Model Reference Adaptive Search (MRAS)

class pypop7.optimizers.cem.mras.MRAS(problem, options)

Model Reference Adaptive Search (MRAS).

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: 1000),

  • ’p’ - percentage of samples as parents (int, default: 0.1),

  • ’alpha’ - increasing factor of samples/individuals (float, default: 1.1),

  • ’v’ - smoothing factor for search distribution update (float, default: 0.2).

Examples

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

>>> import numpy  # engine for numerical computing
>>> from pypop7.benchmarks.base_functions import rosenbrock  # function to be minimized
>>> from pypop7.optimizers.cem.mras import MRAS
>>> 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,
...            'sigma': 10}  # the global step-size may need to be tuned for better performance
>>> mras = MRAS(problem, options)  # initialize the optimizer class
>>> results = mras.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"MRAS: {results['n_function_evaluations']}, {results['best_so_far_y']}")
MRAS: 5000, 0.18363570418709932

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

alpha

increasing factor of samples/individuals.

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

p

percentage of samples as parents.

Type:

float

sigma

initial global step-size, aka mutation strength,

Type:

float

v

smoothing factor for search distribution update.

Type:

float

References

Hu, J., Fu, M.C. and Marcus, S.I., 2007. A model reference adaptive search method for global optimization. Operations Research, 55(3), pp.549-568. https://pubsonline.informs.org/doi/abs/10.1287/opre.1060.0367