Matrix Adaptation Evolution Strategy (MAES)

class pypop7.optimizers.es.maes.MAES(problem, options)[source]

Matrix Adaptation Evolution Strategy (MAES).

Note

MAES is a powerful simplified version of the well-established CMA-ES algorithm nearly without significant performance loss, designed in 2017 by Beyer and Sendhoff. One obvious advantage of such a simplification is to help better understand the underlying working principles (e.g., invariance and unbias) of CMA-ES, which are often thought to be rather complex for newcomers. It is highly recommended to first attempt more advanced ES variants (e.g., LMCMA, LMMAES) for large-scale black-box optimization, since MAES has a cubic time complexity (w.r.t. each sampling). Note that another improved version called FMAES provides a relatively more efficient implementation for MAES with quadratic time complexity (w.r.t. each sampling).

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)).

Examples

Use the optimizer MAES 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.maes import MAES
 4>>> problem = {'fitness_function': rosenbrock,  # 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,  # set optimizer options
 9...            'seed_rng': 2022,
10...            'mean': 3.0*numpy.ones((2,)),
11...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
12>>> maes = MAES(problem, options)  # initialize the optimizer class
13>>> results = maes.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"MAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16MAES: 5000, 2.129367016460251e-19

For its correctness checking of coding, refer to this code-based repeatability report for more details.

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

final global step-size, aka mutation strength.

Type:

float

References

Beyer, H.G., 2020, July. Design principles for matrix adaptation evolution strategies. In Proceedings of ACM Conference on Genetic and Evolutionary Computation Companion (pp. 682-700).

Loshchilov, I., Glasmachers, T. and Beyer, H.G., 2019. Large scale black-box optimization by limited-memory matrix adaptation. IEEE Transactions on Evolutionary Computation, 23(2), pp.353-358.

Beyer, H.G. and Sendhoff, B., 2017. Simplify your covariance matrix adaptation evolution strategy. IEEE Transactions on Evolutionary Computation, 21(5), pp.746-759.

See the official Matlab version from Prof. Beyer: https://homepages.fhv.at/hgb/downloads/ForDistributionFastMAES.tar