Schwefel’s Self-Adaptation Evolution Strategy (SSAES)
- class pypop7.optimizers.es.ssaes.SSAES(problem, options)[source]
Schwefel’s Self-Adaptation Evolution Strategy (SSAES).
Note
SSAES adapts all the individual step-sizes (aka coordinate-wise standard deviations) on-the-fly, proposed by Schwefel (one recipient of IEEE Evolutionary Computation Pioneer Award 2002 and IEEE Frank Rosenblatt Award 2011). Since it often needs a relatively large population (e.g., larger than number of dimensionality) for reliable self-adaptation, SSAES suffers easily from slow convergence for large-scale black-box optimization. Therefore, it is recommended to first attempt more advanced ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization. Here we include SSAES mainly for benchmarking and theoretical purpose. Currently the restart process is not implemented owing to its typically slow convergence.
- 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: 5*problem[‘ndim_problem’]),
’n_parents’ - number of parents, aka parental population size (int, default: int(options[‘n_individuals’]/4)),
’lr_sigma’ - learning rate of global step-size self-adaptation (float, default: 1.0/np.sqrt(problem[‘ndim_problem’])),
’lr_axis_sigmas’ - learning rate of individual step-sizes self-adaptation (float, default: 1.0/np.power(problem[‘ndim_problem’], 1.0/4.0)).
Examples
Use the black-box optimizer SSAES to minimize the well-known test function Rosenbrock:
1>>> import numpy # engine for numerical computing 2>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized 3>>> from pypop7.optimizers.es.ssaes import SSAES 4>>> problem = {'fitness_function': rosenbrock, # to define problem arguments 5... 'ndim_problem': 2, 6... 'lower_boundary': -5.0*numpy.ones((2,)), 7... 'upper_boundary': 5.0*numpy.ones((2,))} 8>>> options = {'max_function_evaluations': 5000, # to set optimizer options 9... 'seed_rng': 2022, 10... 'mean': 3.0*numpy.ones((2,)), 11... 'sigma': 3.0} # global step-size may need to be tuned 12>>> ssaes = SSAES(problem, options) # to initialize the black-box optimizer class 13>>> results = ssaes.optimize() # to run the optimization/evolution process 14>>> # to return the number of function evaluations and the best-so-far fitness 15>>> print(f"SSAES: {results['n_function_evaluations']}, {results['best_so_far_y']}") 16SSAES: 5000, 0.00023558230456829403
For its correctness checking of coding, refer to this code-based repeatability report for more details.
- best_so_far_x
final best-so-far solution found during entire optimization.
- Type:
array_like
- best_so_far_y
final best-so-far fitness found during entire optimization.
- Type:
array_like
- lr_axis_sigmas
learning rate of individual step-sizes self-adaptation.
- Type:
float
- lr_sigma
learning rate of global step-size self-adaptation.
- Type:
float
- mean
initial (starting) point, aka mean of Gaussian search distribution.
- Type:
array_like
- n_individuals
number of offspring, aka offspring population size.
- Type:
int
- n_parents
number of parents, aka parental population size.
- Type:
int
- sigma
initial global step-size, aka mutation strength.
- Type:
float
- _axis_sigmas
final individuals step-sizes (updated during optimization).
- Type:
array_like
References
Hansen, N., Arnold, D.V. and Auger, A., 2015. Evolution strategies. In Springer Handbook of Computational Intelligence (pp. 871-898). Springer, Berlin, Heidelberg.
Beyer, H.G. and Schwefel, H.P., 2002. Evolution strategies–A comprehensive introduction. Natural Computing, 1(1), pp.3-52.
Schwefel, H.P., 1988. Collective intelligence in evolving systems. In Ecodynamics (pp. 95-100). Springer, Berlin, Heidelberg.
Schwefel, H.P., 1984. Evolution strategies: A family of non-linear optimization techniques based on imitating some principles of organic evolution. Annals of Operations Research, 1(2), pp.165-167.