Cumulative Step-size Adaptation Evolution Strategy (CSAES)¶
- class pypop7.optimizers.es.csaes.CSAES(problem, options)¶
Cumulative Step-size self-Adaptation Evolution Strategy (CSAES).
Note
CSAES adapts all the individual step-sizes on-the-fly with a relatively small population, according to the well-known CSA rule from the Evolutionary Computation community. The default setting (i.e., using a small population) may result in relatively fast (local) convergence, but with the risk of getting trapped in suboptima on multi-modal fitness landscape (which can be alleviated via restart).
AKA cumulative (evolution) path-length control.
- 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(np.floor(3*np.log(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 adaptation (float, default: np.sqrt(options[‘n_parents’]/(problem[‘ndim_problem’] + options[‘n_parents’]))).
Examples
Use the optimizer CSAES to minimize the well-known test function Rosenbrock:
1>>> import numpy 2>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized 3>>> from pypop7.optimizers.es.csaes import CSAES 4>>> problem = {'fitness_function': rosenbrock, # define problem arguments 5... 'ndim_problem': 2, 6... 'lower_boundary': -5*numpy.ones((2,)), 7... 'upper_boundary': 5*numpy.ones((2,))} 8>>> options = {'max_function_evaluations': 5000, # set optimizer options 9... 'seed_rng': 2022, 10... 'mean': 3*numpy.ones((2,)), 11... 'sigma': 0.1} # the global step-size may need to be tuned for better performance 12>>> csaes = CSAES(problem, options) # initialize the optimizer class 13>>> results = csaes.optimize() # run the optimization process 14>>> # return the number of function evaluations and best-so-far fitness 15>>> print(f"CSAES: {results['n_function_evaluations']}, {results['best_so_far_y']}") 16CSAES: 5000, 0.010143683086819875
For its correctness checking of coding, refer to this code-based repeatability report for more details.
- lr_sigma¶
learning rate of global step-size 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
References
Hansen, N., Arnold, D.V. and Auger, A., 2015. Evolution strategies. In Springer Handbook of Computational Intelligence (pp. 871-898). Springer, Berlin, Heidelberg. https://link.springer.com/chapter/10.1007%2F978-3-662-43505-2_44
Kern, S., Müller, S.D., Hansen, N., Büche, D., Ocenasek, J. and Koumoutsakos, P., 2004. Learning probability distributions in continuous evolutionary algorithms–a comparative review. Natural Computing, 3, pp.77-112. https://link.springer.com/article/10.1023/B:NACO.0000023416.59689.4e
Ostermeier, A., Gawelczyk, A. and Hansen, N., 1994, October. Step-size adaptation based on non-local use of selection information In International Conference on Parallel Problem Solving from Nature (pp. 189-198). Springer, Berlin, Heidelberg. http://link.springer.com/chapter/10.1007/3-540-58484-6_263