Estimation of Multivariate Normal Algorithm (EMNA)¶
- class pypop7.optimizers.eda.emna.EMNA(problem, options)¶
Estimation of Multivariate Normal Algorithm (EMNA).
Note
EMNA learns the full covariance matrix of the Gaussian sampling distribution, resulting in a cubic time complexity w.r.t. each sampling. Therefore, it is rarely used for large-scale black-box optimization (LSBBO). It is highly recommended to first attempt other more advanced methods for LSBBO.
- 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 (float, default: np.Inf),
’seed_rng’ - seed for random number generation needed to be explicitly set (int);
- and with the following particular settings (keys):
’n_individuals’ - number of offspring, offspring population size (int, default: 200),
’n_parents’ - number of parents, parental population size (int, default: int(options[‘n_individuals’]/2)).
Examples
Use the optimizer 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.eda.emna import EMNA 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>>> emna = EMNA(problem, options) # initialize the optimizer class 11>>> results = emna.optimize() # run the optimization process 12>>> # return the number of function evaluations and best-so-far fitness 13>>> print(f"EMNA: {results['n_function_evaluations']}, {results['best_so_far_y']}") 14EMNA: 5000, 0.008375142194038284
For its correctness checking of coding, refer to this code-based repeatability report for more details.
- n_individuals¶
number of offspring, aka offspring population size.
- Type:
int
- n_parents¶
number of parents, aka parental population size.
- Type:
int
References
Larrañaga, P. and Lozano, J.A. eds., 2002. Estimation of distribution algorithms: A new tool for evolutionary computation. Springer Science & Business Media. https://link.springer.com/book/10.1007/978-1-4615-1539-5
Larranaga, P., Etxeberria, R., Lozano, J.A. and Pena, J.M., 2000. Optimization in continuous domains by learning and simulation of Gaussian networks. Technical Report, Department of Computer Science and Artificial Intelligence, University of the Basque Country. https://tinyurl.com/3bw6n3x4