Run2 pareto optimization

Pareto Frontier for Multi-Objective Optimization

Definition

Point A dominates Point B iff:

• A.F1 >= B.F1 AND A.delta <= B.delta
• With at least one strict inequality

A point is Pareto-optimal if no other point dominates it.

Efficient Implementation

def find_pareto(results):
    """results: list of (f1, delta, ...) tuples. Maximize f1, minimize delta."""
    # Sort by F1 descending for efficiency
    indexed = sorted(enumerate(results), key=lambda x: -x[1][0])
    pareto = []
    min_delta = float('inf')

    for idx, r in indexed:
        if r[1] <= min_delta:
            pareto.append(r)
            min_delta = r[1]

    return pareto

This O(n log n) approach works because after sorting by F1 descending, a point is Pareto-optimal iff its delta is less than or equal to the minimum delta seen so far.