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:
1>>> import numpy 2>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized 3>>> from pypop7.optimizers.es.r1es import R1ES 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... 'mean': 3*numpy.ones((2,)), 11... 'sigma': 0.1} # the global step-size may need to be tuned for better performance 12>>> r1es = R1ES(problem, options) # initialize the optimizer class 13>>> results = r1es.optimize() # run the optimization process 14>>> # return the number of function evaluations and best-so-far fitness 15>>> print(f"R1ES: {results['n_function_evaluations']}, {results['best_so_far_y']}") 16R1ES: 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