Pareto frontier

Pareto Frontier Identification

A point is Pareto-optimal if no other point is better in all objectives. For this task, we want to maximize F1 and minimize Delta.

Logic

A solution A dominates B if:

1. A.F1 >= B.F1 AND A.Delta <= B.Delta
2. At least one inequality is strict.

Python Implementation

def is_pareto_efficient(costs):
    """
    Find the pareto-efficient points
    :param costs: An (n_points, n_costs) array where costs are to be MINIMIZED.
    :return: A boolean array of length n_points indicating efficiency.
    """
    is_efficient = np.ones(costs.shape[0], dtype=bool)
    for i, c in enumerate(costs):
        if is_efficient[i]:
            # Keep any point that is better than 'c' in at least one attribute
            # OR equal in all attributes (to handle duplicates)
            is_efficient[is_efficient] = np.any(costs[is_efficient] < c, axis=1) | \
                                          np.all(costs[is_efficient] == c, axis=1)
            is_efficient[i] = True  # And keep self
    return is_efficient

# For Max F1 and Min Delta, transform F1:
# costs = np.array([[-f1, delta] for f1, delta in results])
# efficient_mask = is_pareto_efficient(costs)