# Powell’s search method (POWELL)¶

class pypop7.optimizers.ds.powell.POWELL(problem, options)

Powell’s search method (POWELL).

Note

This is a wrapper of the Powell algorithm from SciPy with accuracy control of maximum of function evaluations.

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):
• ’x’ - initial (starting) point (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’].

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.ds.powell import POWELL
4>>> problem = {'fitness_function': rosenbrock,  # define problem arguments
5...            'ndim_problem': 20,
6...            'lower_boundary': -5*numpy.ones((20,)),
7...            'upper_boundary': 5*numpy.ones((20,))}
8>>> options = {'max_function_evaluations': 5000,  # set optimizer options
9...            'seed_rng': 2022,
10...            'x': 3*numpy.ones((20,)),
11...            'verbose_frequency': 500}
12>>> powell = POWELL(problem, options)  # initialize the optimizer class
13>>> results = powell.optimize()  # run the optimization process
14>>> # return the number of function evaluations and best-so-far fitness
15>>> print(f"POWELL: {results['n_function_evaluations']}, {results['best_so_far_y']}")
16POWELL: 50000, 0.0
```

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

x

initial (starting) point.

Type:

array_like

References

https://docs.scipy.org/doc/scipy/reference/optimize.minimize-powell.html

Kochenderfer, M.J. and Wheeler, T.A., 2019. Algorithms for optimization. MIT Press. https://algorithmsbook.com/optimization/files/chapter-7.pdf (See Algorithm 7.3 (Page 102) for details.)

Powell, M.J., 1964. An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Computer Journal, 7(2), pp.155-162. https://academic.oup.com/comjnl/article-abstract/7/2/155/335330