from typing import Callable, Optional
import torch
from evox.core import Algorithm, Mutable
from evox.operators.crossover import simulated_binary
from evox.operators.mutation import polynomial_mutation
from evox.operators.selection import non_dominate_rank, tournament_selection
from evox.utils import clamp, lexsort
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def cal_hv(fit: torch.Tensor, ref: torch.Tensor, pop_size: int, n_sample: int):
n, m = fit.size()
alpha = torch.cumprod(torch.cat([torch.ones(1, device=fit.device), (pop_size - torch.arange(1, n, device=fit.device)) / (n - torch.arange(1, n, device=fit.device))]), dim=0) / torch.arange(1, n + 1, device=fit.device)
alpha = torch.nan_to_num(alpha)
f_min = torch.min(fit, dim=0).values
samples = torch.rand(n_sample, m, device=fit.device) * (ref - f_min) + f_min
ds = torch.zeros(n_sample, dtype=torch.int64, device=fit.device)
pds = (fit.unsqueeze(0).expand(n_sample, -1, -1) - samples.unsqueeze(1).expand(-1, n, -1) <= 0).all(dim=2)
ds = torch.sum(torch.where(pds, ds.unsqueeze(1) + 1, ds.unsqueeze(1)), dim=1)
ds = torch.where(ds == 0, ds, ds - 1)
temp = torch.where(pds.T, ds.unsqueeze(0), -1)
value = torch.where(temp != -1, alpha[temp], torch.tensor(0, dtype=torch.float32))
f = torch.sum(value, dim=1)
f = f * torch.prod(ref - f_min) / n_sample
return f
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class HypE(Algorithm):
"""
The tensorized version of HypE algorithm.
:references:
[1] J. Bader and E. Zitzler, "HypE: An algorithm for fast hypervolume-based many-objective optimization,"
Evolutionary Computation, vol. 19, no. 1, pp. 45-76, 2011. Available:
https://direct.mit.edu/evco/article-abstract/19/1/45/1363/HypE-An-Algorithm-for-Fast-Hypervolume-Based-Many
[2] Z. Liang, H. Li, N. Yu, K. Sun, and R. Cheng, "Bridging Evolutionary Multiobjective Optimization and
GPU Acceleration via Tensorization," IEEE Transactions on Evolutionary Computation, 2025. Available:
https://ieeexplore.ieee.org/document/10944658
"""
def __init__(
self,
pop_size: int,
n_objs: int,
lb: torch.Tensor,
ub: torch.Tensor,
n_sample: int = 10000,
selection_op: Optional[Callable] = None,
mutation_op: Optional[Callable] = None,
crossover_op: Optional[Callable] = None,
device: torch.device | None = None,
):
"""Initializes the HypE algorithm.
:param pop_size: The size of the population.
:param n_objs: The number of objective functions in the optimization problem.
:param lb: The lower bounds for the decision variables (1D tensor).
:param ub: The upper bounds for the decision variables (1D tensor).
:param n_sample: The number of samples for hypervolume calculation (optional).
:param selection_op: The selection operation for evolutionary strategy (optional).
:param mutation_op: The mutation operation, defaults to `polynomial_mutation` if not provided (optional).
:param crossover_op: The crossover operation, defaults to `simulated_binary` if not provided (optional).
:param device: The device on which computations should run (optional). Defaults to PyTorch's default device.
"""
super().__init__()
self.pop_size = pop_size
self.n_objs = n_objs
if device is None:
device = torch.get_default_device()
# check
assert lb.shape == ub.shape and lb.ndim == 1 and ub.ndim == 1
assert lb.dtype == ub.dtype and lb.device == ub.device
self.dim = lb.shape[0]
# write to self
self.lb = lb.to(device=device)
self.ub = ub.to(device=device)
self.n_sample = n_sample
self.selection = selection_op
self.mutation = mutation_op
self.crossover = crossover_op
self.selection = tournament_selection
if self.mutation is None:
self.mutation = polynomial_mutation
if self.crossover is None:
self.crossover = simulated_binary
length = ub - lb
population = torch.rand(self.pop_size, self.dim, device=device)
population = length * population + lb
self.ref = Mutable(torch.ones(n_objs, device=device))
self.pop = Mutable(population)
self.fit = Mutable(torch.full((self.pop_size, self.n_objs), torch.inf, device=device))
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def init_step(self):
"""
Perform the initialization step of the workflow.
Calls the `init_step` of the algorithm if overwritten; otherwise, its `step` method will be invoked.
"""
self.fit = self.evaluate(self.pop)
self.ref = torch.full((self.n_objs,), torch.max(self.fit).item() * 1.2, device=self.fit.device)
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def step(self):
"""Perform the optimization step of the workflow."""
hv = cal_hv(self.fit, self.ref, self.pop_size, self.n_sample)
mating_pool = self.selection(self.pop_size, -hv)
crossovered = self.crossover(self.pop[mating_pool])
offspring = self.mutation(crossovered, self.lb, self.ub)
offspring = clamp(offspring, self.lb, self.ub)
off_fit = self.evaluate(offspring)
merge_pop = torch.cat([self.pop, offspring], dim=0)
merge_fit = torch.cat([self.fit, off_fit], dim=0)
rank = non_dominate_rank(merge_fit)
order = torch.argsort(rank)
worst_rank = rank[order[self.pop_size - 1]]
mask = rank <= worst_rank
hv = cal_hv(merge_fit, self.ref, torch.sum(mask) - self.pop_size, self.n_sample)
dis = torch.where(mask, hv, -torch.inf)
combined_indices = lexsort([-dis, rank])[: self.pop_size]
self.pop = merge_pop[combined_indices]
self.fit = merge_fit[combined_indices]
EvoX