Classic Differential Evolution (CDE)

class pypop7.optimizers.de.cde.CDE(problem, options)

Classic Differential Evolution (CDE).

Note

Typically, DE/rand/1/bin is seen as the classic/basic version of DE. CDE often optimizes on relatively low-dimensional (e.g., << 1000) search spaces. Its two creators (Kenneth Price&Rainer Storn) won the 2017 Evolutionary Computation Pioneer Award from IEEE-CIS.

Parameters:

• problem (dict) –

  problem arguments with the following common settings (keys):

  • ’fitness_function’ - objective/cost 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 (RNG) 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),

  • ’f’ - mutation factor (float, default: 0.5),

  • ’cr’ - crossover probability (float, default: 0.9).

Examples

Use the optimizer CDE 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.cde import CDE
>>> 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}
>>> cde = CDE(problem, options)  # initialize the optimizer class
>>> results = cde.optimize()  # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"CDE: {results['n_function_evaluations']}, {results['best_so_far_y']}")
CDE: 5000, 2.0242437417701847e-07

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

cr

crossover probability.

Type:

float

f

mutation factor.

Type:

float

n_individuals

number of offspring, aka offspring population size.

Type:

int

References

Price, K.V., 2013. Differential evolution. In Handbook of optimization (pp. 187-214). Springer, Berlin, Heidelberg. https://link.springer.com/chapter/10.1007/978-3-642-30504-7_8

Price, K.V., Storn, R.M. and Lampinen, J.A., 2005. Differential evolution: A practical approach to global optimization. Springer Science & Business Media. https://link.springer.com/book/10.1007/3-540-31306-0

Storn, R.M. and Price, K.V. 1997. Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), pp.341–359. https://link.springer.com/article/10.1023/A:1008202821328 (Kenneth Price&Rainer Storn won the 2017 Evolutionary Computation Pioneer Award from IEEE CIS.)