# Lévy distribution based Evolutionary Programming (LEP)¶

class pypop7.optimizers.ep.lep.LEP(problem, options)

Lévy distribution based Evolutionary Programming (LEP).

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),

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

• ’q’ - number of opponents for pairwise comparisons (int, default: 10),

• ’tau’ - learning rate of individual step-sizes self-adaptation (float, default: 1.0/np.sqrt(2.0*np.sqrt(problem[‘ndim_problem’]))),

• ’tau_apostrophe’ - learning rate of individual step-sizes self-adaptation (float, default: 1.0/np.sqrt(2.0*problem[‘ndim_problem’]).

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.ep.lep import LEP
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...            'sigma': 0.1}
11>>> lep = LEP(problem, options)  # initialize the optimizer class
12>>> results = lep.optimize()  # run the optimization process
13>>> # return the number of function evaluations and best-so-far fitness
14>>> print(f"LEP: {results['n_function_evaluations']}, {results['best_so_far_y']}")
15LEP: 5000, 0.0359694938656471
```

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

n_individuals

number of offspring, aka offspring population size.

Type:

int

q

number of opponents for pairwise comparisons.

Type:

int

sigma

initial global step-size, aka mutation strength.

Type:

float

tau

learning rate of individual step-sizes self-adaptation.

Type:

float

tau_apostrophe

learning rate of individual step-sizes self-adaptation.

Type:

float

References

Lee, C.Y. and Yao, X., 2004. Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Transactions on Evolutionary Computation, 8(1), pp.1-13. https://ieeexplore.ieee.org/document/1266370