Rank-One Evolution Strategy (R1ES)

class pypop7.optimizers.es.r1es.R1ES(problem, options)

Rank-One Evolution Strategy (R1ES).

Note

R1ES is a low-rank version of CMA-ES specifically designed for large-scale black-box optimization (LSBBO) by Li and Zhang. It often works well when there is a dominated search direction embedded in a subspace. For more complex landscapes (e.g., there are multiple promising search directions), other LSBBO variants (e.g., RMES, LMCMA, LMMAES) of CMA-ES may be more preferred.

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)),

  • ’c_cov’ - learning rate of low-rank covariance matrix adaptation (float, default: 1.0/(3.0*np.sqrt(problem[‘ndim_problem’]) + 5.0)),

  • ’c’ - learning rate of evolution path update (float, default: 2.0/(problem[‘ndim_problem’] + 7.0)),

  • ’c_s’ - learning rate of cumulative step-size adaptation (float, default: 0.3),

  • ’q_star’ - baseline of cumulative step-size adaptation (float, default: 0.3)，

  • ’d_sigma’ - delay factor of cumulative step-size adaptation (float, default: 1.0).

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.r1es import R1ES
>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
...            'ndim_problem': 2,
...            'lower_boundary': -5*numpy.ones((2,)),
...            'upper_boundary': 5*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000,  # set optimizer options
...            'seed_rng': 2022,
...            'mean': 3*numpy.ones((2,)),
...            'sigma': 0.1}  # the global step-size may need to be tuned for better performance
>>> r1es = R1ES(problem, options)  # initialize the optimizer class
>>> results = r1es.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"R1ES: {results['n_function_evaluations']}, {results['best_so_far_y']}")
R1ES: 5000, 8.942371004351231e-10

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

c

learning rate of evolution path update.

Type:

float

c_cov

learning rate of low-rank covariance matrix adaptation.

Type:

float

c_s

learning rate of cumulative step-size adaptation.

Type:

float

d_sigma

delay factor of cumulative 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

q_star

baseline of cumulative step-size adaptation.

Type:

float

sigma

final global step-size, aka mutation strength.

Type:

float

References

Li, Z. and Zhang, Q., 2018. A simple yet efficient evolution strategy for large-scale black-box optimization. IEEE Transactions on Evolutionary Computation, 22(5), pp.637-646. https://ieeexplore.ieee.org/abstract/document/8080257