# Source code for pyswarms.discrete.binary

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

    r"""
    A Binary Particle Swarm Optimization (binary PSO) algorithm.

    It takes a set of candidate solutions, and tries to find the best
    solution using a position-velocity update method. Unlike
    :mod:`pyswarms.single.gb` and :mod:`pyswarms.single.lb`, this technique
    is often applied to discrete binary problems such as job-shop scheduling,
    sequencing, and the like.

    The update rule for the velocity is still similar, as shown in the
    proceeding equation:

    .. 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)]

    For the velocity update rule, a particle compares its current position
    with respect to its neighbours. The nearest neighbours are being
    determined by a kD-tree given a distance metric, similar to local-best
    PSO. The neighbours are computed for every iteration. However, this whole
    behavior can be modified into a global-best PSO by changing the nearest
    neighbours equal to the number of particles in the swarm. In this case,
    all particles see each other, and thus a global best particle can be established.

    In addition, one notable change for binary PSO is that the position
    update rule is now decided upon by the following case expression:

    .. math::

       X_{ij}(t+1) = \left\{\begin{array}{lr}
            0, & \text{if } \text{rand() } \geq S(v_{ij}(t+1))\\
            1, & \text{if } \text{rand() } < S(v_{ij}(t+1))
            \end{array}\right\}

    Where the function :math:`S(x)` is the sigmoid function defined as:

    .. math::

       S(x) = \dfrac{1}{1 + e^{-x}}

    This enables the algorithm to output binary positions rather than
    a stream of continuous values as seen in global-best or local-best PSO.

    This algorithm was adapted from the standard Binary PSO work of J. Kennedy and
    R.C. Eberhart in Particle Swarm Optimization [SMC1997]_.

    .. [SMC1997] J. Kennedy and R.C. Eberhart, "A discrete binary version of
        particle swarm algorithm," Proceedings of the IEEE International
        Conference on Systems, Man, and Cybernetics, 1997.
    """

    # 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 Ring
    from ..backend.handlers import BoundaryHandler, VelocityHandler
    from ..base import DiscreteSwarmOptimizer
    from ..utils.reporter import Reporter

    class BinaryPSO(DiscreteSwarmOptimizer):

        def __init__(
            self,
            n_particles,
            dimensions,
            options,
            init_pos=None,
            velocity_clamp=None,
            vh_strategy="unmodified",
            ftol=-np.inf,
            ftol_iter=1,
        ):
            """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', 'k', 'p'}`
                a dictionary containing the parameters for the specific
                optimization technique
                    * c1 : float
                        cognitive parameter
                    * c2 : float
                        social parameter
                    * w : float
                        inertia parameter
                    * k : int
                        number of neighbors to be considered. Must be a
                        positive integer less than :code:`n_particles`
                    * p: int {1,2}
                        the Minkowski p-norm to use. 1 is the
                        sum-of-absolute values (or L1 distance) while 2 is
                        the Euclidean (or L2) distance.
            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.
            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 : String
                a strategy for the handling of the velocity of out-of-bounds particles.
                Only the "unmodified" and the "adjust" strategies are allowed.
            ftol : float
                relative error in objective_func(best_pos) acceptable for
                convergence
            ftol_iter : int
                number of iterations over which the relative error in
                objective_func(best_pos) is acceptable for convergence.
                Default is :code:`1`
            """
            # Initialize logger
            self.rep = Reporter(logger=logging.getLogger(__name__))
            # Assign k-neighbors and p-value as attributes
            self.k, self.p = options["k"], options["p"]
            # Initialize parent class
            super(BinaryPSO, self).__init__(
                n_particles=n_particles,
                dimensions=dimensions,
                binary=True,
                options=options,
                init_pos=init_pos,
                velocity_clamp=velocity_clamp,
                ftol=ftol,
                ftol_iter=ftol_iter,
            )
            # Initialize the resettable attributes
            self.reset()
            # Initialize the topology
            self.top = Ring(static=False)
            self.vh = VelocityHandler(strategy=vh_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 : function
                objective function to be evaluated
            iters : int
                number of iterations
            n_processes : int, optional
                number of processes to use for parallel particle evaluation
                Defaut is None with no parallelization.
            verbose : bool
                enable or disable the logs and progress bar (default: True = enable logs)
            kwargs : dict
                arguments for objective function

            Returns
            -------
            tuple
                the local best cost and the local best position among the
                swarm.
            """
            # 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.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
                self.swarm.current_cost = compute_objective_function(
                    self.swarm, objective_func, pool, **kwargs
                )
                self.swarm.pbest_pos, self.swarm.pbest_cost = compute_pbest(
                    self.swarm
                )
                best_cost_yet_found = np.min(self.swarm.best_cost)
                # Update gbest from neighborhood
                self.swarm.best_pos, self.swarm.best_cost = self.top.compute_gbest(
                    self.swarm, p=self.p, k=self.k
                )
                if verbose:
                    # Print to console
                    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=np.mean(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 position velocity update
                self.swarm.velocity = self.top.compute_velocity(
                    self.swarm, self.velocity_clamp, self.vh
                )
                self.swarm.position = self._compute_position(self.swarm)
            # 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()
            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)

        def _compute_position(self, swarm):
            """Update the position matrix of the swarm

            This computes the next position in a binary swarm. It compares the
            sigmoid output of the velocity-matrix and compares it with a randomly
            generated matrix.

            Parameters
            ----------
            swarm: pyswarms.backend.swarms.Swarm
                a Swarm class
            """
            return (
                np.random.random_sample(size=swarm.dimensions)
                < self._sigmoid(swarm.velocity)
            ) * 1

        def _sigmoid(self, x):
            """Helper method for the sigmoid function

            Parameters
            ----------
            x : numpy.ndarray
                Input vector for sigmoid computation

            Returns
            -------
            numpy.ndarray
                Output sigmoid computation
            """
            return 1 / (1 + np.exp(-x))