## File: movingpeaks.py

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deap 1.3.1-2
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398 # 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 . """ Re-implementation of the Moving Peaks Benchmark _ 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): """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): """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*, wich 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 inital 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. =================== ============================= =================== =================== ====================================================================================================================== Dictionnaries :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: Wether 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 exausted 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())