Fast calculation of Pareto front in Python

Question

I have a set of points in a 3D space, from which I need to find the Pareto frontier. Speed of execution is very important here, and time increases very fast as I add points

Answer 1

Peter, nice response.

I just wanted to generalise for those who want to choose between maximisation to your default of minimisation. It's a trivial fix, but nice to document here:

def is_pareto(costs, maximise=False):
    """
    :param costs: An (n_points, n_costs) array
    :maximise: boolean. True for maximising, False for minimising
    :return: A (n_points, ) boolean array, indicating whether each point is Pareto efficient
    """
    is_efficient = np.ones(costs.shape[0], dtype = bool)
    for i, c in enumerate(costs):
        if is_efficient[i]:
            if maximise:
                is_efficient[is_efficient] = np.any(costs[is_efficient]>=c, axis=1)  # Remove dominated points
            else:
                is_efficient[is_efficient] = np.any(costs[is_efficient]<=c, axis=1)  # Remove dominated points
    return is_efficient