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from eaf.eaf import get_empirical_attainment_surface | ||
from eaf.plot_surface import EmpiricalAttainmentFuncPlot | ||
from eaf.utils import pareto_front_to_surface | ||
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__version__ = "0.4.3" | ||
__copyright__ = "Copyright (C) 2023 Shuhei Watanabe" | ||
__licence__ = "Apache-2.0 License" | ||
__author__ = "Shuhei Watanabe" | ||
__author_email__ = "[email protected]" | ||
__url__ = "https://github.com/nabenabe0928/empirical-attainment-func" | ||
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__all__ = [ | ||
"get_empirical_attainment_surface", | ||
"pareto_front_to_surface", | ||
"EmpiricalAttainmentFuncPlot", | ||
] |
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from __future__ import annotations | ||
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from eaf.utils import LOGEPS | ||
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from fast_pareto import is_pareto_front | ||
from fast_pareto.pareto import _change_directions | ||
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import numpy as np | ||
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def _get_pf_set_list(costs: np.ndarray) -> list[np.ndarray]: | ||
""" | ||
Get the list of Pareto front sets. | ||
Args: | ||
costs (np.ndarray): | ||
The costs obtained in the observations. | ||
The shape must be (n_independent_runs, n_samples, n_obj). | ||
For now, we only support n_obj == 2. | ||
Returns: | ||
pf_set_list (list[np.ndarray]): | ||
The list of the Pareto front sets. | ||
The shape is (trial number, Pareto solution index, objective index). | ||
Note that each pareto front set is sorted based on the ascending order of | ||
the first objective. | ||
""" | ||
_cost_copy = costs.copy() | ||
pf_set_list: list[np.ndarray] = [] | ||
for _costs in _cost_copy: | ||
# Sort by the first objective, then the second objective | ||
order = np.lexsort((-_costs[:, 1], _costs[:, 0])) | ||
_costs = _costs[order] | ||
pf_set_list.append(_costs[is_pareto_front(_costs, filter_duplication=True)]) | ||
return pf_set_list | ||
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def _compute_emp_att_surf( | ||
X: np.ndarray, pf_set_list: list[np.ndarray], levels: np.ndarray | ||
) -> np.ndarray: | ||
""" | ||
Compute the empirical attainment surface of the given Pareto front sets. | ||
Args: | ||
x (np.ndarray): | ||
The first objective values appeared in pf_set_list. | ||
This array is sorted in the ascending order. | ||
The shape is (number of possible values, ). | ||
levels (np.ndarray): | ||
A list of `level` described below: | ||
Control the k in the k-% attainment surface. | ||
k = level / n_independent_runs | ||
must hold. | ||
level must be in [1, n_independent_runs]. | ||
level=1 leads to the best attainment surface, | ||
level=n_independent_runs leads to the worst attainment surface, | ||
level=n_independent_runs//2 leads to the median attainment surface. | ||
pf_set_list (list[np.ndarray]): | ||
The list of the Pareto front sets. | ||
The shape is (trial number, Pareto solution index, objective index). | ||
Note that each pareto front set is sorted based on the ascending order of | ||
the first objective. | ||
Returns: | ||
emp_att_surfs (np.ndarray): | ||
The vertices of the empirical attainment surfaces for each level. | ||
If emp_att_surf[i, j, 1] takes np.inf, this is not actually on the surface. | ||
The shape is (levels.size, X.size, 2). | ||
Reference: | ||
Title: On the Computation of the Empirical Attainment Function | ||
Authors: Carlos M. Fonseca et al. | ||
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.705.1929&rep=rep1&type=pdf | ||
NOTE: | ||
Our algorithm is slightly different from the original one, but the result will be same. | ||
More details below: | ||
When we define N = n_independent_runs, K = X.size, and S = n_samples, | ||
the original algorithm requires O(NK + K log K) | ||
and this algorithm requires O(NK log K). | ||
Although our algorithm is a bit worse than the original algorithm, | ||
since the enumerating Pareto solutions requires O(NS log S), | ||
which might be smaller complexity but will take more time in Python, | ||
the time complexity will not dominate the whole process. | ||
""" | ||
n_levels = len(levels) | ||
emp_att_surfs = np.zeros((n_levels, X.size, 2)) | ||
emp_att_surfs[..., 0] = X | ||
n_independent_runs = len(pf_set_list) | ||
y_candidates = np.zeros((X.size, n_independent_runs)) | ||
for i, pf_set in enumerate(pf_set_list): | ||
ub = np.searchsorted(pf_set[:, 0], X, side="right") | ||
y_min = np.minimum.accumulate(np.hstack([np.inf, pf_set[:, 1]])) | ||
y_candidates[:, i] = y_min[ub] | ||
else: | ||
y_candidates = np.sort(y_candidates, axis=-1) | ||
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y_sol = y_candidates[:, levels - 1].T | ||
emp_att_surfs[..., 1] = y_sol | ||
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for emp_att_surf in emp_att_surfs: | ||
idx = np.sum(emp_att_surf[:, 1] == np.inf) | ||
emp_att_surf[:idx, 0] = emp_att_surf[idx, 0] | ||
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return emp_att_surfs | ||
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def get_empirical_attainment_surface( | ||
costs: np.ndarray, | ||
levels: list[int], | ||
larger_is_better_objectives: list[int] | None = None, | ||
log_scale: list[int] | None = None, | ||
) -> np.ndarray: | ||
""" | ||
Get the empirical attainment surface given the costs observations. | ||
Args: | ||
costs (np.ndarray): | ||
The costs obtained in the observations. | ||
The shape must be (n_independent_runs, n_samples, n_obj). | ||
For now, we only support n_obj == 2. | ||
levels (list[int]): | ||
A list of `level` described below: | ||
Control the k in the k-% attainment surface. | ||
k = level / n_independent_runs | ||
must hold. | ||
level must be in [1, n_independent_runs]. | ||
level=1 leads to the best attainment surface, | ||
level=n_independent_runs leads to the worst attainment surface, | ||
level=n_independent_runs//2 leads to the median attainment surface. | ||
larger_is_better_objectives (list[int] | None): | ||
The indices of the objectives that are better when the values are larger. | ||
If None, we consider all objectives are better when they are smaller. | ||
log_scale (list[int] | None): | ||
The indices of the log scale. | ||
For example, if you would like to plot the first objective in the log scale, | ||
you need to feed log_scale=[0]. | ||
In principle, log_scale changes the minimum value of the axes | ||
from -np.inf to a small positive value. | ||
Returns: | ||
emp_att_surfs (np.ndarray): | ||
The costs attained by (level / n_independent_runs) * 100% of the trials. | ||
In other words, (level / n_independent_runs) * 100% of runs dominate | ||
or at least include those solutions in their Pareto front. | ||
Note that we only return the Pareto front of attained solutions. | ||
""" | ||
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if len(costs.shape) != 3: | ||
# costs.shape = (n_independent_runs, n_samples, n_obj) | ||
raise ValueError( | ||
f"costs must have the shape of (n_independent_runs, n_samples, n_obj), but got {costs.shape}" | ||
) | ||
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(n_independent_runs, _, n_obj) = costs.shape | ||
if n_obj != 2: | ||
raise NotImplementedError("Three or more objectives are not supported.") | ||
if not all(1 <= level <= n_independent_runs for level in levels): | ||
raise ValueError( | ||
f"All elements in levels must be in [1, n_independent_runs], but got {levels}" | ||
) | ||
if not np.all(np.maximum.accumulate(levels) == levels): | ||
raise ValueError(f"levels must be an increasing sequence, but got {levels}") | ||
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_costs = costs.copy() | ||
if larger_is_better_objectives is not None: | ||
_costs = _change_directions( | ||
_costs, larger_is_better_objectives=larger_is_better_objectives | ||
) | ||
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log_scale = log_scale if log_scale is not None else [] | ||
pf_set_list = _get_pf_set_list(_costs) | ||
pf_sols = np.vstack(pf_set_list) | ||
X = np.unique( | ||
np.hstack([LOGEPS if 0 in log_scale else -np.inf, pf_sols[:, 0], np.inf]) | ||
) | ||
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emp_att_surfs = _compute_emp_att_surf( | ||
X=X, pf_set_list=pf_set_list, levels=np.asarray(levels) | ||
) | ||
if larger_is_better_objectives is not None: | ||
emp_att_surfs = _change_directions( | ||
emp_att_surfs, larger_is_better_objectives=larger_is_better_objectives | ||
) | ||
if larger_is_better_objectives is not None and 0 in larger_is_better_objectives: | ||
emp_att_surfs = np.flip(emp_att_surfs, axis=1) | ||
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return emp_att_surfs |
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