios of the current Pareto front size for solving OneMinMax ### Overview The chart illustrates the convergence behavior of Pareto front size ratios across different population sizes (n=100, 200, 300, 400) over 3000 generations. All lines exhibit rapid initial growth followed by stabilization near 0.8 ratio values. ### Components/Axes - **X-axis (Generations)**: Linear scale from 0 to 3000 in increments of 500 - **Y-axis (Ratios)**: Logarithmic scale from 0.1 to 0.9 in increments of 0.1 - **Legend**: Positioned in top-right quadrant with four entries: - Black squares: n=100 - Orange diamonds: n=200 - Green triangles: n=300 - Red crosses: n=400 - **Error bars**: Present on all data points, indicating measurement uncertainty ### Detailed Analysis 1. **n=100 (Black squares)**: - Initial ratio: ~0.1 at 0 generations - Rapid ascent to 0.8 by ~500 generations - Plateau maintained with minor fluctuations (±0.02) - Error bars: ~±0.01 2. **n=200 (Orange diamonds)**: - Initial ratio: ~0.1 at 0 generations - Slightly slower ascent (reaches 0.8 by ~750 generations) - Stable plateau with similar error margins 3. **n=300 (Green triangles)**: - Initial ratio: ~0.1 at 0 generations - Gradual increase (reaches 0.8 by ~1000 generations) - Consistent plateau with error bars matching other series 4. **n=400 (Red crosses)**: - Initial ratio: ~0.1 at 0 generations - Slowest ascent (reaches 0.8 by ~1250 generations) - Maintains stable plateau with comparable error margins ### Key Observations - All population sizes converge to similar final ratios (~0.8) - Larger populations (n=400) require more generations to reach convergence - Error margins remain consistently small (±0.01-0.02) across all series - No significant outliers or anomalies detected ### Interpretation The data demonstrates that while larger population sizes (n) require more generations to reach Pareto front convergence, they ultimately achieve similar stabilization ratios. This suggests: 1. **Population efficiency tradeoff**: Smaller populations converge faster but may require more generations for larger problems 2. **Algorithmic stability**: The plateau region indicates algorithmic stability once convergence is achieved 3. **Diminishing returns**: Increasing population size beyond a certain point (n=300-400) yields minimal improvements in final ratio The consistent error margins across all series suggest reliable measurement methodology. The logarithmic y-axis emphasizes early-stage growth differences while compressing the plateau region, highlighting the algorithm's convergence characteristics.