import torch
[docs]
def hv(objs: torch.Tensor, ref: torch.Tensor, num_sample: int = 100000):
"""
Monte Carlo Hypervolume Calculation using bounding cube method.
:param objs: Objective points of shape (n_points, n_objs).
:param ref: Reference point of shape (n_objs, ).
:param num_sample: Number of Monte Carlo samples.
:return: Estimated hypervolume.
"""
points = torch.abs(objs - ref)
bound = torch.max(points, dim=0).values
max_vol = torch.prod(bound)
samples = torch.rand(num_sample, points.size(1)) * bound
in_hypercube = torch.any(torch.all(samples.unsqueeze(1) < points.unsqueeze(0), dim=2), dim=1)
hv = in_hypercube.sum() / num_sample * max_vol
return hv
EvoX