# Source code for deap.benchmarks.movingpeaks

    #    This file is part of DEAP.
    #
    #    DEAP is free software: you can redistribute it and/or modify
    #    it under the terms of the GNU Lesser General Public License as
    #    published by the Free Software Foundation, either version 3 of
    #    the License, or (at your option) any later version.
    #
    #    DEAP is distributed in the hope that it will be useful,
    #    but WITHOUT ANY WARRANTY; without even the implied warranty of
    #    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    #    GNU Lesser General Public License for more details.
    #
    #    You should have received a copy of the GNU Lesser General Public
    #    License along with DEAP. If not, see <http://www.gnu.org/licenses/>.

    """
    Re-implementation of the `Moving Peaks Benchmark
    <http://people.aifb.kit.edu/jbr/MovPeaks/>`_ by Jurgen Branke. With the
    addition of the fluctuating number of peaks presented in *du Plessis and
    Engelbrecht, 2013, Self-Adaptive Environment with Fluctuating Number of
    Optima.*
    """

    import math
    import itertools
    import random

    try:
        from collections.abc import Sequence
    except:
        from collections import Sequence

    def cone(individual, position, height, width):
        r"""The cone peak function to be used with scenario 2 and 3.

        :math:`f(\mathbf{x}) = h - w \sqrt{\sum_{i=1}^N (x_i - p_i)^2}`

        """
        value = 0.0
        for x, p in zip(individual, position):
            value += (x - p)**2
        return height - width * math.sqrt(value)

    def sphere(individual, position, height, width):
        value = 0.0
        for x, p in zip(individual, position):
            value += (x - p)**2
        return height * value

    def function1(individual, position, height, width):
        r"""The function1 peak function to be used with scenario 1.

        :math:`f(\mathbf{x}) = \\frac{h}{1 + w \sqrt{\sum_{i=1}^N (x_i - p_i)^2}}`

        """
        value = 0.0
        for x, p in zip(individual, position):
            value += (x - p)**2
        return height / (1 + width * value)

    class MovingPeaks:
        """The Moving Peaks Benchmark is a fitness function changing over time. It
        consists of a number of peaks, changing in height, width and location. The
        peaks function is given by *pfunc*, which is either a function object or a
        list of function objects (the default is :func:`function1`). The number of
        peaks is determined by *npeaks* (which defaults to 5). This parameter can
        be either a integer or a sequence. If it is set to an integer the number
        of peaks won't change, while if set to a sequence of 3 elements, the
        number of peaks will fluctuate between the first and third element of that
        sequence, the second element is the initial number of peaks. When
        fluctuating the number of peaks, the parameter *number_severity* must be
        included, it represents the number of peak fraction that is allowed to
        change. The dimensionality of the search domain is *dim*. A basis function
        *bfunc* can also be given to act as static landscape (the default is no
        basis function). The argument *random* serves to grant an independent
        random number generator to the moving peaks so that the evolution is not
        influenced by number drawn by this object (the default uses random
        functions from the Python module :mod:`random`). Various other keyword
        parameters listed in the table below are required to setup the benchmark,
        default parameters are based on scenario 1 of this benchmark.

        =================== ============================= =================== =================== ======================================================================================================================
        Parameter           :data:`SCENARIO_1` (Default)  :data:`SCENARIO_2`  :data:`SCENARIO_3`    Details
        =================== ============================= =================== =================== ======================================================================================================================
        ``pfunc``           :func:`function1`             :func:`cone`        :func:`cone`        The peak function or a list of peak function.
        ``npeaks``          5                             10                  50                  Number of peaks. If an integer, the number of peaks won't change, if a sequence it will fluctuate [min, current, max].
        ``bfunc``           :obj:`None`                   :obj:`None`         ``lambda x: 10``    Basis static function.
        ``min_coord``       0.0                           0.0                 0.0                 Minimum coordinate for the centre of the peaks.
        ``max_coord``       100.0                         100.0               100.0               Maximum coordinate for the centre of the peaks.
        ``min_height``      30.0                          30.0                30.0                Minimum height of the peaks.
        ``max_height``      70.0                          70.0                70.0                Maximum height of the peaks.
        ``uniform_height``  50.0                          50.0                0                   Starting height for all peaks, if ``uniform_height <= 0`` the initial height is set randomly for each peak.
        ``min_width``       0.0001                        1.0                 1.0                 Minimum width of the peaks.
        ``max_width``       0.2                           12.0                12.0                Maximum width of the peaks
        ``uniform_width``   0.1                           0                   0                   Starting width for all peaks, if ``uniform_width <= 0`` the initial width is set randomly for each peak.
        ``lambda_``         0.0                           0.5                 0.5                 Correlation between changes.
        ``move_severity``   1.0                           1.5                 1.0                 The distance a single peak moves when peaks change.
        ``height_severity`` 7.0                           7.0                 1.0                 The standard deviation of the change made to the height of a peak when peaks change.
        ``width_severity``  0.01                          1.0                 0.5                 The standard deviation of the change made to the width of a peak when peaks change.
        ``period``          5000                          5000                1000                Period between two changes.
        =================== ============================= =================== =================== ======================================================================================================================

        Dictionaries :data:`SCENARIO_1`, :data:`SCENARIO_2` and
        :data:`SCENARIO_3` of this module define the defaults for these
        parameters. The scenario 3 requires a constant basis function
        which can be given as a lambda function ``lambda x: constant``.

        The following shows an example of scenario 1 with non uniform heights and
        widths.

        .. plot:: code/benchmarks/movingsc1.py
           :width: 67 %
        """
        def __init__(self, dim, random=random, **kargs):
            # Scenario 1 is the default
            sc = SCENARIO_1.copy()
            sc.update(kargs)

            pfunc = sc.get("pfunc")
            npeaks = sc.get("npeaks")
            self.dim = dim

            self.minpeaks, self.maxpeaks = None, None
            if hasattr(npeaks, "__getitem__"):
                self.minpeaks, npeaks, self.maxpeaks = npeaks
                self.number_severity = sc.get("number_severity")

            try:
                if len(pfunc) == npeaks:
                    self.peaks_function = pfunc
                else:
                    self.peaks_function = self.random.sample(pfunc, npeaks)
                self.pfunc_pool = tuple(pfunc)
            except TypeError:
                self.peaks_function = list(itertools.repeat(pfunc, npeaks))
                self.pfunc_pool = (pfunc,)

            self.random = random
            self.basis_function = sc.get("bfunc")

            self.min_coord = sc.get("min_coord")
            self.max_coord = sc.get("max_coord")

            self.min_height = sc.get("min_height")
            self.max_height = sc.get("max_height")
            uniform_height = sc.get("uniform_height")

            self.min_width = sc.get("min_width")
            self.max_width = sc.get("max_width")
            uniform_width = sc.get("uniform_width")

            self.lambda_ = sc.get("lambda_")
            self.move_severity = sc.get("move_severity")
            self.height_severity = sc.get("height_severity")
            self.width_severity = sc.get("width_severity")

            self.peaks_position = [[self.random.uniform(self.min_coord, self.max_coord) for _ in range(dim)] for _ in range(npeaks)]

            if uniform_height != 0:
                self.peaks_height = [uniform_height for _ in range(npeaks)]
            else:
                self.peaks_height = [self.random.uniform(self.min_height, self.max_height) for _ in range(npeaks)]

            if uniform_width != 0:
                self.peaks_width = [uniform_width for _ in range(npeaks)]
            else:
                self.peaks_width = [self.random.uniform(self.min_width, self.max_width) for _ in range(npeaks)]

            self.last_change_vector = [[self.random.random() - 0.5 for _ in range(dim)] for _ in range(npeaks)]

            self.period = sc.get("period")

            # Used by the Offline Error calculation
            self._optimum = None
            self._error = None
            self._offline_error = 0

            # Also used for auto change
            self.nevals = 0

        def globalMaximum(self):
            """Returns the global maximum value and position."""
            # The global maximum is at one peak's position
            potential_max = list()
            for func, pos, height, width in zip(self.peaks_function,
                                                self.peaks_position,
                                                self.peaks_height,
                                                self.peaks_width):
                potential_max.append((func(pos, pos, height, width), pos))
            return max(potential_max)

        def maximums(self):
            """Returns all visible maximums value and position sorted with the
            global maximum first.
            """
            # The maximums are at the peaks position but might be swallowed by
            # other peaks
            maximums = list()
            for func, pos, height, width in zip(self.peaks_function,
                                                self.peaks_position,
                                                self.peaks_height,
                                                self.peaks_width):
                val = func(pos, pos, height, width)
                if val >= self.__call__(pos, count=False)[0]:
                    maximums.append((val, pos))
            return sorted(maximums, reverse=True)

        def __call__(self, individual, count=True):
            """Evaluate a given *individual* with the current benchmark
            configuration.

            :param indidivudal: The individual to evaluate.
            :param count: Whether or not to count this evaluation in
                          the total evaluation count. (Defaults to
                          :data:`True`)
            """
            possible_values = []

            for func, pos, height, width in zip(self.peaks_function,
                                                self.peaks_position,
                                                self.peaks_height,
                                                self.peaks_width):
                possible_values.append(func(individual, pos, height, width))

            if self.basis_function:
                possible_values.append(self.basis_function(individual))

            fitness = max(possible_values)

            if count:
                # Compute the offline error
                self.nevals += 1
                if self._optimum is None:
                    self._optimum = self.globalMaximum()[0]
                    self._error = abs(fitness - self._optimum)
                self._error = min(self._error, abs(fitness - self._optimum))
                self._offline_error += self._error

                # We exhausted the number of evaluation, change peaks for the next one.
                if self.period > 0 and self.nevals % self.period == 0:
                    self.changePeaks()

            return fitness,

        def offlineError(self):
            return self._offline_error / self.nevals

        def currentError(self):
            return self._error

        def changePeaks(self):
            """Order the peaks to change position, height, width and number."""
            # Change the number of peaks
            if self.minpeaks is not None and self.maxpeaks is not None:
                npeaks = len(self.peaks_function)
                u = self.random.random()
                r = self.maxpeaks - self.minpeaks
                if u < 0.5:
                    # Remove n peaks or less depending on the minimum number of peaks
                    u = self.random.random()
                    n = min(npeaks - self.minpeaks, int(round(r * u * self.number_severity)))
                    for i in range(n):
                        idx = self.random.randrange(len(self.peaks_function))
                        self.peaks_function.pop(idx)
                        self.peaks_position.pop(idx)
                        self.peaks_height.pop(idx)
                        self.peaks_width.pop(idx)
                        self.last_change_vector.pop(idx)
                else:
                    # Add n peaks or less depending on the maximum number of peaks
                    u = self.random.random()
                    n = min(self.maxpeaks - npeaks, int(round(r * u * self.number_severity)))
                    for i in range(n):
                        self.peaks_function.append(self.random.choice(self.pfunc_pool))
                        self.peaks_position.append([self.random.uniform(self.min_coord, self.max_coord) for _ in range(self.dim)])
                        self.peaks_height.append(self.random.uniform(self.min_height, self.max_height))
                        self.peaks_width.append(self.random.uniform(self.min_width, self.max_width))
                        self.last_change_vector.append([self.random.random() - 0.5 for _ in range(self.dim)])

            for i in range(len(self.peaks_function)):
                # Change peak position
                shift = [self.random.random() - 0.5 for _ in range(len(self.peaks_position[i]))]
                shift_length = sum(s**2 for s in shift)
                shift_length = self.move_severity / math.sqrt(shift_length) if shift_length > 0 else 0

                shift = [shift_length * (1.0 - self.lambda_) * s
                         + self.lambda_ * c for s, c in zip(shift, self.last_change_vector[i])]

                shift_length = sum(s**2 for s in shift)
                shift_length = self.move_severity / math.sqrt(shift_length) if shift_length > 0 else 0

                shift = [s*shift_length for s in shift]

                new_position = []
                final_shift = []
                for pp, s in zip(self.peaks_position[i], shift):
                    new_coord = pp + s
                    if new_coord < self.min_coord:
                        new_position.append(2.0 * self.min_coord - pp - s)
                        final_shift.append(-1.0 * s)
                    elif new_coord > self.max_coord:
                        new_position.append(2.0 * self.max_coord - pp - s)
                        final_shift.append(-1.0 * s)
                    else:
                        new_position.append(new_coord)
                        final_shift.append(s)

                self.peaks_position[i] = new_position
                self.last_change_vector[i] = final_shift

                # Change peak height
                change = self.random.gauss(0, 1) * self.height_severity
                new_value = change + self.peaks_height[i]
                if new_value < self.min_height:
                    self.peaks_height[i] = 2.0 * self.min_height - self.peaks_height[i] - change
                elif new_value > self.max_height:
                    self.peaks_height[i] = 2.0 * self.max_height - self.peaks_height[i] - change
                else:
                    self.peaks_height[i] = new_value

                # Change peak width
                change = self.random.gauss(0, 1) * self.width_severity
                new_value = change + self.peaks_width[i]
                if new_value < self.min_width:
                    self.peaks_width[i] = 2.0 * self.min_width - self.peaks_width[i] - change
                elif new_value > self.max_width:
                    self.peaks_width[i] = 2.0 * self.max_width - self.peaks_width[i] - change
                else:
                    self.peaks_width[i] = new_value

            self._optimum = None

    SCENARIO_1 = {"pfunc": function1,
                  "npeaks": 5,
                  "bfunc": None,
                  "min_coord": 0.0,
                  "max_coord": 100.0,
                  "min_height": 30.0,
                  "max_height": 70.0,
                  "uniform_height": 50.0,
                  "min_width": 0.0001,
                  "max_width": 0.2,
                  "uniform_width": 0.1,
                  "lambda_": 0.0,
                  "move_severity": 1.0,
                  "height_severity": 7.0,
                  "width_severity": 0.01,
                  "period": 5000}

    SCENARIO_2 = {"pfunc": cone,
                  "npeaks": 10,
                  "bfunc": None,
                  "min_coord": 0.0,
                  "max_coord": 100.0,
                  "min_height": 30.0,
                  "max_height": 70.0,
                  "uniform_height": 50.0,
                  "min_width": 1.0,
                  "max_width": 12.0,
                  "uniform_width": 0,
                  "lambda_": 0.5,
                  "move_severity": 1.0,
                  "height_severity": 7.0,
                  "width_severity": 1.0,
                  "period": 5000}

    SCENARIO_3 = {"pfunc": cone,
                  "npeaks": 50,
                  "bfunc": lambda x: 10,
                  "min_coord": 0.0,
                  "max_coord": 100.0,
                  "min_height": 30.0,
                  "max_height": 70.0,
                  "uniform_height": 0,
                  "min_width": 1.0,
                  "max_width": 12.0,
                  "uniform_width": 0,
                  "lambda_": 0.5,
                  "move_severity": 1.0,
                  "height_severity": 1.0,
                  "width_severity": 0.5,
                  "period": 1000}

    def diversity(population):
        nind = len(population)
        ndim = len(population[0])
        d = [0.0] * ndim
        for x in population:
            d = [di + xi for di, xi in zip(d, x)]
        d = [di / nind for di in d]
        return math.sqrt(sum((di - xi)**2 for x in population for di, xi in zip(d, x)))

    if __name__ == "__main__":
        mpb = MovingPeaks(dim=2, npeaks=[1, 1, 10], number_severity=0.1)
        print(mpb.maximums())
        mpb.changePeaks()
        print(mpb.maximums())