tools.py 文件源码

def diversity(first_front, first, last):
    """Given a Pareto front `first_front` and the two extreme points of the 
    optimal Pareto front, this function returns a metric of the diversity 
    of the front as explained in the original NSGA-II article by K. Deb.
    The smaller the value is, the better the front is.
    """
    df = hypot(first_front[0].fitness.values[0] - first[0],
               first_front[0].fitness.values[1] - first[1])
    dl = hypot(first_front[-1].fitness.values[0] - last[0],
               first_front[-1].fitness.values[1] - last[1])
    dt = [hypot(first.fitness.values[0] - second.fitness.values[0],
                first.fitness.values[1] - second.fitness.values[1])
          for first, second in zip(first_front[:-1], first_front[1:])]

    if len(first_front) == 1:
        return df + dl

    dm = sum(dt)/len(dt)
    di = sum(abs(d_i - dm) for d_i in dt)
    delta = (df + dl + di)/(df + dl + len(dt) * dm )
    return delta