Limited Memory Matrix Adaptation Evolution Strategy (LMMAES)

class pypop7.optimizers.es.lmmaes.LMMAES(problem, options)

Limited-Memory Matrix Adaptation Evolution Strategy (LMMAES).

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_evolution_paths’ - number of evolution paths (int, default: 4 + int(3*np.log(problem[‘ndim_problem’]))),

  • ’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)),

  • ’c_s’ - learning rate of evolution path update (float, default: 2.0*options[‘n_individuals’]/problem[‘ndim_problem’]).

Examples

Use the optimizer to minimize the well-known test function Rosenbrock:

>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.es.lmmaes import LMMAES
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 200,
...            'lower_boundary': -5*numpy.ones((200,)),
...            'upper_boundary': 5*numpy.ones((200,))}
>>> options = {'max_function_evaluations': 500000,  # set optimizer options
...            'seed_rng': 0,
...            'mean': 3*numpy.ones((200,)),
...            'sigma': 0.1,  # the global step-size may need to be tuned for better performance
...            'is_restart': False}
>>> lmmaes = LMMAES(problem, options)  # initialize the optimizer class
>>> results = lmmaes.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"LMMAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
LMMAES: 500000, 1.0745854362945823e-06

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

c_s

learning rate of evolution path update.

Type:

float

mean

initial (starting) point, aka mean of Gaussian search distribution.

Type:

array_like

n_evolution_paths

number of evolution paths.

Type:

int

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

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. https://ieeexplore.ieee.org/abstract/document/8410043

See the official Python version from Prof. Glasmachers: https://www.ini.rub.de/upload/editor/file/1604950981_dc3a4459a4160b48d51e/lmmaes.py