-
Notifications
You must be signed in to change notification settings - Fork 27
/
saes.py
165 lines (145 loc) · 8.39 KB
/
saes.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
import numpy as np # engine for numerical computing
from pypop7.optimizers.es.es import ES # abstract class of all evolution strategies (ES)
class SAES(ES):
"""Self-Adaptation Evolution Strategy (SAES).
.. note:: `SAES` adapts only the *global* step-size on-the-fly with a *relatively small* population, often
resulting in *slow* (and even *premature*) convergence for large-scale black-box optimization (LBO),
especially on *ill-conditioned* fitness landscapes. Therefore, it is recommended to first attempt more
advanced ES variants (e.g. `LMCMA`, `LMMAES`) for LBO. Here we include `SAES` mainly for *benchmarking*
and *theoretical* purpose.
Parameters
----------
problem : dict
problem arguments with the following common settings (`keys`):
* 'fitness_function' - objective function to be **minimized** (`func`),
* 'ndim_problem' - number of dimensionality (`int`),
* 'upper_boundary' - upper boundary of search range (`array_like`),
* 'lower_boundary' - lower boundary of search range (`array_like`).
options : dict
optimizer options with the following common settings (`keys`):
* 'max_function_evaluations' - maximum of function evaluations (`int`, default: `np.inf`),
* 'max_runtime' - maximal runtime to be allowed (`float`, default: `np.inf`),
* 'seed_rng' - seed for random number generation needed to be *explicitly* set (`int`);
and with the following particular settings (`keys`):
* 'sigma' - initial global step-size, aka mutation strength (`float`),
* 'mean' - initial (starting) point, aka mean of Gaussian search distribution (`array_like`),
* if not given, it will draw a random sample from the uniform distribution whose search range is
bounded by `problem['lower_boundary']` and `problem['upper_boundary']`.
* 'n_individuals' - number of offspring, aka offspring population size (`int`, default:
`4 + int(3*np.log(problem['ndim_problem']))`),
* 'n_parents' - number of parents, aka parental population size (`int`, default:
`int(options['n_individuals']/2)`),
* 'lr_sigma' - learning rate of global step-size (`float`, default:
`1.0/np.sqrt(2*problem['ndim_problem'])`).
Examples
--------
Use the black-box optimizer `SAES` to minimize the well-known test function
`Rosenbrock <http://en.wikipedia.org/wiki/Rosenbrock_function>`_:
.. code-block:: python
:linenos:
>>> import numpy # engine for numerical computing
>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized
>>> from pypop7.optimizers.es.saes import SAES
>>> problem = {'fitness_function': rosenbrock, # to define problem arguments
... 'ndim_problem': 2,
... 'lower_boundary': -5.0*numpy.ones((2,)),
... 'upper_boundary': 5.0*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000, # to set optimizer options
... 'seed_rng': 2022,
... 'mean': 3.0*numpy.ones((2,)),
... 'sigma': 3.0} # global step-size may need to be tuned
>>> saes = SAES(problem, options) # to initialize the optimizer class
>>> results = saes.optimize() # to run the optimization/evolution process
>>> # to return the number of function evaluations and the best-so-far fitness
>>> print(f"SAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
SAES: 5000, 0.012622712890954227
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/mvkspst4>`_ for more details.
Attributes
----------
best_so_far_x : `array_like`
final best-so-far solution found during entire optimization.
best_so_far_y : `array_like`
final best-so-far fitness found during entire optimization.
lr_sigma : `float`
learning rate of global step-size adaptation.
mean : `array_like`
initial (starting) point, aka mean of Gaussian search distribution.
n_individuals : `int`
number of offspring, aka offspring population size.
n_parents : `int`
number of parents, aka parental population size.
sigma : `float`
final global step-size, aka mutation strength (changed during optimization).
References
----------
Beyer, H.G., 2020, July.
`Design principles for matrix adaptation evolution strategies.
<https://dl.acm.org/doi/abs/10.1145/3377929.3389870>`_
In Proceedings of ACM Conference on Genetic and Evolutionary Computation Companion (pp. 682-700). ACM.
http://www.scholarpedia.org/article/Evolution_strategies
See its official Matlab/Octave version from `Prof. Beyer <https://homepages.fhv.at/hgb/>`_:
https://homepages.fhv.at/hgb/downloads/mu_mu_I_lambda-ES.oct
"""
def __init__(self, problem, options):
ES.__init__(self, problem, options)
if self.lr_sigma is None:
self.lr_sigma = 1.0/np.sqrt(2*self.ndim_problem)
def initialize(self, is_restart=False):
x = np.empty((self.n_individuals, self.ndim_problem)) # offspring population
mean = self._initialize_mean(is_restart) # mean of Gaussian search distribution
sigmas = np.ones((self.n_individuals,)) # global step-sizes for all offspring
y = np.empty((self.n_individuals,)) # fitness (no evaluation)
self._list_initial_mean.append(np.copy(mean))
return x, mean, sigmas, y
def iterate(self, x=None, mean=None, sigmas=None, y=None, args=None):
for k in range(self.n_individuals): # to sample offspring population
if self._check_terminations():
return x, sigmas, y
sigmas[k] = self.sigma*np.exp(self.lr_sigma*self.rng_optimization.standard_normal())
x[k] = mean + sigmas[k]*self.rng_optimization.standard_normal((self.ndim_problem,))
y[k] = self._evaluate_fitness(x[k], args)
return x, sigmas, y
def restart_reinitialize(self, y):
min_y = np.min(y)
if min_y < self._list_fitness[-1]:
self._list_fitness.append(min_y)
else:
self._list_fitness.append(self._list_fitness[-1])
is_restart_1, is_restart_2 = self.sigma < self.sigma_threshold, False
if len(self._list_fitness) >= self.stagnation:
is_restart_2 = (self._list_fitness[-self.stagnation] - self._list_fitness[-1]) < self.fitness_diff
is_restart = bool(is_restart_1) or bool(is_restart_2)
if is_restart:
self._print_verbose_info([], y, True)
if self.verbose:
print(' ....... *** restart *** .......')
self._n_restart += 1
self._list_generations.append(self._n_generations) # for each restart
self._n_generations = 0
self.n_individuals *= 2
self.n_parents = int(self.n_individuals/2)
self._list_fitness = [np.inf]
return is_restart
def restart_initialize(self, x=None, mean=None, sigmas=None, y=None):
if self.restart_reinitialize(y):
self.sigma = np.copy(self._sigma_bak)
x, mean, sigmas, y = self.initialize(True)
return x, mean, sigmas, y
def optimize(self, fitness_function=None, args=None): # for all generations (iterations)
fitness = ES.optimize(self, fitness_function)
x, mean, sigmas, y = self.initialize()
while True:
# sample and evaluate offspring population
x, sigmas, y = self.iterate(x, mean, sigmas, y, args)
if self._check_terminations():
break
self._print_verbose_info(fitness, y)
self._n_generations += 1
order = np.argsort(y)[:self.n_parents]
# use intermediate multi-recombination
mean = np.mean(x[order], axis=0)
self.sigma = np.mean(sigmas[order])
if self.is_restart:
x, mean, sigmas, y = self.restart_initialize(x, mean, sigmas, y)
return self._collect(fitness, y, mean)