I am trying to implement a genetic algorithm using fixed-length vectors of real numbers. I found a simple implementation online using a binary encoded values. My confusion arises when I am trying to figure out a way to initialise the array and set the bounds for this algorithm.
Below is a snippet of the code with binary decoded code:
def decode(bounds, n_bits, bitstring):
decoded = list()
largest = 2**n_bits
for i in range(len(bounds)):
# extract the substring
start, end = i * n_bits, (i * n_bits)+n_bits
substring = bitstring[start:end]
# convert bitstring to a string of chars
chars = ''.join([str(s) for s in substring])
# convert string to integer
integer = int(chars, 2)
# scale integer to desired range
value = bounds[i][0] + (integer/largest) * (bounds[i][1] - bounds[i][0])
# store
decoded.append(value)
return decoded
Can this be rewritten as an array of real numbers to encode a solution and not a bit string?
The full code is from the following article: Simple Genetic Algorithm From Scratch in Python
# genetic algorithm search for continuous function optimization
from numpy.random import randint
from numpy.random import rand
# objective function
def objective(x):
return x[0] ** 2.0 + x[1] ** 2.0
# decode bitstring to numbers
def decode(bounds, n_bits, bitstring):
decoded = list()
largest = 2 ** n_bits
for i in range(len(bounds)):
# extract the substring
start, end = i * n_bits, (i * n_bits) + n_bits
substring = bitstring[start:end]
# convert bitstring to a string of chars
chars = ''.join([str(s) for s in substring])
# convert string to integer
integer = int(chars, 2)
# scale integer to desired range
value = bounds[i][0] + (integer / largest) * (bounds[i][1] - bounds[i][0])
# store
decoded.append(value)
return decoded
# tournament selection
def selection(pop, scores, k=3):
# first random selection
selection_ix = randint(len(pop))
for ix in randint(0, len(pop), k - 1):
# check if better (e.g. perform a tournament)
if scores[ix] < scores[selection_ix]:
selection_ix = ix
return pop[selection_ix]
# crossover two parents to create two children
def crossover(p1, p2, r_cross):
# children are copies of parents by default
c1, c2 = p1.copy(), p2.copy()
# check for recombination
if rand() < r_cross:
# select crossover point that is not on the end of the string
pt = randint(1, len(p1) - 2)
# perform crossover
c1 = p1[:pt] + p2[pt:]
c2 = p2[:pt] + p1[pt:]
return [c1, c2]
# mutation operator
def mutation(bitstring, r_mut):
for i in range(len(bitstring)):
# check for a mutation
if rand() < r_mut:
# flip the bit
bitstring[i] = 1 - bitstring[i]
# genetic algorithm
def genetic_algorithm(objective, bounds, n_bits, n_iter, n_pop, r_cross, r_mut):
# initial population of random bitstring
pop = [randint(0, 2, n_bits * len(bounds)).tolist() for _ in range(n_pop)]
# keep track of best solution
best, best_eval = 0, objective(decode(bounds, n_bits, pop[0]))
# enumerate generations
for gen in range(n_iter):
# decode population
decoded = [decode(bounds, n_bits, p) for p in pop]
# evaluate all candidates in the population
scores = [objective(d) for d in decoded]
# check for new best solution
for i in range(n_pop):
if scores[i] < best_eval:
best, best_eval = pop[i], scores[i]
print(">%d, new best f(%s) = %f" % (gen, decoded[i], scores[i]))
# select parents
selected = [selection(pop, scores) for _ in range(n_pop)]
# create the next generation
children = list()
for i in range(0, n_pop, 2):
# get selected parents in pairs
p1, p2 = selected[i], selected[i + 1]
# crossover and mutation
for c in crossover(p1, p2, r_cross):
# mutation
mutation(c, r_mut)
# store for next generation
children.append(c)
# replace population
pop = children
return [best, best_eval]
# define range for input
bounds = [[-5.0, 5.0], [-5.0, 5.0]]
# define the total iterations
n_iter = 100
# bits per variable
n_bits = 16
# define the population size
n_pop = 100
# crossover rate
r_cross = 0.9
# mutation rate
r_mut = 1.0 / (float(n_bits) * len(bounds))
# perform the genetic algorithm search
best, score = genetic_algorithm(objective, bounds, n_bits, n_iter, n_pop, r_cross, r_mut)
print('Done!')
decoded = decode(bounds, n_bits, best)
print('f(%s) = %f' % (decoded, score))
It appears that you are referencing the code in this article: Simple Genetic Algorithm From Scratch in Python.
The bit-vector representation of individuals that is used in the starting code is an encoding of a real-valued vector. If you want your representation of an individual to be a real-valued vector, it means that you don't have do any decoding or encoding at all.
Initialize your population to be a vector of random real values within the bounds
def genetic_algorithm(objective, bounds, n_iter, n_pop, r_cross, r_mut):
# initial population of random real-valued vectors
pop = [[random.uniform(bound[0], bound[1]) for bound in bounds] for _ in range(n_pop)]
...
Then, in the genetic algorithm itself, there is no need to decode the population, since they are already real-valued vectors.
# genetic algorithm
def genetic_algorithm(objective, bounds, n_iter, n_pop, r_cross, r_mut):
# initial population of random real-valued vectors
pop = [[random.uniform(bound[0], bound[1]) for bound in bounds] for _ in range(n_pop)]
# keep track of best solution
best, best_eval = 0, objective(pop[0])
# enumerate generations
for gen in range(n_iter):
# evaluate all candidates in the population
scores = [objective(d) for d in pop]
# check for new best solution
for i in range(n_pop):
if scores[i] < best_eval:
best, best_eval = pop[i], scores[i]
print(">%d, new best f(%s) = %f" % (gen, pop[i], scores[i]))
# select parents
selected = [selection(pop, scores) for _ in range(n_pop)]
# create the next generation
children = list()
for i in range(0, n_pop, 2):
# get selected parents in pairs
p1, p2 = selected[i], selected[i + 1]
# crossover and mutation
for c in crossover(p1, p2, r_cross):
# mutation
mutation(c, r_mut)
# store for next generation
children.append(c)
# replace population
pop = children
return [best, best_eval]
The one thing that remains to be addressed is to modify the mutation and crossover functions so that they operate on real-valued vectors, instead of bit-strings. There are many approaches to how you could implement mutation and cross-over for real-valued vectors; some examples are listed in this StackOverflow post.
You have a genome with certain genes:
genome = { GeneA: value, GeneB: value, GeneC: value }So take for example:
genome = { GeneA: 1, GeneB: 2.5, GeneC: 3.4 }A few examples of mutation could be:
- Switch around two genes:
{ GeneA: 1, GeneB: 3.4, GeneC: 2.5 }- Add/substract a random value from a gene:
{ GeneA: 0.9, GeneB: 2.5, GeneC: 3.4 }Suppose you have two genomes:
genome1 = { GeneA: 1, GeneB: 2.5, GeneC: 3.4 } genome2 = { GeneA: 0.4, GeneB: 3.5, GeneC: 3.2 }A few examples of crossover could be:
- Taking the average:
{ GeneA: 0.7, GeneB: 3.0, GeneC: 3.3 }- Uniform (50% chance):
{ GeneA: 0.4, GeneB: 2.5, GeneC: 3.2 }- N-point crossover:
{ GeneA: 1, | CROSSOVER POINT | GeneB: 3.5, GeneC: 3.2 }