Limited Memory Matrix Adaptation Evolution Strategy (LMMAES)

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

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 LMMAES 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.lmmaes import LMMAES
 4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
 5...            'ndim_problem': 200,
 6...            'lower_boundary': -5.0*numpy.ones((200,)),
 7...            'upper_boundary': 5.0*numpy.ones((200,))}
 8>>> options = {'max_function_evaluations': 500000,  # set optimizer options
 9...            'seed_rng': 0,
10...            'mean': 3.0*numpy.ones((200,)),
11...            'sigma': 0.1,  # the global step-size may need to be tuned for better performance
12...            'is_restart': False}
13>>> lmmaes = LMMAES(problem, options)  # initialize the optimizer class
14>>> results = lmmaes.optimize()  # run the optimization process
15>>> # return the number of function evaluations and best-so-far fitness
16>>> print(f"LMMAES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
17LMMAES: 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.

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