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Identify Pareto-optimal solutions from multi-objective optimization results.
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| name | pareto-frontier-analysis |
| description | Identify Pareto-optimal solutions from multi-objective optimization results. |
The Pareto frontier identifies non-dominated solutions where you cannot improve one objective without worsening another. For this task: maximize F1 score and minimize delta distance.
import numpy as np
import pandas as pd
def compute_pareto_frontier(results_df):
"""
Find Pareto-optimal solutions from results.
Args:
results_df: DataFrame with columns 'f1' and 'delta'
Returns:
pareto_indices: Boolean array marking Pareto-optimal solutions
"""
f1_scores = results_df['f1'].values
deltas = results_df['delta'].values
n = len(results_df)
is_pareto = np.ones(n, dtype=bool)
for i in range(n):
# Check if solution i is dominated
for j in range(n):
if i == j:
continue
# Solution j dominates solution i if:
# - j has better F1 (higher) AND
# - j has better delta (lower)
if f1_scores[j] > f1_scores[i] and deltas[j] < deltas[i]:
is_pareto[i] = False
break
return is_pareto
def compute_pareto_frontier_fast(f1_scores, deltas):
"""Fast vectorized computation of Pareto frontier."""
n = len(f1_scores)
is_pareto = np.ones(n, dtype=bool)
# For each solution, check if any other solution dominates it
for i in range(n):
dominated = (f1_scores > f1_scores[i]) & (deltas < deltas[i])
if np.any(dominated):
is_pareto[i] = False
return is_pareto
import matplotlib.pyplot as plt
def plot_pareto_frontier(results_df, pareto_mask):
"""Visualize the Pareto frontier."""
plt.figure(figsize=(10, 6))
# Plot all points
plt.scatter(results_df[~pareto_mask]['delta'],
results_df[~pareto_mask]['f1'],
alpha=0.3, label='Dominated', s=30)
# Plot Pareto points
pareto_df = results_df[pareto_mask]
plt.scatter(pareto_df['delta'], pareto_df['f1'],
color='red', label='Pareto-optimal', s=100, marker='*')
plt.xlabel('Delta (Average Distance)')
plt.ylabel('F1 Score')
plt.title('Pareto Frontier')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()
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