Adaptive Differential Evolution (JADE)

class pypop7.optimizers.de.jade.JADE(problem, options)

Adaptive Differential Evolution (JADE).

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):

  • ’n_individuals’ - number of offspring, aka offspring population size (int, default: 100),

  • ’mu’ - mean of normal distribution for adaptation of crossover probability (float, default: 0.5),

  • ’median’ - median of Cauchy distribution for adaptation of mutation factor (float, default: 0.5),

  • ’p’ - level of greediness of mutation strategy (float, default: 0.05),

  • ’c’ - life span (float, default: 0.1),

  • ’is_bound’ - flag to limit all samplings inside the search range (boolean, default: False).

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.de.jade import JADE
>>> 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': 0}
>>> jade = JADE(problem, options)  # initialize the optimizer class
>>> results = jade.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"JADE: {results['n_function_evaluations']}, {results['best_so_far_y']}")
JADE: 5000, 4.844728910084905e-05

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

c

life span.

Type:

float

is_bound

flag to limit all samplings inside the search range.

Type:

boolean

median

median of Cauchy distribution for adaptation of mutation factor.

Type:

float

mu

mean of normal distribution for adaptation of crossover probability.

Type:

float

n_individuals

number of offspring, offspring population size.

Type:

int

p

level of greediness of mutation strategy.

Type:

float

References

Zhang, J., and Sanderson, A. C. 2009. JADE: Adaptive differential evolution with optional external archive. IEEE Transactions on Evolutionary Computation, 13(5), pp.945–958. https://ieeexplore.ieee.org/document/5208221/