# Source code for pyswarms.single.global_best

    # -*- coding: utf-8 -*-

    r"""
    A Global-best Particle Swarm Optimization (gbest PSO) algorithm.

    It takes a set of candidate solutions, and tries to find the best
    solution using a position-velocity update method. Uses a
    star-topology where each particle is attracted to the best
    performing particle.

    The position update can be defined as:

    .. math::

       x_{i}(t+1) = x_{i}(t) + v_{i}(t+1)

    Where the position at the current timestep :math:`t` is updated using
    the computed velocity at :math:`t+1`. Furthermore, the velocity update
    is defined as:

    .. math::

       v_{ij}(t + 1) = w * v_{ij}(t) + c_{1}r_{1j}(t)[y_{ij}(t) − x_{ij}(t)]
                       + c_{2}r_{2j}(t)[\hat{y}_{j}(t) − x_{ij}(t)]

    Here, :math:`c1` and :math:`c2` are the cognitive and social parameters
    respectively. They control the particle's behavior given two choices: (1) to
    follow its *personal best* or (2) follow the swarm's *global best* position.
    Overall, this dictates if the swarm is explorative or exploitative in nature.
    In addition, a parameter :math:`w` controls the inertia of the swarm's
    movement.

    An example usage is as follows:

    .. code-block:: python

        import pyswarms as ps
        from pyswarms.utils.functions import single_obj as fx

        # Set-up hyperparameters
        options = {'c1': 0.5, 'c2': 0.3, 'w':0.9}

        # Call instance of GlobalBestPSO
        optimizer = ps.single.GlobalBestPSO(n_particles=10, dimensions=2,
                                            options=options)

        # Perform optimization
        stats = optimizer.optimize(fx.sphere, iters=100)

    This algorithm was adapted from the earlier works of J. Kennedy and
    R.C. Eberhart in Particle Swarm Optimization [IJCNN1995]_.

    .. [IJCNN1995] J. Kennedy and R.C. Eberhart, "Particle Swarm Optimization,"
        Proceedings of the IEEE International Joint Conference on Neural
        Networks, 1995, pp. 1942-1948.
    """

    # Import standard library
    import logging

    # Import modules
    import numpy as np
    import multiprocessing as mp

    from collections import deque

    from ..backend.operators import compute_pbest, compute_objective_function
    from ..backend.topology import Star
    from ..backend.handlers import BoundaryHandler, VelocityHandler, OptionsHandler
    from ..base import SwarmOptimizer
    from ..utils.reporter import Reporter

    class GlobalBestPSO(SwarmOptimizer):
        def __init__(
            self,
            n_particles,
            dimensions,
            options,
            bounds=None,
            oh_strategy=None,
            bh_strategy="periodic",
            velocity_clamp=None,
            vh_strategy="unmodified",
            center=1.00,
            ftol=-np.inf,
            ftol_iter=1,
            init_pos=None,
        ):
            """Initialize the swarm

            Attributes
            ----------
            n_particles : int
                number of particles in the swarm.
            dimensions : int
                number of dimensions in the space.
            options : dict with keys :code:`{'c1', 'c2', 'w'}`
                a dictionary containing the parameters for the specific
                optimization technique.
                    * c1 : float
                        cognitive parameter
                    * c2 : float
                        social parameter
                    * w : float
                        inertia parameter
            bounds : tuple of numpy.ndarray, optional
                a tuple of size 2 where the first entry is the minimum bound while
                the second entry is the maximum bound. Each array must be of shape
                :code:`(dimensions,)`.
            oh_strategy : dict, optional, default=None(constant options)
                a dict of update strategies for each option.
            bh_strategy : str
                a strategy for the handling of out-of-bounds particles.
            velocity_clamp : tuple, optional
                a tuple of size 2 where the first entry is the minimum velocity and
                the second entry is the maximum velocity. It sets the limits for
                velocity clamping.
            vh_strategy : str
                a strategy for the handling of the velocity of out-of-bounds particles.
            center : list (default is :code:`None`)
                an array of size :code:`dimensions`
            ftol : float
                relative error in objective_func(best_pos) acceptable for
                convergence. Default is :code:`-np.inf`
            ftol_iter : int
                number of iterations over which the relative error in
                objective_func(best_pos) is acceptable for convergence.
                Default is :code:`1`
            init_pos : numpy.ndarray, optional
                option to explicitly set the particles' initial positions. Set to
                :code:`None` if you wish to generate the particles randomly.
            """
            super(GlobalBestPSO, self).__init__(
                n_particles=n_particles,
                dimensions=dimensions,
                options=options,
                bounds=bounds,
                velocity_clamp=velocity_clamp,
                center=center,
                ftol=ftol,
                ftol_iter=ftol_iter,
                init_pos=init_pos,
            )

            if oh_strategy is None:
                oh_strategy = {}
            # Initialize logger
            self.rep = Reporter(logger=logging.getLogger(__name__))
            # Initialize the resettable attributes
            self.reset()
            # Initialize the topology
            self.top = Star()
            self.bh = BoundaryHandler(strategy=bh_strategy)
            self.vh = VelocityHandler(strategy=vh_strategy)
            self.oh = OptionsHandler(strategy=oh_strategy)
            self.name = __name__

        def optimize(
            self, objective_func, iters, n_processes=None, verbose=True, **kwargs
        ):
            """Optimize the swarm for a number of iterations

            Performs the optimization to evaluate the objective
            function :code:`f` for a number of iterations :code:`iter.`

            Parameters
            ----------
            objective_func : callable
                objective function to be evaluated
            iters : int
                number of iterations
            n_processes : int
                number of processes to use for parallel particle evaluation (default: None = no parallelization)
            verbose : bool
                enable or disable the logs and progress bar (default: True = enable logs)
            kwargs : dict
                arguments for the objective function

            Returns
            -------
            tuple
                the global best cost and the global best position.
            """

            # Apply verbosity
            if verbose:
                log_level = logging.INFO
            else:
                log_level = logging.NOTSET

            self.rep.log("Obj. func. args: {}".format(kwargs), lvl=logging.DEBUG)
            self.rep.log(
                "Optimize for {} iters with {}".format(iters, self.options),
                lvl=log_level,
            )
            # Populate memory of the handlers
            self.bh.memory = self.swarm.position
            self.vh.memory = self.swarm.position

            # Setup Pool of processes for parallel evaluation
            pool = None if n_processes is None else mp.Pool(n_processes)

            self.swarm.pbest_cost = np.full(self.swarm_size[0], np.inf)
            ftol_history = deque(maxlen=self.ftol_iter)
            for i in self.rep.pbar(iters, self.name) if verbose else range(iters):
                # Compute cost for current position and personal best
                # fmt: off
                self.swarm.current_cost = compute_objective_function(self.swarm, objective_func, pool=pool, **kwargs)
                self.swarm.pbest_pos, self.swarm.pbest_cost = compute_pbest(self.swarm)
                # Set best_cost_yet_found for ftol
                best_cost_yet_found = self.swarm.best_cost
                self.swarm.best_pos, self.swarm.best_cost = self.top.compute_gbest(self.swarm)
                # fmt: on
                if verbose:
                    self.rep.hook(best_cost=self.swarm.best_cost)
                # Save to history
                hist = self.ToHistory(
                    best_cost=self.swarm.best_cost,
                    mean_pbest_cost=np.mean(self.swarm.pbest_cost),
                    mean_neighbor_cost=self.swarm.best_cost,
                    position=self.swarm.position,
                    velocity=self.swarm.velocity,
                )
                self._populate_history(hist)
                # Verify stop criteria based on the relative acceptable cost ftol
                relative_measure = self.ftol * (1 + np.abs(best_cost_yet_found))
                delta = (
                    np.abs(self.swarm.best_cost - best_cost_yet_found)
                    < relative_measure
                )
                if i < self.ftol_iter:
                    ftol_history.append(delta)
                else:
                    ftol_history.append(delta)
                    if all(ftol_history):
                        break
                # Perform options update
                self.swarm.options = self.oh(
                    self.options, iternow=i, itermax=iters
                )
                # Perform velocity and position updates
                self.swarm.velocity = self.top.compute_velocity(
                    self.swarm, self.velocity_clamp, self.vh, self.bounds
                )
                self.swarm.position = self.top.compute_position(
                    self.swarm, self.bounds, self.bh
                )
            # Obtain the final best_cost and the final best_position
            final_best_cost = self.swarm.best_cost.copy()
            final_best_pos = self.swarm.pbest_pos[
                self.swarm.pbest_cost.argmin()
            ].copy()
            # Write report in log and return final cost and position
            self.rep.log(
                "Optimization finished | best cost: {}, best pos: {}".format(
                    final_best_cost, final_best_pos
                ),
                lvl=log_level,
            )
            # Close Pool of Processes
            if n_processes is not None:
                pool.close()
            return (final_best_cost, final_best_pos)