Direct Search (DS)

class pypop7.optimizers.ds.ds.DS(problem, options)

Direct Search (DS).

This is the abstract class for all DS classes. Please use any of its instantiated subclasses to optimize the black-box problem at hand.

Note

Most of modern DS adopt the population-based sampling strategy, no matter deterministic or stochastic.

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),

    • ’sigma’ - initial global step-size (float).

sigma

final global step-size (changed during optimization).

Type:

float

x

initial (starting) point.

Type:

array_like

References

Kochenderfer, M.J. and Wheeler, T.A., 2019. Algorithms for optimization. MIT Press. https://algorithmsbook.com/optimization/ (See Chapter 7: Direct Methods for details.)

Larson, J., Menickelly, M. and Wild, S.M., 2019. Derivative-free optimization methods. Acta Numerica, 28, pp.287-404. https://tinyurl.com/4sr2t63j

Audet, C. and Hare, W., 2017. Derivative-free and blackbox optimization. Berlin: Springer International Publishing. https://link.springer.com/book/10.1007/978-3-319-68913-5

Torczon, V., 1997. On the convergence of pattern search algorithms. SIAM Journal on Optimization, 7(1), pp.1-25. https://epubs.siam.org/doi/abs/10.1137/S1052623493250780

Wright, M.H. , 1996. Direct search methods: Once scorned, now respectable. Pitman Research Notes in Mathematics Series, pp.191-208. https://nyuscholars.nyu.edu/en/publications/direct-search-methods-once-scorned-now-respectable

Nelder, J.A. and Mead, R., 1965. A simplex method for function minimization. The Computer Journal, 7(4), pp.308-313. https://academic.oup.com/comjnl/article-abstract/7/4/308/354237

Hooke, R. and Jeeves, T.A., 1961. “Direct search” solution of numerical and statistical problems. Journal of the ACM, 8(2), pp.212-229. https://dl.acm.org/doi/10.1145/321062.321069

Fermi, E. and Metropolis N., 1952. Numerical solution of a minimum problem. Los Alamos Scientific Lab., Los Alamos, NM. https://www.osti.gov/servlets/purl/4377177

DSs: