ds.py

import numpy as np

from pypop7.optimizers.core.optimizer import Optimizer


class DS(Optimizer):
    """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`).

    Attributes
    ----------
    sigma : `float`
            final global step-size (changed during optimization).
    x     : `array_like`
            initial (starting) point.

    Methods
    -------

    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. <https://www.informs.org/Explore/History-of-O.R.-Excellence/Biographical-Profiles/Wright-Margaret-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
    """
    def __init__(self, problem, options):
        Optimizer.__init__(self, problem, options)
        self.x = options.get('x')  # initial (starting) point
        self.sigma = options.get('sigma', 1.0)  # initial global step-size
        assert self.sigma > 0.0
        self._n_generations = 0  # number of generations
        # set for restart
        self.sigma_threshold = options.get('sigma_threshold', 1e-12)  # stopping threshold of sigma for restart
        assert self.sigma_threshold >= 0.0
        self.stagnation = options.get('stagnation', np.maximum(30, self.ndim_problem))
        assert self.stagnation > 0
        self.fitness_diff = options.get('fitness_diff', 1e-12)  # stopping threshold of fitness difference for restart
        assert self.fitness_diff >= 0.0
        self._sigma_bak = np.copy(self.sigma)  # bak for restart
        self._fitness_list = [self.best_so_far_y]  # to store `best_so_far_y` generated in each generation
        self._n_restart = 0  # number of restarts
        self._printed_evaluations = self.n_function_evaluations

    def initialize(self):
        raise NotImplementedError

    def iterate(self):
        raise NotImplementedError

    def _initialize_x(self, is_restart=False):
        if is_restart or (self.x is None):
            x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary)
        else:
            x = np.copy(self.x)
        assert x.shape == (self.ndim_problem,)
        return x

    def _print_verbose_info(self, fitness, y, is_print=False):
        if y is not None:
            if self.saving_fitness:
                if not np.isscalar(y):
                    fitness.extend(y)
                else:
                    fitness.append(y)
        if self.verbose:
            is_verbose = self._printed_evaluations != self.n_function_evaluations  # to avoid repeated printing
            is_verbose_1 = (not self._n_generations % self.verbose) and is_verbose
            is_verbose_2 = self.termination_signal > 0 and is_verbose
            is_verbose_3 = is_print and is_verbose
            if is_verbose_1 or is_verbose_2 or is_verbose_3:
                info = '  * Generation {:d}: best_so_far_y {:7.5e}, min(y) {:7.5e} & Evaluations {:d}'
                print(info.format(self._n_generations, self.best_so_far_y, np.min(y), self.n_function_evaluations))
                self._printed_evaluations = self.n_function_evaluations

    def _collect(self, fitness, y=None):
        if len(y) > 0:
            self._print_verbose_info(fitness, y)
        results = Optimizer._collect(self, fitness)
        results['_n_generations'] = self._n_generations
        return results