# Trigonometric-mutation Differential Evolution (TDE)¶

class pypop7.optimizers.de.tde.TDE(problem, options)

Trigonometric-mutation Differential Evolution (TDE).

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: 30),

• ’f’ - mutation factor (float, default: 0.99),

• ’cr’ - crossover probability (float, default: 0.85),

• ’tm’ - trigonometric mutation probability (float, default: 0.05).

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.de.tde import TDE
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': 0}
10>>> tde = TDE(problem, options)  # initialize the optimizer class
11>>> results = tde.optimize()  # run the optimization process
12>>> # return the number of function evaluations and best-so-far fitness
13>>> print(f"TDE: {results['n_function_evaluations']}, {results['best_so_far_y']}")
14TDE: 5000, 6.420787226215637e-21
```

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

cr

crossover probability.

Type:

float

f

mutation factor.

Type:

float

tm

trigonometric mutation probability.

Type:

‘float

n_individuals

number of offspring, aka offspring population size.

Type:

int

References

Fan, H.Y. and Lampinen, J., 2003. A trigonometric mutation operation to differential evolution. Journal of Global Optimization, 27(1), pp.105-129. https://link.springer.com/article/10.1023/A:1024653025686