from __future__ import absolute_import, division, print_function from scitbx.array_family import flex from scitbx.stdlib import random from six.moves import range from six.moves import zip class differential_evolution_optimizer(object): """ This is a python implementation of differential evolution It assumes an evaluator class is passed in that has the following functionality data members: n :: The number of parameters domain :: a list [(low,high)]*n with approximate upper and lower limits for each parameter x :: a place holder for a final solution also a function called 'target' is needed. This function should take a parameter vector as input and return a the function to be minimized. The code below was implemented on the basis of the following sources of information: 1. http://www.icsi.berkeley.edu/~storn/code.html 2. http://www.daimi.au.dk/~krink/fec05/articles/JV_ComparativeStudy_CEC04.pdf 3. http://ocw.mit.edu/NR/rdonlyres/Sloan-School-of-Management/15-099Fall2003/A40397B9-E8FB-4B45-A41B-D1F69218901F/0/ses2_storn_price.pdf The developers of the differential evolution method have this advice: (taken from ref. 1) If you are going to optimize your own objective function with DE, you may try the following classical settings for the input file first: Choose method e.g. DE/rand/1/bin, set the number of parents NP to 10 times the number of parameters, select weighting factor F=0.8, and crossover constant CR=0.9. It has been found recently that selecting F from the interval [0.5, 1.0] randomly for each generation or for each difference vector, a technique called dither, improves convergence behaviour significantly, especially for noisy objective functions. It has also been found that setting CR to a low value, e.g. CR=0.2 helps optimizing separable functions since it fosters the search along the coordinate axes. On the contrary this choice is not effective if parameter dependence is encountered, something which is frequently occuring in real-world optimization problems rather than artificial test functions. So for parameter dependence the choice of CR=0.9 is more appropriate. Another interesting empirical finding is that rasing NP above, say, 40 does not substantially improve the convergence, independent of the number of parameters. It is worthwhile to experiment with these suggestions. Make sure that you initialize your parameter vectors by exploiting their full numerical range, i.e. if a parameter is allowed to exhibit values in the range [-100, 100] it's a good idea to pick the initial values from this range instead of unnecessarily restricting diversity. Keep in mind that different problems often require different settings for NP, F and CR (have a look into the different papers to get a feeling for the settings). If you still get misconvergence you might want to try a different method. We mostly use DE/rand/1/... or DE/best/1/... . The crossover method is not so important although Ken Price claims that binomial is never worse than exponential. In case of misconvergence also check your choice of objective function. There might be a better one to describe your problem. Any knowledge that you have about the problem should be worked into the objective function. A good objective function can make all the difference. Note: NP is called population size in the routine below.) Note: [0.5,1.0] dither is the default behavior unless f is set to a value other then None. """ def __init__(self, evaluator, population_size=50, f=None, cr=0.9, eps=1e-2, n_cross=1, max_iter=10000, monitor_cycle=200, out=None, show_progress=False, show_progress_nth_cycle=1, insert_solution_vector=None, dither_constant=0.4): self.dither=dither_constant self.show_progress=show_progress self.show_progress_nth_cycle=show_progress_nth_cycle self.evaluator = evaluator self.population_size = population_size self.f = f self.cr = cr self.n_cross = n_cross self.max_iter = max_iter self.monitor_cycle = monitor_cycle self.vector_length = evaluator.n self.eps = eps self.population = [] self.seeded = False if insert_solution_vector is not None: assert len( insert_solution_vector )==self.vector_length self.seeded = insert_solution_vector for ii in range(self.population_size): self.population.append( flex.double(self.vector_length,0) ) self.scores = flex.double(self.population_size,1000) self.optimize() self.best_score = flex.min( self.scores ) self.best_vector = self.population[ flex.min_index( self.scores ) ] self.evaluator.x = self.best_vector if self.show_progress: self.evaluator.print_status( flex.min(self.scores), flex.mean(self.scores), self.population[ flex.min_index( self.scores ) ], 'Final') def optimize(self): # initialise the population please self.make_random_population() # score the population please self.score_population() converged = False monitor_score = flex.min( self.scores ) self.count = 0 while not converged: self.evolve() location = flex.min_index( self.scores ) if self.show_progress: if self.count%self.show_progress_nth_cycle==0: # make here a call to a custom print_status function in the evaluator function # the function signature should be (min_target, mean_target, best vector) self.evaluator.print_status( flex.min(self.scores), flex.mean(self.scores), self.population[ flex.min_index( self.scores ) ], self.count) self.count += 1 if self.count%self.monitor_cycle==0: if (monitor_score-flex.min(self.scores) ) < self.eps: converged = True else: monitor_score = flex.min(self.scores) rd = (flex.mean(self.scores) - flex.min(self.scores) ) rd = rd*rd/(flex.min(self.scores)*flex.min(self.scores) + self.eps ) if ( rd < self.eps ): converged = True if self.count>=self.max_iter: converged =True def make_random_population(self): for ii in range(self.vector_length): delta = self.evaluator.domain[ii][1]-self.evaluator.domain[ii][0] offset = self.evaluator.domain[ii][0] random_values = flex.random_double(self.population_size) random_values = random_values*delta+offset # now please place these values ni the proper places in the # vectors of the population we generated for vector, item in zip(self.population,random_values): vector[ii] = item if self.seeded is not False: self.population[0] = self.seeded def score_population(self): for vector,ii in zip(self.population,range(self.population_size)): tmp_score = self.evaluator.target(vector) self.scores[ii]=tmp_score def evolve(self): for ii in range(self.population_size): rnd = flex.random_double(self.population_size-1) permut = flex.sort_permutation(rnd) # make parent indices i1=permut[0] if (i1>=ii): i1+=1 i2=permut[1] if (i2>=ii): i2+=1 i3=permut[2] if (i3>=ii): i3+=1 # x1 = self.population[ i1 ] x2 = self.population[ i2 ] x3 = self.population[ i3 ] if self.f is None: use_f = random.random()/2.0 + 0.5 else: use_f = self.f vi = x1 + use_f*(x2-x3) # prepare the offspring vector please rnd = flex.random_double(self.vector_length) permut = flex.sort_permutation(rnd) test_vector = self.population[ii].deep_copy() # first the parameters that sure cross over for jj in range( self.vector_length ): if (jjself.cr): test_vector[ permut[jj] ] = vi[ permut[jj] ] # get the score please test_score = self.evaluator.target( test_vector ) # check if the score if lower if test_score < self.scores[ii] : self.scores[ii] = test_score self.population[ii] = test_vector def show_population(self): print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++++") for vec in self.population: print(list(vec)) print("+++++++++++++++++++++++++++++++++++++++++++++++++++++++++")