# Genetic Algorithm From Scratch

In this section, we will develop an implementation of the genetic algorithm.

The first step is to create a population of random bitstrings. We could use boolean values True and False, string values ‘0’ and ‘1’, or integer values 0 and 1. In this case, we will use integer values.

We can generate an array of integer values in a range using the randint() function, and we can specify the range as values starting at 0 and less than 2, e.g. 0 or 1. We will also represent a candidate solution as a list instead of a NumPy array to keep things simple.

An initial population of random bitstring can be created as follows, where “n_pop” is a hyperparameter that controls the population size and “n_bits” is a hyperparameter that defines the number of bits in a single candidate solution:

# initial population of random bitstring

pop = [randint(0, 2, n_bits).tolist() for _ in range(n_pop)]

# initial population of random bitstring

pop = [randint(0, 2, n_bits).tolist() for _ in range(n_pop)]
Next, we can enumerate over a fixed number of algorithm iterations, in this case, controlled by a hyperparameter named “n_iter“.

# enumerate generations

``````for gen in range(n_iter):
...
``````

# enumerate generations

``````for gen in range(n_iter):
...
``````

The first step in the algorithm iteration is to evaluate all candidate solutions.

We will use a function named objective() as a generic objective function and call it to get a fitness score, which we will minimize.

# evaluate all candidates in the population

scores = [objective(c) for c in pop]

# evaluate all candidates in the population

scores = [objective(c) for c in pop]
We can then select parents that will be used to create children.

The tournament selection procedure can be implemented as a function that takes the population and returns one selected parent. The k value is fixed at 3 with a default argument, but you can experiment with different values if you like.

# 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]

# 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]
We can then call this function one time for each position in the population to create a list of parents.

# select parents

selected = [selection(pop, scores) for _ in range(n_pop)]

# select parents

selected = [selection(pop, scores) for _ in range(n_pop)]
We can then create the next generation.

This first requires a function to perform crossover. This function will take two parents and the crossover rate. The crossover rate is a hyperparameter that determines whether crossover is performed or not, and if not, the parents are copied into the next generation. It is a probability and typically has a large value close to 1.0.

The crossover() function below implements crossover using a draw of a random number in the range [0,1] to determine if crossover is performed, then selecting a valid split point if crossover is to be performed.

# 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]

# 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]
We also need a function to perform mutation.

This procedure simply flips bits with a low probability controlled by the “r_mut” hyperparameter.

# 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]

# 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]
We can then loop over the list of parents and create a list of children to be used as the next generation, calling the crossover and mutation functions as needed.

# 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)

# 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)
We can tie all of this together into a function named genetic_algorithm() that takes the name of the objective function and the hyperparameters of the search, and returns the best solution found during the search.

# genetic algorithm

def genetic_algorithm(objective, n_bits, n_iter, n_pop, r_cross, r_mut):
# initial population of random bitstring
pop = [randint(0, 2, n_bits).tolist() 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(c) for c 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) = %.3f" % (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]

# genetic algorithm

def genetic_algorithm(objective, n_bits, n_iter, n_pop, r_cross, r_mut):
# initial population of random bitstring
pop = [randint(0, 2, n_bits).tolist() 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(c) for c 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) = %.3f" % (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]