I’m teaching a numerical methods class that’s partly an introduction to programming, and partly a survey of numerical solutions to different types of problems students might encounter in the wild. I thought I’d look into doing a session on genetic algorithms, which are an important precursor to things like networks that have been found to be useful in a wide variety of fields including image and character recognition, stock market prediction and medical diagnostics.
The ai-junkie, bare-essentials page on genetic algorithms seemed a reasonable place to start. The site is definitely readable and I was able to put together a code to try to solve its example problem: to figure out what series of four mathematical operations using only single digits (e.g. +5*3/2-7) would give target number (42 in this example).
The procedure is as follows:
- Initialize: Generate several random sets of four operations,
- Test for fitness: Check which ones come closest to the target number,
- Select: Select the two best options (which is not quite what the ai-junkie says to do, but it worked better for me),
- Mate: Combine the two best options semi-randomly (i.e. exchange some percentage of the operations) to produce a new set of operations
- Mutate: swap out some small percentage of the operations randomly,
- Repeat: Go back to the second step (and repeat until you hit the target).
And this is the code I came up with:
genetic_algorithm2.py
''' Write a program to combine the sequence of numbers 0123456789 and the operators */+- to get the target value (42 (as an integer)) ''' ''' Procedure: 1. Randomly generate a few sequences (ns=10) where each sequence is 8 charaters long (ng=8). 2. Check how close the sequence's value is to the target value. The closer the sequence the higher the weight it will get so use: w = 1/(value - target) 3. Chose two of the sequences in a way that gives preference to higher weights. 4. Randomly combine the successful sequences to create new sequences (ns=10) 5. Repeat until target is achieved. ''' from visual import * from visual.graph import * from random import * import operator # MODEL PARAMETERS ns = 100 target_val = 42 #the value the program is trying to achieve sequence_length = 4 # the number of operators in the sequence crossover_rate = 0.3 mutation_rate = 0.1 max_itterations = 400 class operation: def __init__(self, operator = None, number = None, nmin = 0, nmax = 9, type="int"): if operator == None: n = randrange(1,5) if n == 1: self.operator = "+" elif n == 2: self.operator = "-" elif n == 3: self.operator = "/" else: self.operator = "*" else: self.operator = operator if number == None: #generate random number from 0-9 self.number = 0 if self.operator == "/": while self.number == 0: self.number = randrange(nmin, nmax) else: self.number = randrange(nmin, nmax) else: self.number = number self.number = float(self.number) def calc(self, val=0): # perform operation given the input value if self.operator == "+": val += self.number elif self.operator == "-": val -= self.number elif self.operator == "*": val *= self.number elif self.operator == "/": val /= self.number return val class gene: def __init__(self, n_operations = 5, seq = None): #seq is a sequence of operations (see class above) #initalize self.n_operations = n_operations #generate sequence if seq == None: #print "Generating sequence" self.seq = [] self.seq.append(operation(operator="+")) # the default operation is + some number for i in range(n_operations-1): #generate random number self.seq.append(operation()) else: self.seq = seq self.calc_seq() #print "Sequence: ", self.seq def stringify(self): seq = "" for i in self.seq: seq = seq + i.operator + str(i.number) return seq def calc_seq(self): self.val = 0 for i in self.seq: #print i.calc(self.val) self.val = i.calc(self.val) return self.val def crossover(self, ingene, rate): # combine this gene with the ingene at the given rate (between 0 and 1) # of mixing to create two new genes #print "In 1: ", self.stringify() #print "In 2: ", ingene.stringify() new_seq_a = [] new_seq_b = [] for i in range(len(self.seq)): if (random() < rate): # swap new_seq_a.append(ingene.seq[i]) new_seq_b.append(self.seq[i]) else: new_seq_b.append(ingene.seq[i]) new_seq_a.append(self.seq[i]) new_gene_a = gene(seq = new_seq_a) new_gene_b = gene(seq = new_seq_b) #print "Out 1:", new_gene_a.stringify() #print "Out 2:", new_gene_b.stringify() return (new_gene_a, new_gene_b) def mutate(self, mutation_rate): for i in range(1, len(self.seq)): if random() < mutation_rate: self.seq[i] = operation() def weight(target, val): if val <> None: #print abs(target - val) if abs(target - val) <> 0: w = (1. / abs(target - val)) else: w = "Bingo" print "Bingo: target, val = ", target, val else: w = 0. return w def pick_value(weights): #given a series of weights randomly pick one of the sequence accounting for # the values of the weights # sum all the weights (for normalization) total = 0 for i in weights: total += i # make an array of the normalized cumulative totals of the weights. cum_wts = [] ctot = 0.0 cum_wts.append(ctot) for i in range(len(weights)): ctot += weights[i]/total cum_wts.append(ctot) #print cum_wts # get random number and find where it occurs in array n = random() index = randrange(0, len(weights)-1) for i in range(len(cum_wts)-1): #print i, cum_wts[i], n, cum_wts[i+1] if n >= cum_wts[i] and n < cum_wts[i+1]: index = i #print "Picked", i break return index def pick_best(weights): # pick the top two values from the sequences i1 = -1 i2 = -1 max1 = 0. max2 = 0. for i in range(len(weights)): if weights[i] > max1: max2 = max1 max1 = weights[i] i2 = i1 i1 = i elif weights[i] > max2: max2 = weights[i] i2 = i return (i1, i2) # Main loop l_loop = True loop_num = 0 best_gene = None ##test = gene() ##test.print_seq() ##print test.calc_seq() # initialize genes = [] for i in range(ns): genes.append(gene(n_operations=sequence_length)) #print genes[-1].stringify(), genes[-1].val f1 = gcurve(color=color.cyan) while (l_loop and loop_num < max_itterations): loop_num += 1 if (loop_num%10 == 0): print "Loop: ", loop_num # Calculate weights weights = [] for i in range(ns): weights.append(weight(target_val, genes[i].val)) # check for hit on target if weights[-1] == "Bingo": print "Bingo", genes[i].stringify(), genes[i].val l_loop = False best_gene = genes[i] break #print weights if l_loop: # indicate which was the best fit option (highest weight) max_w = 0.0 max_i = -1 for i in range(len(weights)): #print max_w, weights[i] if weights[i] > max_w: max_w = weights[i] max_i = i best_gene = genes[max_i] ## print "Best operation:", max_i, genes[max_i].stringify(), \ ## genes[max_i].val, max_w f1.plot(pos=(loop_num, best_gene.val)) # Pick parent gene sequences for next generation # pick first of the genes using weigths for preference ## index = pick_value(weights) ## print "Picked operation: ", index, genes[index].stringify(), \ ## genes[index].val, weights[index] ## ## # pick second gene ## index2 = index ## while index2 == index: ## index2 = pick_value(weights) ## print "Picked operation 2:", index2, genes[index2].stringify(), \ ## genes[index2].val, weights[index2] ## (index, index2) = pick_best(weights) # Crossover: combine genes to get the new population new_genes = [] for i in range(ns/2): (a,b) = genes[index].crossover(genes[index2], crossover_rate) new_genes.append(a) new_genes.append(b) # Mutate for i in new_genes: i.mutate(mutation_rate) # update genes array genes = [] for i in new_genes: genes.append(i) print print "Best Gene:", best_gene.stringify(), best_gene.val print "Number of iterations:", loop_num ##
When run, the code usually gets a valid answer, but does not always converge: The figure at the top of this post shows it finding a solution after 142 iterations (the solution it found was: +8.0 +8.0 *3.0 -6.0). The code is rough, but is all I have time for at the moment. However, it should be a reasonable starting point if I should decide to discuss these in class.
Citing this post: Urbano, L., 2016. Experimenting with Genetic Algorithms, Retrieved January 17th, 2017, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.